is 397-1 (2003): method for statistical quality control ... · of adopting control charts...

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Disclosure to Promote the Right To Information Whereas the Parliament of India has set out to provide a practical regime of right to information for citizens to secure access to information under the control of public authorities, in order to promote transparency and accountability in the working of every public authority, and whereas the attached publication of the Bureau of Indian Standards is of particular interest to the public, particularly disadvantaged communities and those engaged in the pursuit of education and knowledge, the attached public safety standard is made available to promote the timely dissemination of this information in an accurate manner to the public. इंटरनेट मानक !ान $ एक न’ भारत का +नम-णSatyanarayan Gangaram Pitroda “Invent a New India Using Knowledge” प0रा1 को छोड न’ 5 तरफJawaharlal Nehru “Step Out From the Old to the New” जान1 का अ+धकार, जी1 का अ+धकारMazdoor Kisan Shakti Sangathan “The Right to Information, The Right to Live” !ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता ह Bharthari—Nītiśatakam “Knowledge is such a treasure which cannot be stolen” IS 397-1 (2003): Method for Statistical Quality Control During Production, Part 1: Control Charts for Variables [MSD 3: Statistical Methods for Quality and Reliability]

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Disclosure to Promote the Right To Information

Whereas the Parliament of India has set out to provide a practical regime of right to information for citizens to secure access to information under the control of public authorities, in order to promote transparency and accountability in the working of every public authority, and whereas the attached publication of the Bureau of Indian Standards is of particular interest to the public, particularly disadvantaged communities and those engaged in the pursuit of education and knowledge, the attached public safety standard is made available to promote the timely dissemination of this information in an accurate manner to the public.

इंटरनेट मानक

“!ान $ एक न' भारत का +नम-ण”Satyanarayan Gangaram Pitroda

“Invent a New India Using Knowledge”

“प0रा1 को छोड न' 5 तरफ”Jawaharlal Nehru

“Step Out From the Old to the New”

“जान1 का अ+धकार, जी1 का अ+धकार”Mazdoor Kisan Shakti Sangathan

“The Right to Information, The Right to Live”

“!ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता है”Bhartṛhari—Nītiśatakam

“Knowledge is such a treasure which cannot be stolen”

“Invent a New India Using Knowledge”

है”ह”ह

IS 397-1 (2003): Method for Statistical Quality ControlDuring Production, Part 1: Control Charts for Variables[MSD 3: Statistical Methods for Quality and Reliability]

IS 397 (Patt 1) :2003

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Indian Standard

METHODS FOR STATISTICAL QUALITYCONTROL DURING PRODUCTION

PART 1 CONTROL CHARTS FOR VARIABLES.

(Second Revision) 1,

ICS 03.120.30

0 BIS 2003

BUREAU OF INDIAN STANDARDSMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

December 2003 Price Group 9

... ,,%.

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Statistical Methods for Quality and Reliability Sectional Committee, MSD 3

FOREWORD

This Indian Standard (Part 1) (Second Revision) was adopted by the Bureau of Indian Standards, atler the draftfinalized by the Statistical Methods for Quality and Reliability Sectional Committee had been approved by theManagement and Systems Division Council.

Controlling the quality of products so as to maintain it at a given level is a major problem with all the producers.From the early days of industrial production manufacturers have tried to use the same men, machines and methodsand similar raw materials in the hope of turning out products of uniform quality. But neither men nor machinesare infallible and causes of irregularity often creep inadvertently. As a result, rejections in finished materials arerarely eliminated and inspection and screening become necessary to varied extents determined by the nature ofthe product and the goodwill and policy of the manufacturer.

Since screening is not an effective control, the question remained a lively issue with the production managementand various systems of control were devised from time-to-time. In 1924 Dr. W.A. Shewhart of the Bell TelephoneLaboratories, USA developed the control chart method of controlling the quality during production which ismeant to be an integral part of the production process, This technique based on statistical methods, however,does not provide an automatic corrective action in the way mechanical or electrical systems do. Instead, it givesa warning signal to the operator that he must take here and now the corrective action on his machine or processto ensure maintenance of quality in further production. Its effectiveness, therefore, depends on the promptnesswith which the warning is heeded to and action taken, keeping in view the fact that the work involved in applyingthe method is largely based on judgement, knowledge of the process and technical skill in tracing down assignablecauses of variation to their source.

This standard, was originally published in 1952, was largely a reproduction of the American Defence EmergencyStandard Z 1.3-1942 ‘Control chart method of controlling quality during production’ which had proved quiteuseful in the military stores purchases during second war. The first revision of this standard had been taken upwith a view to make the standard more comprehensive by including control charts for medians and mid-rangeswhich are quicker, easy to operate and at the same time quite efficient for small samples. Further, the methodologyof adopting control charts techniques for use when manufacturing is undertaken to a predetermined specificationwas also included. As the original standard was bulky, it was split into two parts during this revision, namely,Part 1 dealing with control charts for variables and Part 2 dealing with control charts for attributes.

This second revision of the standard has been taken up to inc)ude:

a)b)c)d)

e)

f)g)

difference between assignable causes and chance causes in a tabular form,choice of measuring equipment during the preliminaries to installation of control charts,tiu-ther guidance for deciding the frequency during the preliminaries to installation of control charts,explanation for not considering lower control limit (LCZ,) for homogenization of range values inR-chart and further necessary actions,conditions under which modified control chart should not be used,many editorial corrections, andamendment issued to this standard at appropriate place.

Further in this revision the text on process capability and its comparison with the tolerance have been suitablymodified and reference has been given m 1S 10645 :2002 ‘Methods for estimation of process capability andprocess performance’, is the necessary adjunct to this standard.

In addition to this Part 3, 1S397 has the four parts. The other parts are:

(Part O) :2003 Guidelines for selection of control charts (#h-st revision)

(Part 2) :2003 Control charts for attributes (third revision)

(Part 3): 2003 Special control charts by variables (first revision)

(Part 4): 2003 Special control charts by attributes (first revision)

The composition of the Committee responsible for the formulation of this standard is given in Annex I).

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IS 397 (part 1) :2003

Indian Standard

METHODS FOR STATISTICAL QUALITYCONTROL DURING PRODUCTION

PART 1 CONTROL CHARTS FOR VARIABLES

(Second Revision)

1 SCOPE

1.1 This standard (Part 1)outlines the method of controlchart by variables for controlling the quality duringproduction. The principles of procedure pertaining tocontrol charts for individual observations, averages,medians, mid-ranges, ranges and standard deviationsare given in general terms.

1.2 The standard also lays down the procedures forthe construction of modified control charts whichcan be usefully adopted when the manufacture isundertaken to predetermined specifications.

1.3 The principles of control charts have beenillustrated with a variety of examples. Certain broadguidelines as to the interpretation of the data resultingfrom control charts are also included.

2 REFERENCES

The following standards contain provisions, whichthrough reference in this text constitute provisions ofthis standard. At the time of publication, the editionsindicated were valid. All standards are subject torevision and parties to agreements based on thisstandard are encouraged to investigate the possibilityof applying the most recent editions of the standardsindicated below:

1SNo. Title

7920 Statistical vocabulary andsymbols:

(Part 1): 1994 Probability and general statisticalterms (second revision)

(Part 2): 1994 Statistical quality control (secondrevision)

9300 (Part 2): 1989 Statistical models for industrial

IS No. Title

applications: Part 2 Continuousmodels (first revision)

10645:1998 Method for estimation of processcapability (first revision)

5420 Guide on precision oftest metho&(Part 1): 1969 Principles and applications(Part 2): 1973 Inter laboratory testing

3 TERMINOLOGY

For the purpose of this standard the definitions givenin IS 7920 (Part 1) and IS 7920 (Part 2) shall apply.

4 BASIC CONCEPTS UNDERLYING CONTROLCHART TECHNIQUE

4.1 Variation and Its Causes

In the repetitive making of a product so often met inthe present day industrial production, variation in anychosen quality characteristic is an ever presentphenomenon. Although such variation may be due toa variety of causes and their interaction known andunknown, which constantly influence the process, theycan be broadly classified into following two distinctcategories:

a)

b)

Variation due to assignable causes, such as,different settings of a machine, differentbatches of raw materials that are being fed,and changes in operators who have tien overin a new shift.

Variation due to chance (non-assignable orcommon) causes which are unavoidable in theprocess due to such inherent variation thatexist in raw materials, machines, atmosphericconditions, etc.

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IS 397 (Part 1): 2003

4.2 Difference Between Chance Causes and Assignable Causes

sl Chance (Non-assignable) Causes Assignable CausesNo.

(1) (2) (3)

i)ii)

iii)

iv)

v)

vi)

Consists of many individual causes.Any one chance cause results in a minuteamount of variation (but many chance causesact together to yield a substantial total).Cannot economically be eliminated from aprocess.When only chance cause is present, theprocess is operating at its best.An observation within the control limits ofrandom variation means the process shouldnot be adjusted.Under chance causes, the process is

Consists of one or just a few individual causes.Any one assignable cause can result in a largeamount of variation.

Can be detected. Action to eliminate the cause(s) isusually economically justified.If assignable variation is present the process is notoperating at its best.An observation beyond control limits usually meansthe process should be investigated and corrected.

With assignable causes present, the process is notsufficiently stable to use sampling procedures suftlciently stable to use sampling procedures forto predict the quality of total production or prediction.make process optimization studies.

4.3 Process Under Statistical Control

When no assignable causes of variation are present ina process and it operates only under a system of non-assignable or chance causes, the process is said to bein a state of statistical control. Such variations due tochance causes occur in a random fashion and areusually found to obey certain statistical laws. If largenumber of observations obtained from a process, whichis under a state of statistical control, are studied in theform of a frequency distribution, it will generally fallinto a bell shaped symmetrical pattern wherein mostof the observations cluster around the average valueand fewer observations are found as one moves awayfrom the average value.

4.4 Normal Distribution

4.4.1 The belI shaped symmetric pattern that is obtainedby the observations emanating from a process understatistical control is generally well represented by thenormal distribution. This distribution is characterized bytwo parameters, namely the mean value and the standarddeviation. It is symmetrical and 99,73 percent of theobservationslie within three standard deviations fi-omthemean on both sides. Thus, less than 3 in a thousandobservationsare expectedto fall beyond the three standarddeviations from the mean on both sides. For fiwtherdescription about the properties of this distribution,attention in invitedto IS 9300 (Part 2). Hence ina processunder statisticalcontrol if any singlemeasurement is takenand it does not fall within *3CTtlom the mean, it can beregarded as not belonging to that dkribution or to thatcause system and the presence of an assignable causeaffecting the process may be inferred.

4.4.2 Just as a large number of individual measurements

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from a process follow a statistical law in the form of aknown distribution, if samples of given size are takenfrom the same process at more or less regular intewals,then sample statistic, such as average or standarddeviation, also follow known distributions. Of course,this distribution is not the same as the one obtained forthe individual obsewations from the process. Generallyspeaking the distribution of the sample statistics thatare dealt with in this standard are of the normal or knowntype whose parameters can be estimated.

4.5 Control Charts

4.5.1 The above mentioned behaviour of the samplestatistics obtaining fkom a process !nfluenced only byrandom causes is the foundation on which the controlchart technique is based. Essentially it is a graphicalmethod representing a sequence (in time) of samplestatistics. It consists of a central line (CL) denoting theaverage value of the statistic being plotted and it has twocontrol limits on either side of the central line which arecalled upper control limit @VCL)and lower control limit(LCL).The control limitsare determined statisticallyfromthe probability distribution of the sample statistic.

4.5.2 The purpose of control chart is to obtain a stateof statistical control by locating and eliminating theassignable causes and then to maintain the productionin this state so as to ensure the manufacture ofconsistent products of acceptable quality. For thispurpose the variation due to non-assignable causes isestimated and then used as the basis for the detectionof the variation due to assignable causes by plottingthe sample statistic on the control chart. As long as theplotted point is within the control limits, the process islefl alone. However, if a point falls either below the

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IS 397 (part 1): 2003

lower control limit or above the upper control limit or found within the sample items should be due to non-depicts other unnatural pattern (see 7.2) there is a assignable or random causes whereas the variation foundpossibility of the existence of some assignable cause(s) between samples should be ascribable to someand an investigation is made for taking action to assignable causes. The division of the production floweliminate such causes. in such a manner that each portion yields a sample having

5 PRELIMINARIES TO THE INSTALLATIONthis property is known as ‘rational sub-grouping’.

OF CONTROL CHARTSA natural sub-group for example would be the outputof a short time period since the variation in items

5.1 Choice of Quality Characteristic

To start with, a decision has to be taken with regard tothe quality characteristics for which a controlprogramme is desired. Characteristics affecting theperformance of the product should normally be theobject of first attention. These may be the features ofthe materials used or components or parts of theproducts, for example, tensile strength of the core wireof cables or thickness of the insulation. Sometimes thecharacteristic may be for the finished product as awhole like the life of incandescent lamps.

5.2 Choice of the Place for Control

5.2.1 In any production process it is of utmostimportance that proper checks through control chartsare exercized at strategic points. To pinpoint the placefor such controls it is desirable to determine the areasof maximum potential for return in the form of directprofits, reduction in scraps, increase in productivity,etc. A proper value analysis of all the performance maybe quite helpful in the context.

5.2.2 Itmay also be worthwhile to study the productionprocess to determine the nature and location of thecauses that tend to give rise to deviations in thecharacteristic chosen. The method of inspectingindividual article or product for the selectedcharacteristic is equally important since factors likeinspection fatigue may give rise to errors inobservations. Thus, irregularities evident in quality datamay arise from errors of inspection as well as fromfaults in the production process. Errors in inspectionmay result from a faulty test apparatus, faulty use ofotherwise correct apparatus, etc. It is also to be decidedbeforehand whether the entire output of productsshould be considered as a single stream having acommon system of causes or as two or more distinctstreams each to be treated separately in the controlprogramme because they come from different causesystems such as different conveyor lines, differentmachines or different shifts of workmen, etc.

5,3 Choice of Rational Sub-groups

manufactured close to each other in the time sequenceare much more likely to represent chance fluctuations.

5.3.2 The problem of forming rational sub-groups alsodepends on the technical knowledge of the productionprocess and the familiarity with the conditions underwhich the product is to be manufactured. Whereas it isnot possible to give exact instructions for the formationof rational sub-groups that will cover all cases, a fewillustrations may be helpfhl in this direction. Thus, ifdifferent machine settings have an effect on the qualitycharacteristic that is being studied, all the units in a singlesub-group should come from the same setting. Again,if different batches of material have an effect, then allunits in one sub-group should be from the same batch.Extending this, it may generally be advisable not to formsub-groups such that a single sub-group will consist ofitems manufactured indifferent shifts, from componentsobtained from different sources, from differentproduction lines, from different machines, moulds,operators, etc. In many situations a small sample takenin the order of production meets the principle of rationalsub-groups, since it is likely to represent the immediatestate of the process at the time sample was selected.However, it should be noted that this is not a universalrecommendation. If one is ttilng sample from a machinewith multiple spindles or multiple positions or heads,then a series of consecutive units from the machine as awhole will not form a rational sub-group capable ofstudying the variation between the different heads. Forexample, if a filling machine has six heads whichsimultaneously fill six consecutive containers in theproduction line, then every sixth unit taken (and not theconsecutive six units) from the process will form arational sub-group, becatise the variations within suchsub-groups would be the inherent variation due to theheads and the variation between the sub-groups wouldbe the variation obtaining from the different heads ofthe machine. In such situations, precise setting of thesix heads becomes very crucial.

5.3.3 To avoid bias inthe formationof rationalsubgroups,the following two precautions must be taken in theselection of consecutive samples: (a) periodic selection

5.3.1 Since the basic aim of control charts is to separate should not coincide with any relevant-periodic featuresthe variation due to assignable and non-assignable in the process, and (b) selection of samples should not becauses, it is evident that each sample should be made on a fixed time schedule if foreknowledge of therepresentative of a homogeneous segment of the selection time would have an influence on the qualityproduction flow. So in the ideal condition the variation characteristic of the article selected.

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IS 397 (Part 1) :2003

5.4 Frequency and Size of Samples

5.4.1 No general rules maybe laid down for frequencyof sub-groups. Each case must be decided on its ownmerits considering both the cost of taking and analyzingmeasurements and the benefits to be derived fromaction based on control charts. In the initial use of thecontrol chart for analyzing a process, it may bedesirable to arrive at conclusions quickly by takingfrequent sampIes. Later on, if troubles have beendiagnosed and corrected and the function of the controlchart has become the maintenance of the processcontrol on current production, it may be advisable toreduce the frequency of sampling. As a guideline, sub-group frequencies for on going production monitoringcould be twice per shift, hourly or some other feasiblerate, however, interval between two sub-groups shouldbe half of the known duration of trouble freeperformance.

5.4.2 The size of the sample to be taken depends on anumber of practical considerations. However, generallyspeaking, large samples taken at less frequent intervalsmay detect a small shift in the process average morequickly, but small samples taken at more frequentintervals will detect a large shift more quickly. In mostof the industrial use of the control charts, samples ofsize 4 or 5 are found to be quite common. A samplesize of 5 is recommended since the computation of theaverage in this case can be considerably simplified.When median charts are used, samples of size 3 or 5are most convenient since they avoid the computationaltogether for the calculation of the median value. Incase the mid-range is used, then also the computationsare considerably simplified since the average of onlytwo observations (Iargest and smallest) are to beobtained. It may, however, be noted that the use ofmedian or mid-range in place of average results in aslight loss of efficiency but this loss is marginal in thecase of small samples. Samples of smailer size mayhave to be used if the cost of measurements is too high.In most of the chemical industries using batch processthe samples of size 1 or 2 are frequently preferred. Itmay, however, be noted that larger the sample size themore desirable it is to use the standard deviation ratherthan range as a measure of sub-group dispersions,

5.5 Choice of Measuring Equipment

The measuring equipment used for measuring the testresults should be calibrated whose least count shouldbe preferably 1/1Ohof tolerance or process capability.The variation due to measuring system should bequantified and minimized [see IS 5420 (Part 1) andIS 5420 (Part 2)]. This variation due to measuringsystem should be less than 10 percent of the totalprocess variation of the characteristic. If this variationis between 10 percent to 30 percent, it may still be

tolerable depending upon the application. Ifit exceeds30 percent, the equipment should be regarded asinappropriate. In addition, the measurement uncertaintyof the measuring equipment should be much less thanthe tolerance of the characteristic.

5.6 Choice of the Types of Control Charts

In the case of measurable quality characteristics it isgenerally the common practice to maintain a pair ofcontrol charts — one for the control of average levelof the process (average chart or median chart ormid-range chart) and the other for the control ofdispersion (range chart or standard deviation chart).Of course, when a chart for individtial measurementsis maintained, there is no possibility of keeping thecompanion chart for dispersion.

6 SETTING UP OF THE CONTROL CHART

6.1 Preliminary Data Collection

After having decided upon the quality characteristicwhich is to be controlled and the frequency and size ofthe sample to be taken, some initial inspection datahas to be collected and analyzed for the purpose ofdetermining the central line and control limits of thestatic. The preliminary data may be colIected sampleby sample (in sub-groups of size as decided in 5.4) tillabout 25 samples are obtained from the continuousrun of the production process. Care is to be exercisedduring the course of this initial data collection that theprocess is not unduly influenced intermittently byextraneous factors like change in the feed of rawmaterials, operators and machine settings.

6.2 Analysis of Preliminary Data

6.2.1 Analysis of the preliminary data is undertakenfirstly by homogenizing the dispersion (range orstandard deviation) of the various sub-groups and thenby homogenizing the central tendency (such asaverage, median or mid-range). This order forhomogenization process becomes necessary since theranges (or standard deviation) also enter into thecalculations needed for homogenizing the averages.

6.2.2 Homogenization for Dispersion

6.2.2.1 Using range method

If the sample size chosen is not more than 6, then foreach of the sub-groups, the range (R) shall be first

calculated and the average range value ( ~ ) shall be

computed from these ranges. Depending upon thesample size, the value of factor D1 shall be chosen fromAnnex A. If al! the ranges are found to be less than or

equal to Dd ~ the initial data collected shall be deemed

to be homogeneous and acceptable for the purpose of

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IS 397 (Part 1): 2003

further calculation of the control limits. In case one or

more range values are found to exceed the value Dq ~,

the observations in the sub-group corresponding to thisrange shall be discarded. For the remaining data, theabove procedure shall be repeated (that is, the

calculation of the new average range R and

comparison of all the remaining ranges with D~ ~ )

tillall the range values are less than DA ~.

6.2.2.2 Using standard deviation method

In case the sample size chosen is fairly large, it isadvisable to use standard deviation instead of the rangesince the later is less efficient for large samples. Theprocedure, however, is almost similar to that givenin 6.2.2.1. For each of the sub-groups, the standarddeviations shall be computed and from these values

the average standard deviation F shall be computed.If all the individuals values are less than or equal to

Ed T (where Ed is a factor chosen from Annex A forthe corresponding sample size) then the initial data shallbe considered to be homogeneous. However, if one or

more s values are found to be exceeding B~ I theobservations corresponding to these sub-groups shallbe discarded. For the remaining data the aboveprocedure shall be repeated (that is, the calculation

of a new average standard deviation F. and the

comparison of the remainings values with Bi F) till

all the standard deviation values are less than Ed F.

NOTE — LCL is not considered for the homogenization ofrangesor standard deviations values as minimum variation inthe processis intended and therefore is always welcome. Theonly point to be investigated at that stage is the correctnessofthis less value of range or standard deviation. If such a lowvalue has really been obtained then such situations should beinstitutionalized for future,

6,2.2.3 In the above process of homogenization, ifmore than 25 percent of the sub-groups are discardedfor being out of control, the entire set of data maybediscarded. The fresh data should be collected afterchecking the process and eliminating the assignablecause(s) which were responsible for the high rate ofoutliers in the preliminary data.

6.2.3 Homogenization for Central Tendenqv

6.2.3.1 Using average method

From the homogenized data for dispersion (see 6.2.2.1

or 6.2.2.2), the average of each sub-group ( X ) shallbe calculated. The average of these averages or the

grand average (~) for all the sub-groups shall thenbe calculated. In case the data has earlier beenhomogenized by using ranges (see 6.2.2.1) then a

quantity A2 ~ shall be calculated, where the factor Azis chosen from Annex A for the corresponding sample

size. If any of the averages are found to lie outside the

interval ~ ~ A2 ~ then the observations in the sub-groups corresponding to these averages shall bediscarded. From the remaining data, a fresh grandaverage shall be computed and the above procedureshall be repeated till all the average values are found

to lie within Y k Az ~. In case the data has earlierbeen homogenized by using standard deviation

(see 6.2.1.2), then instead of A2 ~ the quantity Al F

shall be used in the above homogenization processwhere the factor A ~ is suitably chosen tlom Annex Afor the corresponding sample size.

6.2.3.2 Using median method

From the homogenized data for dispersion(see 6.2.1.1), the median for each sample (M,) shall be

calculated and the average ofthese medians ( ~~ ) shall

then be computed. A quantity F2 ~ shall be calculatedwhere the value of factor F2 is chosen from Annex Adepending upon the sample size. If any of the medians

are found to lie outside the interval fi, ~ F2 R then

the sub-groups corresponding to those medians shallbe discarded. From the remaining sub-groups, a freshaverage median value shall be computed and the aboveprocedure shall be repeated till all the median values

are found to lie within ~, ~ Fz ~.

6.2.3.3 Using mid-range method

The process of homogenization in this case is similarto that for the homogenization of the medians exceptthat the mid-range (M) has to be calculated for eachsub-groups (instead of median) and the factor Fz hasto be replaced by G2. The value of factor G2is chosenfrom Annex A depending upon the sample size.

6.3 Control Limits

6.3.1 Control Limits for Measures of Dispersion

6.3.1.1 Range (R) chart

The central line for the range chart is given by thehomogenized average range value (ii ) obtainedaccording to 6.2.2.1. The upper control limit (UCL)

and the lower control limit (LCL) for the range chartare obtained as D~ ~ and DJ ~ where values of factorsD~ and D~ are obtained from Annex A depending uponthe sample size.

NOTE — ML for the range chart coincides with the X-axis asD,= O.

6.3.1.2 Standard deviation (s) chart

The central line for the standard deviation chart is givenby the homogenized average standard deviation value

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IS 397 (Part 1): 2003

(~) obtained according to 6.2.2.2. The upper controllimit (UCL) and the lower control limit (LCL) for the

standard deviation chart are obtained as B1 F and BJ F

where values of the factors Bi and B~ are chosen tlomAnnex A depending upon the sample size.

6.3.2 Control Limits for Central Tendenq

6.3.2.1 Average (~) chart

The cent~al line for the average chart is the grandaverage x calculated fi-omthe homogenized averagesas indicated in 6.2.3.1. In case the range has been usedin the earlier homogenization process, then UCL andthe LCL for the average chart are obtained as follows:

UCL=~+A,~ and LCL=~–Az~

The value of the factor A2 is suitably chosen fromAnnex A depending upon the sample size.

In case, standard deviation has been used in the earlierhomogenization process, then UCL and LCL for theaverage chart are obtained as follows:

UCL=~ +A, F and LCL=~ –A, I

The value of the factor A, is chosen from Annex Adepending upon the’sample size.

NOTE — When the upperspecification limit (U) andthe lowerspecification limit (L) for the characteristic are stipulated, itmay be better to have the central line for the average chart at(U+ L)/2 for control purposesinsteadof usingthe homogenizedgrand average value, However, for further details a referenceis invited to 6.4.

6.3.2.2 Median (A4J chart

The central line for the median chart is the average of

the homogenized median values ( fi, ) and the control

limits are obtained as follows:

UCL= fi,+F,~ and LCL= fi~-FzE

The value of the factor F2 is chosen from Annex Adepending upon the sample size.

6.3.2.3 Mid-range (M) chart

The average of the homogenized mid-range ( m )values is the central line for the mid-range chart. TheUCL and the LCL for the mid-range chart are obtainedas follows:

UCL=fi+Gz E and LCL=M– G,E

The value of factor G2 is chosen from Annex Adepending upon the sample size.

6.3.3 Control Limits for Individual Control Chart

6.3.3.1 When variation within the sub-group is

expected to be negligible, for example, in liquidformulations or powder or when the cost of inspectionis prohibitive; it may not be desirable to have morethan one sample from each sub-group. In suchsituations, individual control chart is used. As in suchcases, the sample size would be one, the range valuefor each sub-group can not be calculated and thereforethe homogenization procedure recommended in 6.2.2.1is not applicable. Hence, after collecting the initialobservations (numbering 25 or more) the method ofmoving range is used. For this purpose the successivedifferences of the individual values, that is, thedifference between the first and the second observation,between the second and the third observation, and soon shall be calculated, ignoring the sign of thedifference. Thus, for 25 observations, there will be 24values of the moving range. From these moving ranges

the value of the average moving range ~ is calculated.

If each of the individual moving range (R) is less than

or equal to 3.267 ~ then the preliminary data is

considered to be homogeneous. If, however, one ormore range values exceed this limit, then those rangesshall be eliminated and the procedure shall be repeatedtill all the ranges are found to be homogeneous.

6.3.3.2 From the entire data, overall average (x) shall

be computed. The UCL and the LCL for individual

chart are obtained as ~ + 2.66 ~ and ~ – 2.66 R

where R is the average of the homogenized moving

ranges. If any of the individual values are found to lieoutside the control limits, they shall be eliminated andthe new average shall be calculated from the remainingobservations. This process shall be repeated till all theremaining observations are found to be within thecontrol limits.

6.4 Control Charts Based on Known StandardValues

6.4.1 In some cases there may not be any need for thecollection and analysis of preliminary data as indicatedin 6.1 and 6.2, if from the, past knowledge or recordsthe standard values of the parameters of the processare known-the process average to be maintained at alevel p and the standard deviation of the processrealistically estimated as O. While controlling thesecharacteristics, for which both an upper specificationlimit (U) and a lower specification limit (L) arestipulated, it is advantageous to control the process atan average level p = (U + L)/2. Even in the caseswhere initial control chart had been set upon the basisof collection and analysis of preliminary data, aftercertain lapse of time when the process had stabilizedand is. in a state of statistical control, it becomesnecessary to re-evaluate the parameters used in thecalculation of control limits.

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6

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IS 397 (Part 1): 2003

6.4.2 The value of process average (p) and process paper the control charts are normally drawn. Thestandard deviation (c$ normally based on about horizontal scale indicates the sub-group numberhundred or more points plotted on the initial control (possibly designated by the date and sample number)charts may be taken as the standard values for the whereas statistical measures chosen such as average,re-calculation of the control limits. Using the standard median, range, etc, are represented on the vertical scale.values, the control limits are calculated as given It is usually satisfactory to use millimetre graph paperin 6.4.3. wherein the sub-group numbers are indicated on the

NOTE — In casethe initial control limits are basedon averagerange ( ~ ), then a good estimate of the process standarddeviation is obtained as c = ~ /d, where ~ is based onhundredor more sample rangesandd, is asuitable factor takenfrom Annex A depending upon the sample size.

6.4.3 Control Limits for Measures of Dispersion

6.4.3.1 Control limits for range chart

The central line for the range chart is placed at d~cand the ,UCL and LCL are drawn at D2CJand Dlrs

respectively where the factors dz, D2 and D, are suitablychosen from Annex A depending upon the size of thesample.

horizontal scale at intervals of not less than 0.5 cm.Whenever charts for central tendency (average, medianor mid-range) and dispersion (standard deviation orrange) are simultaneously maintained, the chart forcentral tendency is placed at the top and the one formeasure of dispersion is placed below using the samehorizontal and vertical scales. Every care should betaken to exactly align the horizontal axis of the twographs. Thus for each sub-group hvo points should besimultaneously available which are plotted on therespective control charts on the same vertical line.

6.5.2 Atypical proforma for collection of data is givenat Annex B.

6.4.3.2 Control limits for standard deviation chart 7 MAINTENANCE OF CONTROL CHARTSThe central line for the standard deviation chart is

7.1 Using the Control Chart During Productionplaced at C2Gand the UCL and LCL are placed at B2CSand BIO respectively where values for the factors Cz, 7.1.1 The control charts have to be displayed in a

B2 and B, are chosen from Annex A depending upon conspicuous place where they may be readily viewed

the sample size. by those concerned, such as, operator, foreman,superintendent, chief inspector and quality control

6.4.4 Control Limits forA4easures of Central Tendency engineer.

6.4.4.1 Control limits for average chart

The central line for the average chart is drawn at ~,and UCL and LCL are drawn at p + Aq and p – ArJrespectively where the value for factor A is chosen fromAnnex A depending upon the sample size.

6.4.4.2 Control [imitsfor median chart

The central line of the median chart is drawn at p andUCL and LCL are drawn at p + FcJ and p – FOrespectively where the value for factor F is chosen fromAnnex A depending upon the sample size.

6.4.4.3 Control limits for mid-range chart

The central lie for the mid-range chart is drawn at p,and UCL and LCL are drawn at p + GO and p – GcJrespectively, where the value for factor G is chosenfrom Annex A depending upon the sample size.

6.4.4.4 Control limits for individual chart

7.1.2 There should be no delay in plotting all the pointson the control chart after the sample has been taken.

7.1.3 When a point falls outside the control limits, thetype of the action to be taken should be predetermined.Two kinds of actions maybe involved, namely, action”on the lot of product and the action on the process. Inthe case of action on the lot of products, examinationof additional samples from the lot with a view todetermining whether it should be held up or releasedmay be pertinent. The action on the process may consistof investigating the suitability of raw materials, thecorrectness of the testing procedure, etc, so that thecause for the lack of conttol is identified and if possible,corrective action is taken immediately to prevent itsrecurrence.

7.1.4 After the causes of trouble are located andeliminated, the control limits have to be periodicallyreviewed and altered. A definite schedule for suchreviews is to be set up and followed as a routine

The central line for the individual chart is placed at p, reamer, for example, every 50 or 100 points, everyand the UCL and LCL are drawn at p + 3cJand p – 36 month, etc, depending on the frequency of samplingrespectively. and the degree of control shown by the charted history.

6.5 Some Practical Guidelines for Drawing theWhile reviewing the control limits, it may be noted

Control Charts that, as far as possible, they should not become widerthan the earlier limits obtained as this will affect the

6.5.1 On a suitable form or cross-sectional or graph better process control achieved earlier.

7

IS 397 (Part 1): 2003

7.1.5 Brief notes may be added on the control chartregarding the causes of trouble found in themanufacturing process or inspection methods and thecorrective action taken. In fact it is desirable to recordthe changes taking place in the inputs which may beuseful in identifying the assignable causes forcorrective action. The completed control charts maybe kept in the permanent tile for a specified usefidperiod as a record of the quality of the product.

7.2 Detection of Assignable Causes

7.2.1 Since the basic aim of the control chart is to detectthe presence of any unnatural pattern in the process ofmanufacture, which will have to be removed, it is usefilto have an idea about the following characteristics ofa natural pattern:

a) Majority of the points are near the central line,

b) A few of the points are spread out andapproach the control limits, and

c) None of the points (or at least only a veryrare and occasional point) exceeds the controllimit.

7.2.2 There are different types of unnatural patternswhich may be noticed in the control chart. The easeand the fi-equency with which an operator will be ableto spot any unnatural pattern will depend on hisexperience in running the control chart as also hisknowledge of the process. However, the following aresome of the unnatural patterns, which occur moreoften:

a)

b)

c)

d)

e)

Instability — The presence of points outsidethe control limits.

Stratljication — Up and down variations arevery small in comparison with the width ofthe control limits and absence of points nearthe control limits.

Mixture — A tendency to avoid the centralline with too many points near the controllimits.

Cyclic or systematic system — A long seriesof points which are high, low, high, lowwithout any interruption in this regularsequence.

Trend — A series of consecutive points(seven) without a change in direction.

7.2.3 The above unnatural pattern may be observedwhen there is lack of control in:

a) Average (or median or mid-range) chart only,

b) Range (or standard deviation) chart only, and

c) Both the average and range charts.

7.2.3.1 Lack of control in the average chart only

This is the common type of lack of control observed

8

in manufacturing wherein a shift in the process averageoccurs with little or no changes in the processdispersion. In such cases the control chart is ofien ofgreat value to the machine setter to help him to centrethe machine setting in order to produce a desiredprocess average. This type of lack of control is shownon the average chart. Unless the changes in the processaverage take place within a sub-group, the range chartwill show control. Since the control limits are set farenough from the central line on the chart with thepossibility of very few points outside the limit withouta real change in the process, small shifts in the processaverage will not cause many points to fall out ofcontrol. Suftlcient grounds exist for suspicion that theprocess average has shifted when:

a) 7 successive points on the control chart areon the same side of the central line,

b) 10 out of 11 successive points are on the sameside of the central line,

c) 12 out of 14 successive points are on the sameside of the central line,

d) 14 out of 17 successive points are on the sameside of the central line, and

e) 16 out of 20 successive points are on the sameside of the central line.

7.2.3.2 Lack of control in the dispersion chart oidy

The inherent variability of a process may change fromtime-to-time even though there is no change in theprocess average. For any process where the skill andcare of the operator is an important factor, the commoncause of increase in variability is a change from oneoperator to another who is less skilful or less careful.In fact an operator’s skill and care may also vary fromday-to-day or ftom hour-to-hour. Extreme runs abovethe central line on the range chart also give strongevidence of lack of control in the process variability.Generally speaking, variability of a process dispersionis particularly likely to be found in those processeswhere the skill of the operator is important. Hence thefirst step in improving such processes should be anattempt to bring the proce!w dispersion into statisticalcontrol. The value of the average range ( ~ ) used forthe calculation of the control limits should be reviewedtlom time-to-time since it has a direct bearing on thecalculation of the control limits for both the centraltendency and dispersion.

7.2.3.3 Changes in both process average and

dispersion

When the process dispersion as well as the processaverage are shitling, it is obvious that lack of controlwill be indicated in both the range chart and the averagechart. This state of affairs is generally found in theinitial stages of the use of control chart for variables

for analysis of many manufacturing operations. Whereseveral assignable causes of variation exist, theelimination of some of the causes will decrease thenumber of out-of-control points but will not eliminateall of them. In such circumstances, one should not bediscouraged by the continuance of some points out ofcontrol. On the other hand the chart should be viewedas an indication that further improvement is possibleand as an incentive to keep hunting for more sourcesof trouble.

It is also worthwhile examining whether an error inmeasurement may be an assignable cause of variationin the values resulting from the measurements, becausean error in setting a measuring device may makeapparent sudden shifls in process average. Frequenterrors in setting may also make irregular shifts in theaverage. Some type of wear of measuring device maycause increase in the process dispersion. Yet other typesof wear may give rise to trends in averages.

8 CONTROL LIMITS AND SPECIFICATIONLIMITS

Since most of the control charts, like average chartand range chart are to be maintained in the productionoperations for the detection of assignable causes ofvariation, a common source of confusion is theexistence of specification limits side-by-side. It shouldnot be confused that the control limits for average chartare the same as the specification limits. Control chartsenable one to control process compatible with itscapability. In fact, the specification limits generallyapply to the individual values whereas the control limitsof the average chart apply to the distribution of theaverage. For this reason it is always advisable thatspecification limits are not drawn on the average chart.However, it should not be presumed that the controllimits and specification limits are not related in anymanner.

NOTE — Only in the case of control charts for individuals(see6.3.3 or 6.4.4.4), the specification limits maybe indicatedon the chart itself for comparison purposes.

9 ESTIMATION OF PROCESS CAPABILITY

From a process which is under statistical control for areasonably long time, a good estimation of the processcapability may obtained from the control chart fordispersion of the process (standard deviation chart orrange chart). In case the standard deviation chartis maintained, the process capability is obtained as

6 F fczwhere value of czis given in Annex A dependingupon the size of the sample. In the case of range chart,

the estimate is obtained as 6 F /d2 where value of d2 ischosen from Annex A depending upon the sample size.If, however, the process standard deviation (c$ isknown beforehand, the process capability is estimated

9

IS 397 (Part 1): 2003

as 6 (s. In physical terms, the estimate of the processcapability gives an upper limit to the variation that canbe found in all the items emanating from the processas long as it is kept in the state of statistical control.For fiwther details of estimation of process capability,reference may be made to IS 10645.

10 SETTING SPECIFICATION LIMITS ANDINSTALLATION OF MODIFIED CONTROLLIMITS

10.1 In a realistic situation where the specificationlimits are drawn after a thorough study of themanufacturing process, the difference between theupper specification limit (f-l)and the lower specificationlimit (L) should not vary unduly from the processcapability as estimated in 9. But in many of the existingsituations, specification limits are set in advance forthe manufacture of an item on the basis of engineering,technological or other practical considerations. In suchcases, after the manufacture has commenced and theprocess is studied and found to be in a state of statisticalcontrol, one of the following three situations may arise.

The tolerance difference between the upper and lowerspecification limits is:

a)

b)

c)

Smaller than the estimate of processcapability,

Of the same order as the estimate of processcapability, and

Larger than the estimate of process capability.

The probable actions to be taken in each of the abovethree situations have been discussed in IS 10645.

10.2 When the difference between the upper and thelower specification limits (U–L) is larger than theestimated process capability, then one of the probableactions recommended in IS 10645 is the use ofmodified control chart.

10.3 The adoption of the modified control limits hasmany economic advantages since it permits limitedshifts in the process average, thereby avoiding theunnecessary stoppage of production to hunt for troublewhenever the shifts in process average are not sufilcientto cause the production of defective products.Therefore, this chart may be particularly usefi.dwhenapplied to intermittent short production runs inmachining operations where the process capability hasbeen determined from previous runs. The more (U-L)exceeds the estimated process capability the greaterthe permissible latitude in machine setting. The use ofmodified control limits may simplifi the problem ofmaintaining machine settings that are good enough forpractical purposes. The modified control limits havealso been found usetil when a process is subject totool wear, since the natural spread of the process at

1

,. ,.

IS 397 (Part 1): 2003

any time is much less than the spread over the whole machine maintenance, etc, the initial data as given inlife of the tooI. Table 1 and also plotted in Fig. 1 spread over a week

10.4 Modified control chart, however, is notwere collected.

recommended when components are meant for 11.1.3 As a first step for the installation of controlassembly or final finishing operations or clearance is charts, the ranges were homogenized as follows:important. Further, modified control limits areworkable as long as the estimate of the process

11.1.3.1 From the 25 ranges (see CO111 of Table 1)the average range was calculated as:

capability remains constant. In other words the processdispersion must remain in statistical control. Wherever ~ = 8.58/25 = 0.34process dispersion behaves erratically, modified 11.1.3.2 Upper control limit (UCL) for the range chartcontrol limits are not appropriate. For this reason a is then calculated as:chart for range (or standard deviation) shouldaccompany any average chart using modified control Dd ~ =2.1 15 x 0.34 = 0.72, the value of Ddbeinglimits. taken from Annex A for a sample of size 5. It was

10.5 The upper and lower control limits for modifiedfound that the range for sub-group number 11 was

control charts are placed within the range of upper andoutside UCL and so this sub-group was discarded.

lower specification limits in such a manner that thecontrol limits are equidistant from the specificationlimits in the following manner:

UCL= U- V,cj

LCL=L+V, O

where the value of factor VI is suitably chosen fromAnnex C depending upon the sample size. In case thecontrol charts are maintained after calculating the

11.1.3.3 The average range calculated from theremaining 24 sub-groups was obtained as:

~ = 7.84/24 = 0.33 and Db ~= 2,115 x 0.33 =0.70. Again the range for the sub-group number9 was outside the UCL and hence this sub-groupwas also discarded.

11.1.3.4 The average range for the remaining23 sub-groups was obtained as:

average range ( R), the upper and lower control limits ~ =0.31 andDd~ =2.115x0.31 =0.65 .Itwasare obtained as follows: found that all the 23 ranges were now less

than UCL and hence the average range valueUCL= U– V, ~

(~) =0.3 1was taken as homogenized range value

LCL=L+V. ~ for the purpose of drawing the control limits. The/.

The value of Vz is chosen from Annex C dependinglower control limit for the range chart was now

upon the sample size. The central line in both the above obtained as DJ ~ = Oas the value of DBfor sample

cases is drawn at (U + L)/2. size 5 is zero.

11 ILLUSTRATIVE EXAMPLES

11.1 Example for Installing Control Charts forAverage and Range

11.1.1 In a firm manufacturing cuprous oxide dustingpowder by continuous process, the average dailyproduction was around 25 tonnes (for a shifl of 8 h).The product was packed in bags of 50 kg each so thatin a day about 500 bags were filled for despatch. Sincethe cuprous oxide content (percent by weight) is animportant characteristic, which has to be controlled, itwas felt desirable to install suitable control charts(average and range) for the purpose.

11.1.2 Five consecutive bags filled at the final stagewere considered to constitute a desirable sample sizeand on practical considerations it was agreed that afrequency of sampling of once in every two hourswould be adequate. After taking proper care withregard to the homogeneity of raw materials, mixing,

11.1.4 For the 23 samples, which were found to behomogeneous with regard to range, the grand average

~ was calculated as 10.05 and A2 E = 0.58 x 0.31 =0.18, where the value of factor Az = 0.58 is chosenfrom Annex A for a sample of size 5. The controllimits for the average chart were then obtained as

~ ~ Az jj which came out as 10.23 and 9.87. It wasfound that for the sub-groups number 3,5,6 and 7 theaverage values fell outside the control limits. Thisperhaps could be explained by the fact that there wassome erratic behaviour in the amount of cuprous oxidecontent when the programme for the installation ofcontrol charts was initiated by collecting suitablesamples. Hence these 4 sub-groups were discarded and

a new grand average was calculated as ~ = 10.04leading to the control limits of 10.22 and 9.86. It wasthen found that all the remaining 19 sub-groups werewithin the control limits and these limits were takenfor the installation of average chart.

10

NOTE — The elimination of the four points falling outsidethe average chart has resulted in the proper centering of theprocess by bringing down the grand average from 10.05to 10.04.

11.1.5 Afier the installation of the average and rangecharts, further data was regularly plotted in these chartsat 2 h intervals on subsequent dates. A typical extractof such a data is given in Table 2 and also plottedin Fig. 2. It maybe noticed that the point of the averagechart corresponding to sub-group number 3 has fallenbelow the lower control limit indicating that theremay be an assignable cause worth investigating.Accordingly the foreman in charge of the productionwho did a thorough investigation, found that the lowaverage value of the technical content was due to zeroerror in the balance used for weighing the technicalcontent before mixing. This error was suitably rectifiedand thereafter the process was found to be in statisticalcontrol.

11.2 Example for Installing Modified ControlCharts

11.2.1 In the earlier example given in 11.1 if the firmwere to produce cuprous oxide dusting powder to thenominal value of 10 percent (by weight) with atolerance of – 5 to + 10 percent then the upperspecification limit for cuprous oxide content would be11.00 percent whereas the lower specification limitwould be 9.50 percent. If the process is controlled atthe levels obtained in 11.1 then the over all averagerange for the entire period works out as ~ = 15.89/43= 0.37. Hence an estimate of the process capability isobtained as 6 ~ /d2 = 0.95. It may be noticed that thisestimate of process capability is much smaller than thedifference between the upper and lower specificationlimits U–L = 1.50 percent. Hence the firm decided toinstali the modified control chart for averages. Theupper and lower control limits for the modified chartwere then calculated as follows:

UCL=U– VZ ~ = 11.0–0.713 xO.37

= 11.00- 0.26= 10.74

LCL=L+ Vl ~ ‘9.50+0.713 xO.37

= 9.50+ 0.26= 9.76

11,2.2 Thus, the new control limits for average werefrom 9.76 to 10.74 percent as compared to the earlierlimits of 9.86 percent to 10,22 percent. This widerrange for the control chart for averages greatly helpedthe firm in meeting the stipulated specifications withoutunduly worrying about the permissible shifls in theprocess average value thereby leading to economy inproduction.

IS 397 (Part 1) :2003

11.3 Example for Installing Individual ControlCharts

11.3.1 In a firm, the oil of turpentine of Grade I wasbeing manufactured on a batch process. Specificgravity was one of the important characteristics ofthe oil which had to be controlled properly. However,due to limitations of testing, only one compositesample (collected from different portions of thematerials in a batch) could be analyzed for a batchand so it was decided to install a control chart forindividuals.

11.3.2 The collection of the initial data spread overthe production of 22 batches is given in Table 3. Fromthe 22 results obtained for 22 batches, moving rangesof two successive values were computed. Thus therewere 21 moving range values obtained fi-om22 results.The average range R was then calculated as

~ = 0.064/21 = 0.003. For the homogenization of theranges the upper control limit for the range chart wasthen calculated as Dh ~ = 3.267 x 0.003 = 0.0098.Since all the range values were found to be less thanthis upper limit, this average range value of 0.003 wasused for the construction of controI chart forindividuals. The UCL and the LCL for the individual

chart were obtained as ~ t 2.66 ~ = 0.859 t 0.008leading to the limits 0.851 to 0.867. The individualvalues got by analyzing the composite sample for eachbatch were also plotted in Fig. 3. It would be seen thatall the individual values were within the control limits.This indicated that the process was in a state ofstatistical control.

11.3.3 The specification limits for specific gravity ofoil of turpentine (Grade 1)were given as 0.852 to 0.862.Unlike in the case of averages where the indication ofthe specification limits on the control charts is strictlyforbidden, in the case of individual chart it would bealways advantageous to draw the specification limitsalong with control limits so as to find out how theprocess is behaving with regard to the specificationlimits. Specification limits were hence drawn in thecontrol chart for individuals. It would be noticed thatthe lower specification limit was just above the lowercontrol limit whereas upper specification limit waslower than the upper control limit. As a result threevalues out of 22 were found to be lying outside theupper specification limit although they were within theupper control limit. An estimate of the processcapability is obtained as 6 R /d2 = 0.016. This is inexcess of the difference between the upper and lowerspecification limits (U – L) which comes out to 0.010This indicated the need for either lowering the variationwithin the process or modifiing the specification limits.

11

Table 1 Control Chart Data Sheet (Initial Data) z(Clauses 11.1.2 andll.1.3.1) uw4

Product: Cuprousoxide dusting powder Production Order No.: ~

Characteristics: Cuprous oxide content (percent by weight) Normal Daily Output: 25 tonnes x

Unit of Measurement: Weightby percentage SampleSize: 5 w..Nominal Value: 10 percent Frequency: Once in every 2 h ~Specified Tolerance: +1() percent of the nominai value Inspector:

ou

– 5 percent of the nominal value

Specification No.: IS 1669

Sub-group Date Time Percentageof CuprousOxide Content in Total Average Range RemdsNo. the Sample Bag

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

1

2

L 3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

July 1

July 1

July 1

July 1

July 2

July 2

July 2

July 2

July 3

July 3

July 3

July 3

July 4

July 4

July 4

July 4

July 5

July 5

July 5

July 5

830

1030

1230

1430

830

1030

1230

1430

830

1030

1230

1430

830

1030

1230

1430

830

1030

1230

1430

9.99

10

10.34

9.8

10,27

9.63

9.86

9.97

9.88

9.88

9.68

10.35

10.23

9.87

9.9

9.72

9.96

9.81

10.05

10.29

9.6

10.29

10.43

10.14

10.21

9.75

9.77

10.16

10.39

9.78

10.42

10.12

9.99

10.12

9.96

9.84

10.07

9.95

9.90

10.10

9.8

10.14

10.24

10.24

10.44

9.99

9.77

10.16

9.68

9.78

10.23

10.12

10.23

10.08

9,78

10.02

10.1

9.85

10

9.81

10.05

10.07

10.43

9.99

10.39

9.87

9.%

10.07

10.14

9.98

9.86

9.99

10.35

9.99

10.14

10.02

10.17

9.9

10.05

10.05

9.91

10.14

10.34

10.24

10.39

9.75

9.96

10.26

10.05

9.98

9.97

10.35

10.35

10.12

10.2

10.08

10.12

10.2

10.15

10.05

49,35

50.64

51.78

50.41

51.7

48,99

49,32

50.62

50.14

49.4

49.96

51.04

51.04

50.33

50.1

49.44

50.34

49.96

50

50.49

9.87

10.13

10.36

10.08

10.34

9.8

9.86

10.12

10.03

9.88

9.99

10.21

10.21

10.07

10.02

9.89

10.07

9.99

10

10.1

0.45

0.29

0.19

0.44

0.23

0.36

0.19

0.29

0.71

0.20

0.74

0.36

0.36

0.36

0.24

0.36

0.21

0.39

0.30

0,29

._-L. . .

I1A1<I1<III14IIII< IIIIII:4II

2IIII

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II

>III

J’III

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IIIII

3IIIIIII

>1,-.

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397(Part

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13

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Table 2 Control Chart Data Sheet (Subsequent Data)(Clause 11. 1.5)

Product: Cuprous oxide dusting powder Production Order No.:

Characteristics: Cuprous oxide content (percent by weight) Production Department No.:

Unit of Measurement: Weight by percentage Normal DaiIy Output: 25 tonnes

Nominal Value: 10 percent Sample Size: 5

Specified Tolerance: +] 0 percent of the nominal value Frequency: Once in every 2 h

-5 percent of the nominal value Inspector

Specification No.: 1S 1969

S1No. Sub-group Date Time Percentageof CuprousOxide Content in Total Average Range RemarksNo. the Sample Bag

(1) (2) (3) (4) (5) (6) (7) (8) (9) (lo) (11) (12) (13)

i) 1 1 August 830 10.09 10.39 10.09 9.78 10.19 50.54 10.11 0.61ii) 2 1 August 1030 9.68 9.88 9,98 10.09 9.78 49.41 9.88 0.41

iii) 3 1 Augustz

1230 9.82 9.63 9,80 9,76 10.11 49,12 9.82 0.48

iv) 4 1 August 1430 9.88 9.88 10.39 10.39 9.18 50.42 10.08 0.51

v) 5“ 2 August 830 10.29 10.09 9,88 10.09 10,09 50.64 10.13 0.41

vi) 6 2 August 1030 9.78 10.29 10.19 10.29 9.98 50.53 10.11 0.51

vii) 7 2 August 1230 10.09 10.09 10.29 9.88 9,78 50.13 10.03 0.51

viii) 8 2 August 1430 10,09 9.88 10.19 9.88 10.09 50.13 10.03 0.31

ix) 9 3 August 830 10.04 9.87 9,99 10.09 9,81 49.80 9.96 0.28

x) 10 3 August 1030 9.77 10.05 10.18 9.85 9.92 49.77 9.95 0.41

xi) 11 3 August 1230 10.10 9.87 10.03 10.11 9.89 50.00 10.00 0.24

xii) 12 3 August 1430 10.03 9,84 10.31 10.01 10.21 50.40 10.08 0.47

xiii) 13 4 August 830 10.08 10.11 10.24 10.12 10.10 50.65 10.13 0.16

xiv) 14 4 August 1030 9.86 9,90 10.02 9.85 9.92 49.55 9.91 0.17

xv) 15 4 August 1230 10.18 10.29 10.11 9.92 9.90 50.40 10.08 0,39

xvi) 16 4 August 1430 10.14 10.20 10.08 10.17 9.94 50.53 10.11 0.26

..

WI

Table 2.— Concluded

(1) (2) (3) (4) (5) (6) (7) (8) (9) (lo) (11) (12) (13)

xvii) 17 5 August 830 10.19 9.84 9.81 10.15 10.19 50.18 10.04 0.38

xviii) 18 5 August 1030 9.69 9.84 9.70 10,02 10.19 49.44 9.89 0.50

xix) 19 5 August 1230 10.06 9.72 10.27 9.97 9.90 49.92 9.98 0.55

10.40-

g 10.30-——— —.. ___ _ ——— .—— ———

} 10.20-

= lo.lo -Ix% 10.00-P

9.80-

1 2 3 4 5 6 7 8 9 10 11 12 13 )4 15 16 17 18 19

% 0.70-

2——————————— ————————

c.-&g o.30-

5 0.10

I 2 3 4 5 6 7 8 9 10 Ii f2 13 14 15 16 17 18 19

SubgroupNo.

FIG.2 AVERAGE AND RANGE CHARTS (SUBSEQUENT DATA)

UCL

CL

LCL

UCL

CL

LCL

..2 .....

IS 397 (Part 1): 2003

11.4 Example for Installing Control Charts forMedian and Range

11.4.1 Control Chart for Median andRange (see Table4 and Fig. 4).

11.4.2 Range Chart

R = 22.0/25= 0.888

UCL = D,~ ‘2.115 X0.888= 1.88

As range hour No. 20 is greater than UCL, this rangevalue is deleted for homogenization and calculationsare done again.

~ = 22.2- 2.0 20.2

24= — = 0.84

24

UCL=2.115 xO.84 = 1.78

Since all the values of range are within UCL, this value

of ~ = 0.84 is taken as homogenized range.

11.4.3 Median Chart

~ =1264 .6-52.3 1212.3 =5051e

24 ‘— 24 “

UCL = M= + Fz ~ = 50.51 + 0.691 x 0.84

= 50.51 + 0.58= 51.09

LCL = @e – Fx ~ = 50.51 – 0.58

= 49.93

Since the median values for hour number 18 and 19are more than UCL, these values are deleted forhomogenization.

~ = 1212.3 -52.1 –52.3 1107.9e

22= — = 50.36

22

UCL = 50.36 + 0.58 = 50.94

LCL = 50.36-0.58 = 49.78

Since all the median values are within LCL and UCL,

these are taken as the control limits for medianchart.

Table 3 Values of Specific Gravity of Composite Samples Analyzed for Different Batches

(Clause 11.3.2)

S1No. Batch No. Specific Gravity Value Moving Range of the Two

(1) (2) (3) (4)

i) 1 0.861 —

ii) 2 0.860 0.001iii) 3 0.861 0.001iv) 4 0.865 0.004v) 5 0,861 0.004

vi) 6 0.860 0.001vii) 7 0.862 0.004

viii) 8 0.858 0.004ix) 9 0.860 0.004x) 10 0.859 0.001

xi) 11 0.864 0.005xii) 12 0,856 0.008

xiii) 13 0.852 0.004xiv) 14 0.856 0.004xv) 15 0.857 0.001

xvi) 16 0,856 0.001xvii) 17, 0.861 0.005

xviii) 18 0.855 0.006xix) 19 0.856 0.001xx) 20 0.856 0.000

xxi) 21 0.858 0.002

xxii) 22 0.865 0.007

Total 18,899 0.064

16

,. .,,.

IS 397 (Part 1) :2003

0.868

0.866

0.864+i-= 0.862uuu 0.860uG~ 0.858w~ 0.856

0.854

0.852

L———————————————————————————I -------------------

v

----- ----- ----- ----- -- ----- ----- --——— ——— ——— ——— ——— ——— ——— ——— ———

UCL

USL

CL

LSLLCL

0.850

123456789 10 11 12 13 14 15 16 17 18 19 20 21 22

BA’ICHNUMBH/

FIG. 3 CHART FOR INDMDUALS

Table 4 Bag Weights

(Clause 11.4.1)

Product : Ordinary Portland Cement, 33 Grade IS No.: 269 Characteristic : Weighment (kg)

Sample size: 5 bags each of 50 kg Frequency : Every hour from a(nominal mass) nozzle of a machine

Hour Test Results Mdlan RangeA

(1) ‘(2) (3) (4) (5) (6)> (7) (8)

1

2

3

4

5

6

7

8

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

50.0050.2050.60

50.80

50.40

49.80

50,40

50.20

50.20

50.40

50.40

50.60

50.60

49,50

50.60

50.80

52.10

51.00

50.40

50.80

50,80

50.50

50.40

50.40

50.20

50,00

50.40

50.20

49.80

50.40

50,20

50.20

50.40

50.40

50.40

50.20

49.80

50.20

50.20

50.20

52.30

52.30

52.40

50.20

50.40

50.00

50.40

50.40

50.0050.4050.2049.5049,2050.6050.8050.4050.2050.6049.8050.4049.2050.2050,4051.0052.50

52.10

52.30

50.80

50.20

50.80

49.80

49.80

50.4050.4050.2050.2050.2050.2050.8050,2049.8049.5050.2050.8050.4050.5049.8050.4051.5052.5052.4050.4050.6050.6050.2050.20

50.60

50.40

50,60

49.80

50.40

50.20

50.60

50.80

50.00

50.40

50.40

50.20

50.80

50.80

50.40

50.20

51.50

52.50

51.50

50.00

50.50

50.80

50.40

50.40

50.20

50.40

50.40

50.20

50.20

50.60

50.20

50.60

50.20

50.20

50.20

50.40

50.40

50.40

50.60

50.20

52.10’1

52.30”

52.30

50.40

50.50

50.60

50,40

50,40

0.60

0.40

0.40

1.30

1.20

0.60

0.60

0.60

0.60

0.60

0.60

1.10

0.60

0,60

1.60

1.30

1,00

1.50

2.00”

0.80

0.60

0.80

0.60

1.00

Total 1264.60 22.20

‘) Indicates data dropped for homogenization.

17

.. . . . -.

..

7

IS 397 (Part 1) :2003

52.50-I

52.00-k3&,w.

:51.00- — ——— ——— ——— ——_ ___ ___

u ‘— ——— —UCLu ~,~ .m

+’50.00-

v * w w CL

——— ——— ——— ——— ——— ——_ ___ ___ ___ __/fL

49,501

]2345678 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Howl

RANGE CHART

2.50

12.00

~ 1,50g

aK 1.00

0.50

——— ——— —.— ——— ——— ——_ ___ ——— —__

00041

]234567 8910111213141516 1718192021222324

Howl

UCL

CL

FIG. 4 CONTROL CHART FOR MEDIAN AND RANGE

18

(Clauses 6.2.2.

ANNEX A

,6.2.2.2,6.2.3.1,6.2.3.2, 6.2.3.3,6.3.1.1,6.3.1.2, 6.3.2.1,6.3.2.2,6.3.2.3, 6.4.2,6.4.3.1,6.4.3.2,6.4.4.1,6.4.4.2,6.4.4.3, 9 and 11.1.4)

FACTORS FOR COMPUTING CONTROL LIMITS

Using StandardValuesof ~ and o

Average Median Mid-Range StandardDeviationChart Chart Chart

Range Chart

CL P P P c1G dzoLCL p - Aa p-Fu p-f% BIo LAa(ICL p + Au ~+Fs ~+GC B2 u Lho

No. ofObserva- ~ .—;y. ~

tions inF G c1

Sample(1) (2) (3) (4) (5) (6) (7) (8) (9) (lo)

23456

G 789

10111213141516171819202122

232425

2.1211.7321.5001.3421.2251.!34

1.0611.0000.9490.9050.8660.8320.8020.7750,7500.7280.7070.6880.6710.6550.640

0.6260.612

2.121 2.121 0.56422.009 1.805 0.72361.638 1.638 0.79791.607 1.6532 0.84071.300 1.458 0.8686

0.8882

0.90270.91390.92270,93000.93590.94100.94530.94900.95230,95510,95760,95990.96190.96380.9655

0.96700.9684

0000

0.2260.1050.1670.2190.2620.2990.3310.3590,3840.4060.4270.4450.4610.4770.4910.5040.5160.5270.538

1.8431.8581.8081.7561.7111.6721.6381.6091.5841.5611.5411.5231.5071.4921.4781.4651.4541.4431.4331.4241.4151.4071.399

1 1281.6932.0592.3262.5342.7042.8472.9703.0783.1733.2583.3363.4073.4723.5323.5883.6403.6893.7353.7783.819

3.8583,895

00000

0.2050.3870.5460.6870.8120.9241.0261.1211.2071.2851.3591.4261.4901.5481.6061.659

1.7101.759

3.6864.35846984.9185.0785.2035.3075.3945.4695.5345.5925,6465.6935.7375.7795.8175.8545.8885.9225.9505.979

6.0066,031

0.600 0.9696 0.548 1.392 3,931 1.804 6.059

NOTES

Usings

Average StandardDeviationChart

z T~_,41~ BI~Y+/t, I B4 F

c A\

AI B3 B~

(11) (12) (13)

3.7602.3941.8801.5961.4101.277

1.1751.0941.0280.9730.9250.8840.8480.9160.7880.7620.7380.7170.6970.6790.6620.6470.632

0000

0,0300.1180.1850.2390.2840.3210.3540,3820.4060.4280.4480.4660.4820.4970.5100.5230.534

0.5450.555

3.2672.56822662.08919701.8821.8151.7611.7161.6791.6461,6181.5941.5721.5521.5341.5181.5031.4901.4771.466

1.4551.455

0.619 0.565 1.435

UsingRAverage Median Mid-Range RangeChart

Chart Chart Chart.? a< a 1?

~_& E ~, _FzE. 17&E D3 ?!X+ A2i? Me +)72 ~ ,L7+~i? D4 R

A2 FZ G D] DJ

(14) (15) (16) (17) (18)

1.880 1.880 1,880 0 3.2671.023 1.187 1.067 0 2,5750.729 0,796 0.796 0 2.2820.577 0.691 0.659 0 2.1150.483 0.549 0.575 0 2.004

1 Since the etllciency of medianlmid-range asan estimateof central tendencydeclines as sample size increases,they are not recommendedfor large samplesizes.For this reason,the entries in COI 53 and 4 are restrictedto sample up to 6 only. n

w2 Since rmge is not recommendedfor large sample size, the entries in COI14 to 18 are restrictedto samplesup to 6 only.

. .No0w

..-A

IS 397 (Part 1) :2003

ANNEX B

(Clause 6.5.2)

CONTROL CHART DATA SHEET (VARIABLES)

Sheet No.

Product: Sample size: Production order No.:

Characteristic: Frequency: Workshop :

Unit of measurement: Date: Machine No.:

Nominal value: Operator:

Tolerance: Inspector:

SI Date Time Individual Measurement Total Mean/ Range Remarks

No. A Median4Uid-/ >

123456Range

(1) (2) (3) (4) (5) (6) (7) (8) (9) (lo) (11) (12) (13)

Total

Mean

,-. ~..--

IS 397 (Part 1): 2003

ANNEX C

(Clause 10.5)

FACTORS FOR COMPUTING MODIFIED CONTROL LIMITS

No. of VI V2 No. of VI V2Observations in

Using Known Using AverageObservations in

the Sample the SampleUsing Known Using Average

Standard Range R Standard Range Rn Deviation n Deviation

(1) (2) (3) (1) (2) (3)

2

3

4

5

6

7

8

9

10

111213

0.879

1.268

1.5001.658

1.7751.866

1.939

2.0002.051

2.0952.1341.168

0.779

0.749

0.729

0.713

0.7000.6900.6810.6730.666

0.6600.6550.650

1415

16

17

18

19

20

21

22

23

24

25

2.1982.225

2.250

2.272

2.293

2.312

2.329

2.3452.3600.3742.3882.400

0.6450.641

0.6370.6330.6300.6270.624

0.6210.6180.6150.6130.611

21

IS 397 (Part 1) :2003

ANNEX D

(Foreworcf)

COMMITTEE COMPOSITION

Statistical Methods for Quality and Reliability Sectional Committee, MSD 3

Organization

Kolkata University, Kolkata

Bharat Heavy Electrical Limited, Hyderabad

Continental Devices India Ltd, New Delhi

Directorate General of Quality Assurance, New Delhi

Laser Science and Technology Centre, DRDO, New Delhi

Escorts Limited, Faridabad

HMT Ltd, R & D Centre, Bangalore

Indian Agricultural Statistics Research Institute, New Delhi

Indian Association for Productivity, Quality & Reliability, Kolkata

Indian Institute of Management, Lucknow

Indian Statistical Institute, Kolkata

National Institution for Quality and Reliability, New Delhi

Powergrid Corporation of India Ltd, New Delhi

SRF Limited, Chennai

Standardization, Testing and Quality Certification Directorate,New Delhi

Tata Engineering and Locomotive Co Ltd, Jamshedpur

University of Delhi, Delhi

In personal capacity (B-109, Mahiya Nagar, New DeUri f 10017)

In personal capacity (20/1, Krishna Nagar, .Safdarjurrg Enclave,

New Delhi 110029)

BIS Directorate General

Representative(s)

PROFS. P. MUKHEKIEE(Chairman)

SHRIS. N. JHASHRIA. V. KRISHNAN(Afterrrde)

DR NAVIN KAPURSHRIVIPULGUPTA(Alternate)

SHRIS. K. SRIVASTVALT-COLP. VIJAYAN(Alternate)

DR ASHOKKUMAR

SHRIC. S. V. NARENORA

SHRI K. VIJAYAMMA

DR S. D. SHARMADR A. K. SRJVASTAVA(Alternate)

DR B. DAS

PROFS. CHAKRABORTV

PROFS. R, MOHAN

PROFARVINOSETH(Alternate)

SHRIY. K, BHAT

SHRIG. W. DATEY(Alternate)

DR S. K. AGARWAL

SHRID. CHAKRABORTV(Alternafe)

SHRJA. SANJEEVARAO

SHRJC, DESIGAN(Afterrrate)

SHRIS. K. KIMOTHI

SHRJP. N. SRIKANTH(Alternate)

SHRI S. KUMAR

SHRISHANTISARUP(Alternate)

PROFM. C. AGRAWAL

PROFA, N. NANKANA

SHRJD. R. SEN

SHRIP. K. GAMBHIR,Director & Head (MSD)[Representing Director General (Ex-o#kio)]

Member Secretary

SHRILALITKUMARMEHTADeputy Director (MSD), BIS

Basic Statistical Methods Subcommittee, MSD 3:1

Kolkata University, Kolkata PROFS. P. MUKHERJEE(Convener)

Laser Science and Technology Centre, DRDO, New Delhi DR ASHOKKUMAR

Indian Agricultural Statistics Research Institute, New Delhi DR S. D. SHARMA

(Continued on page 23)

22

IS 397 (Part 1) :2003

(ContinuedJ-om page 22)

Organization

Indian Association for Productivity, Quality and Reliability, Kolkata

Indian Institute of Management, Lucknow

Indian Statistical Institute, Kolkata

National Institution for Quality and Reliability, New Delhi

Powergrid Corporation of India Ltd, New Delhi

Standardization, Testing and Quality Certification Directorate,New Delhi

Tata Engineering and Locomotive Co Ltd, Pune

University College of Medical Sciences, Delhi

University of Delhi, Delhi

In personal capacity (B-109, Malviya Nagar, New Delhi 110017)

In personal capacity (20/1, Krishna Nagar, Safdarjung Enclave,

New Delhi 110029)

Representative(s)

DR B. DASDR A. LAHIRI(Alternate)

PROFS. CHAKkABORTV

PROFS. R. MOHAN

SHRIY. K. BHATSHP.IG. W. DATEY(Alternate)

DR S. K. AGARWAL

SHRIS. K. KIMOTHi

SHRI SHANTISARUP

DR A. INORAYAN

PROFM. C. AGRAWAL

PROFA. N. NANKANA

SHRID. R. SEN

j

Panel for Process Control, MSD 3: l/P-2

In personal capacity (B-109, J4a[viya Nagar, New Delhi 110 017.) PROFA. N. NANKANA(Convener)

National Institution for Quality and Reliability, New Delhi SHRIY. K. BHAT

Powergrid Corporation of India Limited, New Delhi DR S. K. AGARWAL

Standardization, Testing and Quality Certification Directorate, SHRIS. K. KIMOTHINew Delhi

Tata Engineering and Locomotive Co Ltd, Pune SHRISHANTISARUP

in personal capacity (20/1, Krishna Nagar, Safdarjung Enclave, SHRID. R. SEN

New Delhi 110029)

23

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