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 397-4 (2003): Method for Statistical Quality ControlDuring Production, Part 4: Special Control Charts byAttributes [MSD 3: Statistical Methods for Quality andReliability]

IS 397 (Part 4): 2003

Indian Standard

METHODS FOR STATISTICAL QUALITYCONTROL DURING PRODUCTION

PART 4 SPECIAL CONTROL CHARTS BY ATTRIBUTES

(First Revision)

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

Statistical Methods for Quality and Reliability Sectional Committee, MSD 3

FOREWORD

This Indian Standard (Part 4) (First Revision) was adopted by the Bureau of Indian Standards, after the draftfinalized by the Statistical Methods for Quality and Reliability Sectional Committee had been approved by theManagement and Systems Division Council.

The efficacy of control charts m regulating production is quite well known. Part 2 of this standard coverstraditional control charts for attributes. This Part 4 of the standard dealing with special control charts by attributeshas been prepared for use in those circumstances wherein the traditional control charts are not applicable, lessefficient or more time consuming.

Since the basic philosophy for the use of control charts in manufacturing operations remains unaltered-irrespectiveof the type of chart used, this Part 4 should be read along with Part 2 for obtaining an integrated approach to thetheory and practice of control charts.

Part 2 of the standard is therefore necessary adjunct to this standard since many of the basic principles in theconstruction of control charts and their interpretation explained in Part 2 have not been repeated.

This standard was originally published in 1987. In view of the experience gained with the use of this standard incourse of years, it was felt necessary to revise this standard so as to make the concepts more up-to-date. Followingchanges have been made in this revision:

a) Demerit control chart has been included,

b) Standardized p-chart has been included, and

c) Many editorial mistikes have been corrected.

In addition to this Part, IS 397 has the four parts. The other parts are:

IS No. Title

397 Methods for statistical quality control during production:

(Part O) :2003 Guidelines for selection of control charts (jirst revision)

(Part 1): 2003 Control charts for variables (second revision)

(Part 2): 2003 Control charts for attributes and count of defects (third revision)

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

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

IS 397 (part 4): 2003

Indian Standard

METHODS FOR STATISTICAL QUALITYCONTROL DURING PRODUCTION

PART 4 SPECIAL CONTROL CHARTS BY AITRIBUTES

(First Revision)

1 SCOPE

This standard (Part 4) describes the following control‘k-+” .vith examples:

Master control systems chart for controllingthe quality during production anddetermining significant cause(s) of variationaffecting quality.

Demerit control chart.

Standardized p-chart.

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:

IS No.

397 (Part 2): 2003

7920

(Part 1): 1994

(Part 2): 1994

Title

Methods for statistical qualitycontrol during production: Part 2Control charts for attributes andcount of defects (third revision)

Statistical vocabulary andsymbols:Probability and general statisticalterms (second revision)

Statistical quality control (secondrevision)

3 TERMINOLOGY

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

4 MASTER CONTROL SYSTEMS CHART

4.1 Master control systems make use of enormousamount of attribute type of data for designing a qualitycontrol system so as to provide a factual basis on whichproduction people should act to prevent non-conformities, serve as an instrument of accountabilityfor supervision at all levels and provide an aid to

judgment by the timely identification of the ‘vital’situations requiring action. This system is essentiallya quality information feedback and i$ based on theroutine inspection data and as such it involves noadditional effort.

4.2 The two main features of master control systemschart are as follows:

a) Master control sheet, and

b) Principle of pyramiding.

4.2.1 Master Control Sheet

4.2.1.1 The master control sheet can be explained bestby an example from speedometer assembly. Table 1forms a typical master control sheet.

4.2,1.2 The lower portion of the master control sheetcontains a table and upper portion a chart (see Table 1).The main body of the table gives the number ofnon-conformities on each day due to various types ofnon-conformities, such as, incorrect reading,sticking and carried oscillation. The total number ofnon-conformities, number of units produced each dayand number of non-conformities per 100 units areentered in the COIS27, 28 and 29 of Table 1. Col 29 ofTable 1 gives the standard values of average numberof non-conformities per 100 units for each type ofnon-conformity, based on past experience frecords andused for calculating the control limits for the currentmonth. Col 28 of Table 1 gives the actual values ofaverage number of non-conformities per 100 units foreach type of non-conformity during the month.

4.2.1.3 While writing down the number of non-conforrnities, the upper control limit (t/CL) and lowercontrol limit (LCL), corresponding to the number ofunits produced and the standard value of averagenumber of non-conformities per 100 units, arecalculated with the help of following relationship:

()

E CiCentral line (CL) = E F = —

n

LCL = .?-3 (loo~)~

Table 1 Main Assembly Speedometer

(Clauses 4.2.1.1,4.2.1.2,4.2. 1.4 and4.2. 1.7),,

Dates ~ 2 3 4 5 6 7 9 10 11 12 13 14 16 17 18 19 20 21 23 24 25 26 27 28 29 Corrected ~ StandardNon-conformities Total z

:) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29)

Incorrect reading 11 18 24 19 24 52 42 35 29 9 41 32 15 29 30 23 28 23 26 73 42 12 23 31 50 551 5.32 5.63Sticking 3618141883 4526 ~5628412 11 25 6 14 4 12 1.49Carried oscillation 6 2 0 0 23 6 4 19 15 13 23 14 10 9 11 23 5 10 12 5 8 3 1 5 13

151 1.33171 1.74 1.92

O-Mark 30 FTO 04000 00000000 0 0 13 6 6 5 14 10 0.10 0.22Odometer 30 30 27 21 7 11 12 5 3 8 17 12 4 7 14 5 23 26 59 41 19 16 20 5 ~ 275 3.34 3.48Front ring 4 10 6 8 26 13 12 XT 9 31 9 17 17 19 17 13 12 6 3 6 1 6 2 3 182 1,64 1.90Glass 9 8 8 6 8 0 9 10 14 11 33 9 1 9 12 9 11 7 1 14 10 8 5 2 0 171 1.43 1.55Dial 32300042 20128241 94120401 7 38 0.35 0.44Pointer 596387116 839075312 82484002 0Dial shift orslant 55123 1104027 6245154 6877132

130 1.04 1.0489 0.71 0.75

Ratio 00000200 00100000 04030000 0 1 0.01 0.05Other defects 6 19 12 9 13 7 9 10 15 16 15 19 13 12 15 17 25 15 17 11 13 20 8 11 26 327 2.73 2.73Free play 131315127604 7101260254 831106460 4 145 1.20 1.33Odo reverse not 12012102 10201210 00000000 0 16 0.13 0.13

workingLamp position 00011000 00003014 00222020 0 14 0.12 0.14

m Total non- 99 124 131 100 121 114 115 108 96 86 194 115 86 103 126 112 143 114 147 191 155 87 92 71 133conformities

—

Total assembled 386 555 547 534 433 414 612 548 531 305 524 377 588 536 441 591 548 440 478 634 605 427 S22 411 486No. of Non- 25.6 22.5 23.9 18.7 27.9 27.5 18.6 19.7 18.1 28.2 37.0 30.5 14.6 19.2 28.6 19.0 26.1 25.9 30.8 30.1 25.6 20.4 17.6 17.3 27.4

conformitiesper 100 units

----A

-----” ----- . . .. . . . . . ..- -

$ 04=

1 234567 8910111213141516 171819202122232425

OAY

CONTROL CHART

UCL

CL

LCL

where FI is the standard value of the average number

of non-conformities per 100 units and n is the numberof units produced.

NOTE — To facilitate computations, UCL and LCL have beencomputed in Annex A.

4.2.1.4 If the number of non-conformities exceeds theupper control limit, a continuous circle is put aroundthe actual number of non-conformities and it fallsbelow the lower control limit, the dotted circle is drawn.At the end of the month, the figures in each row areadded horizontally eliminating the figures which arecircled and the average number of non-conformitiesper 100 units calculated and written down inCO128of Table 1. The new set of average number of non-conformities per 100 units so calculated is comparedwith the corresponding standard values.This new setof calculated values is taken as standard values for thenext month provided these do not exceed thecorresponding standard values for the current month.In case of significant increase in the average numberof non-conformities per 100 units for any particularnon-conformity, corrective actions are initiated.

4.2.1.5 In the upper portion of the master control sheet,that is the control chart for number of non-conformitiesper 100 units are plotted. Once again, points out ofupper control limit are circled continuously and thoseout of lower control limit are circled with dotted lines.While a continuous circle in a master control sheet isan indication for the concerned supervisor of the needfor immediate action, value of any dotted circle shouldnot be underestimated. A dotted circle represents achange for better performance. It tells the supervisorthat opportunity exists to discover the cause and makeit a permanent feature in the process.

4.2.1.6 Instead of number of non-conformities whereinequal importance is given to each type of non-conformity, average demerit score may .be calculatedby giving demerit score to each type of non-conformity(depending upon its criticality). For fhrther details,see 5.

4.2.1.7 One important feature of the master controlsheet is the increases in sensitivity obtained by thebreakdown of the total number of non-conformities.As may be seen from Table 1, the frequency ofoccurrence for out of control points daily for totalnumber of non-conformities during the month is farless than that of each type of non-conformity. Breakingdown the non-conformities due to individual operationsor sources could increase the sensitivity further.

4.2.2 Principle of Pyramiding

4.2.2.1 The central idea behind the principle ofpyramiding is that, as far as practicable, each personin the manufacturing organization should be provided

IS 397 (Part 4) :2003

with a master control sheet pertaining to his sphere ofresponsibility. Persons at the lower levels of theorganization have to actually initiate corrective action.Hence the information given to them should be morepin-pointing. At higher levels, unnecessary detailsshall be avoided and information just sufficient tomonitor the situation be provided.

4.2.2.2 Figure 1 illustrates how the principle ofpyramiding for master control systems works. Charts1 through 11 are the foremen’s charts. Chart 12-is forvendor non-conformities. Chart 13 is for non-conformities whose sources are undetermined, designquality and comprising standards. Charts 14 through17 are the charts for the superintendents. Charts 18and 19 are for the assistant managers. Chart 22 is forthe manager, the apex of the pyramid. Number 20 isfor inspection and 21 is for engineering. The foremen’stotals are pyramided to form the superintendent’scharts. The superintendent’s totals are likewise,pyramided to form the assistant manager’s charts. Thetwo assistant manager’s totals and the totals for vendornon-conformities and engineering non-conformitiesare pyramided to form the manager’s chart.

4.2.2.3 Table 2 shows the manager’s control chart forDecember. It can be observed that the total for themanager is out of control on the high side for.3December. This could be rapidly traced down throughthe pyramid to the three principal non-conformities atfault simply by following the continuous circles.Figure 2 shows the excerpts from the master controlsystems that pin-point these three causes.

4.2.2,4 The-lower the level of the chart in the pyramid,the more sensitive the control becomes. Hence, themen who need to take action have the pin-pointinginformation to guide them daily. As the level in thepyramid becomes higher, the more details areeliminated. The charts are so directly connected toeach other that the entire data directly below a personin the pyramid becomes easily and immediatelyavailable to him at his discretion.

4.2.2.5 The importance of each senior discussing eachcircle on his chart daily with the subordinatesconcerned cannot be over-emphasized. Any personin the pyramid can activate that portion directly belowhim by following the rule. A plant manager thusdevoting a few minutes per day can be assured that allthe men in his organization are regularly investigatingand taking action on the out-of-control conditions thatare indicated by their respective charts.

4.3 Examples

The master control sheet is firther illustrated with avariety of examples. Table 3 gives the master.controlsheet for a textile mill manufacturing sarees wherein

3

IS 397 (Part 4): 2003

22

MANAGER

T FE1

[

I

TTV7

3

I

v)

.!4

.g

7

I

r---

FIG. 1 PYRAMIDIZATION OF INFORMATION

department-wise (weaving, dyeing and printing) break- conformities. However, if the number of classes ofup of non-conformities ;S given. Table 4 gives themaster control sheet for one of these departments,namely, dyeing department. Table 5 is a master controlsheet for a blade section wherein source-wise break-up of rejections is given.

5 DEMERIT CONTROL CHART

5.1 In case of control chart for number of non-conformities, all the non-conformities on an item arecounted and plotted on the control chart. This charthas a disadvantage that it gives equal importance toeach class of non-conformities. But the different non-conformities are unequal in their influence on costs.Some may be corrected by simple inexpensive reworkoperation, other may require costly rework, still othersmay involve the scrapping of the items inspected. Apractical solution to this problem is to classify thevarious non-conformities into some broad categories,like critical, major and minor non-conformities andrun separate control charts for each class of non-

non-conformities increase, it may be ditllcult to haveso many control charts simultaneously. A simplersolution is to give the different demerit rating (weights)to each class of non-conformities and calculate thedemerit score for each item. This demerit score maybe plotted on the demerit control chart.

5.2 In case of demerit score;the underlying distributionis also Poisson type. The non-conformities are givenweights since all types of non-conformities cannot betreated alike. The criteria for selection of demeritweights is discussed in 5.2.1.

5.2.1 The method for selection of demerit weights forvarious non-conformity depends on the type ofproducts under consideration, Broadly, there are twotypes of products. In the first instance, it is possible torectify a non-conformity by either replacing acomponent or by carrying out suitable rework. Theproducts of engineering industry involving assemblyof large number of components is an example of this

4

IS 397 (Part 4) :2003

MANAGER (22)

I 100 p I I Actual No. of Defectives I

3.7 Assistant Manager (18) 180

1.4 Assistant Manager (19) 56

0.3 Vendor 18

4.6 Engineering 142

10.0 Total 396

Assistant Manager (IS)

100p Number

2.1 Superintendent (14) 981.6 Superintendent (15) 82

3.7 Sub-total 180

v v

Superintendent (14) Superintendent (15)

100p Number 100p Number

0.5 Current coil 54 0.6 Electromagnet 20

1.4 Resistors 34 1.0 Test and repair 62

0.2 Potentiometer 10 1.6 Sub-total 82

2.1 Sub-total 98

Current Coil Test and Repair

100p Number 100p Number

0.35 Rubber flows 46 0,2 Digit off zero 3

0.10 Bent loads 6 0.3 Screws loose 25

0.05 Miscellaneous 2 0.4 Pointer off zero 32

0.50 Sub-total 54 0.1 Miscellaneous 2

1.0 Sub-total 62

FIG. 2 BREAKDOWN OF REJECTIONS

type. In the second situation, it may not be possible tocarry out the rectification of the end-product. The partof the end-product or item is graded in three or moregrades and sold as such. The textile products areexamples of thix category. Most of the non-conformities that arise in weaving, finishing, printing,etc, of fabric are graded and sold at varying prices.

The approach for selection of demerit weights for boththe situations is explained below.

5.2.1.1 In cases of the first type of product, the choiceof demerit weights (wi) depends generally on thecriticality of the non-conformity, which is generallydetermined by taking into account various aspects of

5

m

Table 2 Manager’s Control Sheet

(Clause 4.2.2.3)

100 ~ Dates -+ 1 2 3 4 6 7 8 9 10 11 13 14 15 16 17 18 20 21 22 23 24 27 28 29 30 31Factors

43.7 Assistant 80 69 180 58 36 87 106 45 34 39 68 28 33 37 76 29 89 45 78 72 72 50 78 83 71 81

Manager (18)

1.4 Assistant 30 28 56 22 14 55 59 17 11 22 31 11 14 23 22 13 24 16 39 40 2° 18 25 30 27 17Manager (19)

0.3 Vendor 9518643142 31653892 77453668 32

4.6 Engineering 140 60 142 88 86 185 172 68 57 44 54 62 51 53 133 62 83 47 41 78 95 77 100 91 98 86

10.0 Total 259 162 396 174 140 330 351 132 105 106 159 106 101 121 240 106 203 115 162 195 190 151 209 212 199 186Production 2876 1360 3251 1580 1556 3612 3679 1312 1050 1053 2= 1263 902 1281 2827 1348 2421 1261 2~ 1878 1679 1476 2213 2431 2350 2117Percent non- 9.0 11,9 12.2 11.0 9.0 9.1 9.5 10.1 10.0 10.1 6.4 8.4 11.2 9.4 8.5 7.9 8.4 9.1 7.3 10.4 11.3 10.2 9.4 8.7 8.5 8.8conforming

— —

UCL------------- -

CL

k~ a; ..0-. -..-...s-

= 7- --. ”--” -.-- ..a” -.. -. . . . . . . . . . . . . --- LCL--------- . . .-. -~ f3~

--. ..a-

g 51g4~ .—

12345678 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

1M%

CONTROLCHART

Table 3 Master Control Sheet — Textile Mill

-J

(Clause 4.3)

Day 12345678 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Corrected _ StandardTotal c ~

Total number 2868 13773333157915583600 36891326105310502526 1263 90512872620134824211265 22001874168414742222 244423512126of sareesmanufactured

Non-

{

Number 814 4931034 440 48511691128 385 288 301 560 264 278 390 705 4+8 613 405 738 630 449 454 662 669 618 480con for-

—— 9998

Per 100 2~ 35.8 31 27.9 29.8 32.5 30.6 29 27.4 28.7 22.2 20.9 30.7 30.3 ; 31 33.6 32 33.5 33.6 2~ 30.8 29.8 28.2 26.3 22.6.— —

29.8 31.25mities units

—— — — —— —

Department- 257 98 278 113 85 364 334 99 86 77 150 53 58 76 120 f4+ 210 128 278 150 115 136 170 177 160 146(source) wise

— — — 2868 7.9 8.00

break up ofnon-conforrnitiesWeaving

Dyeing 259 202 312 185 115 439 351 162 115 126 259 156 161 141 446 151 340 162 285 274 190 185 274 300 259 150 3687 12.5 13.50

Printing 298 193 ~ 142 ~ 366 = 124 67 98 ~ 55 59 173 140 126 263 115 175 206 144 133 218 212 199 259—.

— — 3090 9.4 9.75

38

20

+. .

-- . . -. ..-...9. ----- -m ---- -. . . . . . -

j

J—-—T ——

12345678

:.

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

DAY

CONTROL CHART

UCL

CL

LCL

Table 4 Master Control Sheet — Textile Mill Dyeing Unit E

(Clause 4.3)we+

Day 12345678 910111213141516 171g 192021222324 25 26 COrre~. _ Standard ~

Total number of sarees 2888 1377 3333 1579 1558 3600 3689 1326 1053 1050 2526 1263 905 1287 2820 1348 2421 1265 2200 1874 1684 1474 2222 2444 2351 2126manufactured

Non-

{

Number 259 202 312 185 115 439 351 162 115 126 259 156 161 141 445 151 340 162 285 274 190 185 274 300 259 150— — —Conformities

— —per loo N 14.7 u 11.7 u 12.2 u 12.2 10.9 12.0 KU 12.4 17.s 11.o 15.8 11.2 14.o 12.8 13.o 14.6 11.3 12.6 12.3 12.3 Lo Q

——

Dueto Dying “nits

Cause/Stage/Source-wise break-up

Stentor

ChheraCreaseTom Pieces

Old dagi

Kachra dagi

Mud dagi

(Dyeing) D-Damagem Madi dagi

Short w]dth

& 69 & ~ 36 ~ ~ 45 34 39 ~ 28 33 37 76 29 89 45 78 72 52 50 78 83 71 G

50 18 74 0 ~ 55 39 17 11 22 31 11 14 23 22 13 34 16 39 40 20 20 25 30 27 15

29 12 41 17 11 45 36 18 8 18 20 3 4 7 106 12 20 11 17 22 12 14 18 20 15 10

108 71 & 50 ~ 179 ~ 40 38 30 ~ 52 69 57 103 52 112 55 89 80 62 65 90 100 86 ~

~ 12 ~ 59 10 ~ 31 14 10 7 28 20 21 5 35 25 10 16 18 18 14 11 17 19 31 10

901012” 642 3166108307 74563688 63

261024211186 56161024289 126109581310 97

2805620108 40101050135 198119831112 116

Q 3 g 55181072316 14302841479 894121435

73233555 00220050 80 11105424 02

ted cTotal

3687 12.0

3.31.3

0.9

4.0

0.9

0.2

0.4

0,4

0,4

0.2

r z*.%ow

13.5

3,7

1.4

1.0

4.6

1.0

0,3

0.4

0.4

0.4

0.3

20-

g 18

u)w 16 + _.. -m...

-q. ..v. .-v.J=------- ----“.*. .-

~fn --”. ----- . . . . . . . . . . . . ------ . . . . . . . . . . . . . UCL~z&g

14- Ao- ,2,

CL

%Z 7 9. ----0’

. . . . . . . . . -------- -m. . . . . .

10 ;~-----

3 6j

64—

i23456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

DAY

CONTROLCHART

Table 5 Master Control Sheet — Blade Section

(Clause 4.3)

Production quantity

Total

{

No.deviations

%

Degree of deviation

{

No.1. Passed

v.

{

No.2, Rework

Y.

{

No.3. Scrap

%

Source-wise detail

1. Operatoru

2. Tool fixture

3. Cutter

4. Machine

5. Gauge

6. Material

1

700

222

31.7

216

30.8

0

0

6

0.9

15

4

86

0

2

115

2

743

174

23.4

172

23.1

0

0

2

0.3

75

0

31

0

2

66

3

667

169

25.3

167

25.0

0

0

2

0.3

166

0

3

0

0

0

4

809

138

17.1

128

15.8

0

0

10

1.3

84

0

2

0

0

52

5 6

695 440

104 8—

15.0 ~—

104 8

15.0 1.8

0 0

0 0

0 0

0 0

99 2

0 0

0 4

0 2

0 0

5 0

7 8

828 1060

43%

5.2 4.2— —

59 44

4.7 4.2

4 0

0.5 0

0 0

0 0

23 40

0 0

12 4

0 0

0 0

8 0

9

881

26—

~

26

3.0

0

0

0

0

26

0

0

0

0

0

10I050

44—

4,2—

40

3.8

0

0

4

0.4

34

0

0

10

0

0

27

762

o

0

00

00

Q

o0000

28

240

~

0.8—

o

0

2

0.8

0

0

2

0

0

0

0

0

29

846

~

0.4—

3

0.4

0

0

0

0

J

o

0

0

0

0

30

558

18—

3.2—

18

3.2

0

0

0

0

18

0

0

0

0

0

31

120

0

0.0—

o

0

0

0

0

0

0

;

o

0

0

0

35-●tso. 9 UCL; . . .

. ..=l. - . . ...-. . . ..- . . ---- .- ------ .-“” -.. _.. . . ..8

. . . ..- . . . ..- . . . ..-#20- CL*o15- ------ m------ ..- -----

-. .‘.-. ●

:1o-.

●b

8LCL

g 5-*

o-DAY

CONTROLCHART

IS 397 (Part 4) :2003

product such as safety, performance and customerreaction. In general, a non-conformity may beclassified into three classes, namely, minor, majorand critical non-conformities. If need arises, thiscategorization may be tin-ther extended by sub-dividingthese classes into two or more. A demerit weight isthen assigned to each class taking into account thevarious aspects mentioned above. Another approachfor selection of demerit weights is by estimating thefinancial loss in the form of scrap, rework or potentialloss of resources due to diversion of production efforts.The financial loss due to passing of a non-conformingitem having particular non-conformity to the assemblyor final product can also be taken in account, Thedemerit weight may then be fixed in proportion to thefinancial loss due to a non-conformity. Generally, fewclasses may then be worked out on the basis of therationalization of these losses and the demerit weightsassigned to each of these classes rather than treatingeach non-conformity separately. An approach wherea combination of critically of non-conformity andfinancial loss is taken into account, for assigning thedemerit weights, may also be followed.

5.2.1.2 In the second situation, the approach followedinvolves the final grading of the end-product initially.This graded product is then inspected for various typesof non-conformities present in it. The demerit weightsto each type of non-conformity are assigned in such away that a distinct total demerit score can be assignedto each grade of the product. The various combinationsof non-conformities giving rise “to a distinct grade ofthe end-product would result in a total demerit scorewhich should not overlap for the different gradesassigned. This process of assigning the demerit weightscan be explained by taking following example offabrics.

a) To begin with a meeting of heads of variousdepartments, namely, weaving, finishing,printing, folding and sales is organized. Thismeeting decides on classification of non-conformities into two or more classes. Theextent of particular type of non-conformityon the fabric may also be taken into accountwhen this classification is carried out, forexample, the broken or missing end can beclassified differently depending on numberand length of missing ends. The finalgrade of the fabric depending on differentcombinations of the non-conformities presenton a cut or piece is also to be arrived at in thismeeting.

b) The next step is to select about 500 piecesfrom a production line and these areindependently graded into, say, three finalgrades, namely, fresh, second and

sub-standard by four or five experiencedinspectors. The pieces which are foundcutable are sub-divided into two and gradedonce again.

c) The pieces which give rise to different gradingby various inspectors are re-examined andafter discussions, properly re-graded. Thepieces on which such a consensus of finalgrading cannot be achieved are not taken intoaccount for the fkther analysis of the data.

d) The various combinations of non-conformities under various grades are thenlisted fkom the pieces on which a consensusof the uniform grading is achieved. This givesa cross check on the definitions of grades andalso enables to complete this definitions byincluding additional combinations of non-conforrnities which might have escaped noticeearlier. The next step is to assign differentcombinations of demerit weights for eachcategory of non-conformity and the totaldemerit score for each piece is calculated. Bytrial and error, the demerit scores shall be soadjusted that there is no overlapping of totaldemerit scores on the pieces which are gradedin different grades.

5.3 Before starting for the chart, for preliminaries toinstallation of the chart, reference may be made toIS 397 (Part 2). One of these is the homogenizationprocess, which has been discussed below.

5.3.1 Homogenization for Demerit Score

5.3.1.1 For the purpose of homogenization, the uppercontrol limit for the demerit score per item is firstcalculated as follows:

Let Cij = number of non-conformities of i th classinj th sub-group,

i =1,2 . . . . . . . . . . . ..k

-i =1,2 . . . . . .. . . . . . ..m

c. = total number of non-conformities of i th1

class in all the sub-groups = y c..j=] lJ

Wi = demerit weight for i th class of non-conformity,

nj = number of items inj th sub-group,

N = total number of items in all the sub-m

grOUPS = ,~lnj

.Dj = total demerit score for j th sub-

kgroup = i~, Wicij

10

IS 397 (Part 4): 2003

~ = demerit score per item for j th sub-

/

Dj kgrOUp = ~j ‘~w~jinj

J=l

d = demerit score per item for all the sub-

*oUps = :1 DJ/N

J–

~ njd, f f Wicijj=l i=l j=l.— .

N N

k Wici_ i=l——

N

Upper Control Limit (UCL) for thej th sub-group

‘CL=2+3[(il~2c’)in’r5.3.1.2 If the demerit score per item for each sub-group is less than or equal to the corresponding uppercontrol limit, the initial data collected shall be deemedto the homogeneous for the purpose of starting thecontrol chart. If the demerit score per item for one ormore sub-groups exceeds the corresponding uppercontrol limit, then the relevant sub-group(s) shall bediscarded and a new average demerit score per itemshall be computed for calculating the revised uppercontrol limit, This process shall be continued till thedemerit score per item for all the remaining sub-groupsis found to be less than its upper control limit.

5.4 Control Limits

5.4.1 The central line of this chart is drawn a! theaverage demerit score per item, d, as obtained fromthe homogenized data (see 5.3.1). The upper and lowercontrol limits for j th sub-group are obtained asfollows:

‘CL=‘+3(i9’2c’’Nn’?‘CL=‘-3(ii~2’’NnJrIf LCL is negative, it is taken as zero.

5.5 In demerit control chart, a demerit score may beachieved in many ways, that is, it may have few criticalnon-conformities or many minor non-conformities. Soeven if there is a run, it shall not be interpreted in theusual sense that an assignable cause may be present.

5.6 Example

5.6.1 In diesel engine industry, several non-conformities have been identified which directly orindirectly affect the quality of the engine. From thepast experience, the demerit rating for each class ofnon-conformity is given in Table 6. The number ofengines inspected and the number of non-conformitiesobtained for each class of non-conformities are alsogiven in Table 6. Compute the control limits for thedemerit control chart.

5.6.2 Since the number of engines inspected on eachday do not differ much, average number of engines

(z) inspected on each day maybe used for calculatingupper control Iimit for all the sub-groups.

N = ~lnj = 4250 ~ wi~ = 17840i=l

6= ;=177 ~ WiCi ’881400i=]

= 4.20

—— 4.20 +-3~8t?l400/4250x1T7]%

= 4.20+ 3.25 = 7.45

‘CL = 4.20 – 3.25 = 095

5.6.3 Since the demerit score per engine for each ofthe sub-groups is less than UCL, these limits maybetaken as control limits for demerit control chart.

5.6.4 With these control limits, the control chart fordemerit score as maintained. The chart is illustratedin Fig. 3.

6 STANDARDIZED P-CHART

6.1 This chart is recommended when sample size varieserratically. It improves visual appeal and avoidsconfusion when larger ‘p’ for a sub-group is within itsupper control limit and smaller ‘p’ for another sub-group is beyond its upper control limit.-,., . . ..4. –C–, -U ,.. --. —------- –r —-- - .1nls cnarI Consls[s01 plommg sequence 01 production

on x-axis and sample statistic p = [&( P-F)]/

[@(l-@] ony-axis with appropriate scales. The

central line is zero. Upper and Lower Control Limitsare * 3 respectively.

11

IS 397 (Part 4) :2003

6.2 Example

The number of picture tubes processed (n) and foundnon-conforming for a particular model for a period of25 consecutive days are given in Table 7. The analysisof the data with the help of p-chart and standardizedp-chart and also interpretation is given in Table 7.

6.2.1 Calculations for p-Chart

~ = 1 467/27 474= 0.053

UC’L and LCL for each day, depending upon n, is givenin CO16 and 7 of Table 7 respectively.

6.2.2 Calculations for Standardized p-Chart

The values for standardized p for each day is calculatedand given in CO17 of Table 7 and as mentioned above,

UCL and LCL are * 3 respectively.

6.3 Interpretation

Standardized p-Chart has been plotted in Fig. 4 for thesame data. The following is observed:

a) From Table 7, it is observed that p on day 16is higher than p on day 24, yet the former iswithin UCL while the latter is beyond its UCL.

Again p on day 10 is lower than p on day 5,yet the former is within LCL while the latteris beyond its LCL. This is so because largersample size provides stronger evidence/

confidence for discrimination. This anomalyis not seen on standardized p-Chart.

b) On 6 days out of the 25 days examined, theprocess is out of control. On 3 days it is betterand 3 days it is worse in relation to the overallaverage performance of 5.3 percent non-conformities. The reasons for adversedepartures from the standard (average)performance beyond the Upper Control Limit(UCL) are considered feasible for quickidentification of cause(s) for elimination andprevention. Likewise reasons for favorabledepartures fi-om the standard beyond LowerControl Limit (LCL) need to be cultivated forimprove menu.

c) There are two favorable runs of 6 and 7points, from day 8 to day 13 and day 17 today 23 respectively. These provide evidencefor potential recurring benefits. Therefore itis not rational to accept the present observedp = 0.053 as process standard. Instead theaverage of 13 days, 8 to 13 and 17 to 23, of0.039 may accepted as first iterative benchmark, showing an improvement of about 30percent over present average of 0.05.3. Ofcourse, if reasons forp = 0.025,0.026,0.030and 0.032 on days 12, 10,20 and 5 are tracedand cultivated then even the target ofp = 0.026, half of 0.053, is feasible forpotential recurring savings of about 50 percentof existing loss at this iterative stage.

12

IS397

(Part

4):2003

..

ai

1,%I;<IIIIIIIIIIIIIIII<

IIIIIII(IIIIIII 41

I

;1 IIIIIIIIIIII

kcm

t

Cn

g&

w

13

IS 397 (Part 4) :2003

Table 7 Data on Picture Tubes Processed and Found Non-conforming

(Clauses 6.2,6.2.1 and 6.2.2)

Day Number Number Non- /)-Chart StandardisedProcessed conforming p-values

n d p = dln UCL = LCL = ( --&

p+3 J- p-3 Jm &’-~(1-~)

(1) (2) (3) (4) (5) (6) (7)

I 2417 143 0.059 0.067 0.039 + 1.32 2334 165 0.071 0.067 0.039 + 3.93 954 63 0.066 0.075 0.03 I + 1.8

4 1104 55 0.050 0.075 0.03 I -0.45 1246 40 0.032 0.072 0.034 -3.36 792 54 0.068 0.077 0.029 +1.9

7 1298 73 0.056 0.072 0.034 + 0.58 321 12 0.037 0.091 0.015 -1.39 i 204 55 0.046 0.072 0.034 -1.1

10 576 15 0.026 0.081 0.025 -2.911 1151 59 0.051 0.073 0.033 -0.3

12 1256 32 0.025 0.072 0.034 4.413 1099 44 0.040 0.073 0.033 -1.914 811 98 0.121 0.077 0.029 + 8.615 1073 65 0.061 0.074 0.032 + 1.2

16 196 19 0.097 0.101 0.005 + 2.817 1113 53 0.048 0.073 0.033 -0.718 I 066 40 0.038 0.076 0.030 -.2.219 828 38 0.046 0.077 0.029 -0.9

20 1083 33 0.030 0.073 0.033 -3.421 991 39 0.039 0.074 0.032 -2.022 1102 57 0.052 0.073 0.033 -0.223 I 226 60 0.040 0.072 0.034 -2.0

24 1140 90 0.079 0.073 0.033 + 3.925 1093 65 0.059 0.073 0.033 + 0.9

Total 27474 1467

10,

8

-4.— —— —— . —— —— ——

UCL

CL

LCL

FIG.4 STANDARDIZEDP-CHART

14

IS 397 (Part 4): 2003

ANNEX A

(Clause 4.2.1 .3)

U(2L AND LCL FOR CONTROL CHART ON NUMBER OF DEFECTS PER 100 UNITS

~+ 01 02 W3 @4 05 ro 1“5 2“0 25 30 *5 4“0 4s 5“0n

-+10

20

30

40

50

60

70

80

30

100

120

140

160

180

200

250

300

350

400

450

500

600

700

800

3“100“00

’222000

1°830“00

1“600“00

1“440’00

1‘-32000

1“230“00

1“16Omo1“100001“050000970“000“900“000“850“000“810“00W770“000“700000650“000“61croo0“57&oo0550’00&520“000“490“000“460“000440“00

4440“00

3°20OWo

2“65000

2-32Omo

2“1004)0

1“93mo

1“80fYoo

1“70000

1“61000

1“54Voo1“420$001“330“00

1“26000

1“200“00

1“150“00

1“05000

(Y97Omo

0“92000

tY870“00

0“83000

080000

0“75000

0“710-Wo0-670“00

5“50000

3“97000

3“30O’oo

2?)0000

?620’00

2“42000

226OWo2“140“002Q3Woo

1’940“001“800001“69Owo

1“600“00

1-52000

1“46000

1“340“00

1“250“00

1“180“00

1“12(POo

1“070“00

1“03(MO

0970“00

0920“000“88000

6W0“00

4%4mo

3“860’00

3“40Omo

3“08Omo

285Omo

P67Omo20520002“40000

!?30O@o2“13mo2“00000

1“90Omo

1-81000

1“74mo

1%0mo

1“50Owo

1“410=00

1“350“00

1“29000

1“25Owo

1“170“00

1“120“001“07(POo

7°21O@O

5“240’00

437cvoo

!V85000

3“50Omo

3“24OfJo

3m4000

2“87O@2“74MO

2“62Omo2440“00?290“00

!2180“00

2“08O@

MO000

1’840“00

1“72Owo

1“630’00

1“56MO

1“500“00

1“450“00

1“37000

1“300“001“25woo

1049Owo

771Wo

648000

5“74(m)

*24000

Ik87Om

4590004350“00416woo

4WOmo3’74O@o3“54(POo

3“37000

3“240“00

3“12owl

2“90000

273000

2“60000

2“50mo

2“41woo

2“34owl

2“220“00

2“13woo2“06Ow

13”12000

972000

821000

?31Owo

6“70000

624000

5“890“005“610“00Y370“00

5“170004“85Owo*61mo

4400“00

424o(x)

4100“00

?820“00

3“62000

3“460“00

3“34Owo

3“230“00

$140“00

3“000“00

P890112-80&20

1!P420“00

11“49Owl

9750“00

871lwo

8“oOO@o

7“48mo

7“070006’740“006470“00624(MO5“87Owo5“590“00

5“350“00

5-160“00

SooOw

4%80“00

4450“00

427O@o

412000

4000“00

3“90010

3“730“27

Y600“403“50050

17500“00

13”11000

11°16MO

1000Owo

921000

062000

8“170“007“800“007“50woo

7“24Omo&83woo&51Omo

6“25o “00

6“040“00

5“85O@o

5“500“00

5240“00

5“04Omo

4“870“13

4740’26

4“62(Y38

#440“56

4’290“71418O“82

19”430“00

14”620“00

12”43000

11“220“00

I(P35000

9710“00

9210“008“810008“480“00

8“200“007“740“007“390“00

7“110“00

6“870“00

6“670“00

6“290“00

6000“00

5“780“22

5“600“40

5“450“55

5“320“68

5“120“88

4.961“044841“16

21”250“00

16”050“00

1*75000

1237000

11”44Omo

10”750’00

10”210’00

9“770“009420“00

911000

8“62000*24000

7’940“00

7“68000

7“47000

7“050“00

6“74026

650050

tY31069

6“150“85

6“01

099

5“791.21

5“62

1’38

5“48

1’52

22”970’00

1T42000

I*950“00

1349000

1249000

11“75Owo

11”17000

l&71Wo

KM20“00

Xmo0’00-9480009“07000

89740“00

8“470“00

8’240“00

7“790“21

7“46&54

7“210“79

7W01“00

6“831“17

6“681“32

6“451“55

6“271“736“121“88

24620“00

18”73000

1612(MO

14’560“00

13”50000

12072woo

1211000

11“62OwO

11”21000

1086Owl

1031000988croo9“530“009“240“009“00owo8“520“488“17083Tao1“10

7%81“327“501“507“351“657“101“906.912’096“752“25

26-21000

20”00Owo

1725000

l!Y610“00

14”490“00

13%60“00

13”020“00

125004)0

12-0700)

11”71000

11”12000

10’670“00

10”300“00

1000woo

9“740“26

9“240“76

8“871“!3

a591“41

8351“65

8161“84

8“OO200

7“742“26

7“542467“372“63

15

IS 397 (Part 4) :2003

ANNEX A — Contd.

UCL AND LCL FOR CONTROL CHART ON NUMBER OF DEFECTS PER 100 UNITS

+900 W42 0-65 0“85 1“03 1“21 2W0 2“72 S“41 4“08 473 5“37 6“00 6’62 7“24

000 000 0“00 000 0“00 04M) 0“28 (Y59 092 1“27 163 2“00 2“38 2-761000 040 062 0“82 l@O 1“17 1“95 2“66 3“34 400 464 5“27 5“90 651 712

000 0“00 Ow 0“00 000 005 034 0“66 1“00 1“36 1“73 2“10 P49 2“881500 0“34 (P55 0“72 0089 1“05 1“77 245 solo 9“72 &34 495 5“55 614 673

000 (M)O 0“00 000 0“00 029 055 090 1“28 1“66 2“05 2“45 2“86 3“272000 0“31 050 067 0“82 0“97 1“67 2’32 2“95 3“56 416 475 5“34 5“92 650

0“00 0“00 000 woo 0“03 (Y33 068 1“05 1’44 1“84 2“25 2“66 3“08 W502500 0“29 0“47 0“63 0“78 092 1“60 2“23 2“85 3’45 4’04 462 5“20 5“77 &34

0“00 0“00 0“00 0“02 0“08 040 0’77 1“15 1“55 1“96 2“38 2“8(J 3“23 3“663000 0“27 (Y44 0%0 0“75 0“89 1“55 2“17 2“77 3“37 3“95 452 5“10 5“66 6“22

0“00 000 (rOo 0“05 0“11 0“45 0“83 1“23 1’63 2’05 2“48 2-90 3“34 3“785000 0“23 (P39 0“53 0“67 0“80 1“42 2“02 260 *17 3“73 429

0“00 001485 5“40 5“95

@07 0’13 0“20 (Y58 098 1%0 1“83 2.27 2“71 3“15 3“60 4“05

5+ 6’(J 7.0 ~ 9“0 I&o 12’0 14W 160 lWO Zlvo 290 Wo 390 *O 4%n+10 29”24 32”10 3483 37+6 40”00 44’86 49”50 53”95 58o25 62’43 72”43 81”96 91”12 100”00 108”64

0“00 000 0“00 0“00 000 0“00 000 0“00 0“00 0“00 000 0“00 Ow 0“00 0“00

20 22”43 2475 2&97 29”12 31“21 3Y24 3SP1O 4T83 46”46 WOO 58”54 6tY74 74690“00

82”43 90”000“00 0“00 000 0.00 0“00 000 moo 0“00 0“00 000 000 woo 0“00 0“00

30 19’42 21“49 23°49 25”43 27”32 30”97 34”49 37”91 41”240“00

4449 52”39 60”00 67’40 7464 81’740“00 0%)0 0“00 0“00 0“00 0“00 0“00 0“00 0“00 0“00 0“00 2“60 5“36 8“26

40

50

60

70

80

90

1-00

120

140

160

17”62

0“00

16-39

0“00

15”49@oo

l&78

0“00

14’220“00

19’55

000

18”220“00

17”25Ow

16”49

0“00

15”870“00

21”42

000

20W00“00

18°95000

18-14

0“00

17’490“00

23”23

Ow

2i”7S000

20”620“00

1976

0“00

25°00

0“00

23”420“00

28”43

0“00

2&70000

31”75

000

2*87mo

28”49Ow

27”42

&58

26551“45

25”83

2“17

25”22

2“78

2#253“75

23”49451

2P87W13

34”97

0“00

32-970“00

31”49(Y51

30’34

1“66

29’422-88

38”12

0“00

36”00O@o

34431“57

33”21

2“79

32”233“77

41”21

000

38”971“03

37”322“68

3604

3“96

3YO05“00

4&72 55”98

1“28 *O2

46°21 53”24

3“79 676

w36 51”215“64 8“79

42”93 49”647“07 10”36

41”77 48-378“23 11“63

63-06

6“94

6(P1O990

7000

10”00

668313”17

76”82

13”18

73”4616”54

70-9819”0269”05

20’95

67”5022”50

6621

23”79

22”250“00

21-34

0“00

25’42000

24’42

woo

57”9112’09

56”21

13”79

5*841&16

64”4915”51626817.32

2(Y610“00

2*620“38

-61”2118-79

19”060“00

60”00

20’00

5*97

21”03

18”49

Omo

2000

0“00

19490“51

22’!75

1“05

28”65

3“35

2000

400

2&95

5’05

2614Y86

31’42

458

30”735’27

2962638

2W767“24

3+145“86

33”42

658

32”25

7“75

31”34866

40”81 47’329“19 12”68

40-00 46”43

10”00 13”57

38”69 45”00

11”31 Km

37%8 43”8912”32 1611

3686 42”991Y14 17”01

53”71

l&29

52”7517”25

51-20

188o

5(MJO!20wo

13”75

0“00

13”35

0“00

1T71

000

lr21(POO

15”37

0“00

14”940“00

1425

000

13”71(Y29

16-94

0“00

16”490“00

15”75025

15”17(P83

65’12

24-88

63”37

2663

62”0127”99

22’39

1“61

21*49

251

2(T783“22

2@223“78

18”00

0“00

57”32

22”68

5&0423-96

17”22

078

l&6 11“39

18”66

1’34

16021“98

17502“50

2?496951

2W67“94

3(P61

9“39#032*97

55”00

25’00

61Y9129’09

11”810“19

1Y27(Y73

14711“29

16’121“88

16

IS 397 (Part 4): 2003

OF DEFECTS PER 100 UNITS

ANNEX A — Contd.

UCL AND LCL FOR CONTROL CHART ON NUMBER

7’0 100 12”0 1+0 160 Iwo 20’0 2*O 3*O 3%0 4(PO 4*O

48”23

21”7747”5522”45

46”2223”78

45”252475

180 11”48

052

200 11“20080

12”92

1“0812”611“39

120Z1“98

11“582“42

14’32

1“68lWO

MO

13”372“63

12”903“10

15’71

2“2915”!!62“64

14”693“31

1*2O3“80

17”07. 1975

2“93 42516”71 1935

3’29 4’65

16”00 l&57+00 5“4s

15”48 UPoo*52 600

15”07 17”55

493 6-45

14”74 17”205“26 6“80

14”47 16”90

5’53 7“10

14”24 l&655’76 7“35

13”87 16”24

&13 7“76

13”59 l&936“41 8-07

13”35 15-676-65 8“33

13”16 15-46

6“84 8“54

13”00 1Y297“00 8“71

12”45 1*687°55 932

12”12 14”327“88 9“68

11”90 1408&lo 992

11“73 13”90827 10”10

11”34 1*47

&66 10”53

22’37

5“6321”94

6W6

21”106“90

2M87“52

24”94

7“0624”49

7“51

23”59841

22”939“07

27-49

8“5127”00

Wo

26-059“95

25”3510”65

30%0

10”0029”49

10”51

28-4911”51

27”75

12”25

27-17

12-83

3618 42”25

IY82 17-7535”61 41’6214”39 18”38

34”49 40”3915”51 19”61

33-66 39”49l&34 20”51

54”14

25”8653”42

26”58

52”0028”00

50”9529”05

60”00

30”0059”233077

57”7332”27

56”6233”38

250 100651“35

300 10-241“76

33”02 387816”98 21”22

444925-51

50”14

29”86

55”76

34’24

350 9“93

2-07

400 9-67

2“33

11“242“76

1W973“03

12”54

3“46

13”81

4“1920”008“00

22”419“59

24”80

11“20

32”50 38”22

17”50 21”78

43”87

26”13

“12-243“76

13”504“50

19618“39

22”0010”00

24”3611“64

24”0012”00

26”7113”29

49”493&51

350634”94

450 9“46

2“54

500 9“29

2“71

600 9“00

3“00

10”743“26

1(T553“45

1024

3“76

12”C04“00

11”79

421

11”46

+54

13”24476

13-02

498

19”298“71

19”028“98

21”66

10”3426”3213”68

32”07 37”7517”93 22”25

31’71 37”3518-29 22o65

31”12 36”71

1888 23”29

43”372&63

4X.94

27”06

4225

27”75

48”9431’06

48”4931:51

47”75

32-25

54”49

35”51

54”0036”00

53”22

$6”78

23”6912”31

23”20

12”80

2&oo

14’00

25’48

“1452

21 “37

10-63

20-90

11”10

12:67

5“33

1858

942

18249“76

20’5411’46

22”81

13”19

25s071493

3(v67 3&2119”33 23”79

41”71

28”2947”1732”83

52”6137’39

700 8“783“22

1040

4-0011”21

4“79

12””405“60

12-185“82

12”00

6“00

17”9710”03

17”74

1026

17”5510’45

20.~4

11”76

20”00

12”00

22”50

13”50

22”24

13”76

24”7415’26

24”47

15’53

30”30 35-8119”70 24”19

30”00 35”48

20’00 24”52

41”2728”73

40”92

29”08

467133-29

46”3233”68

52”1237”88

51”71

38’29

800 8“60

3“40

900 8-45

3“55

9-81*19

9“65

435

11”00YOO

I(Y83

5“17

19”79

12”2122”0213”98

2P24

15”76

29’74 35”2020’26 24”80

40”6129”39

46-00

3’+”00

51”36

38’641090 8“32

3“68

9“51*49

10”68

5-3211“856“15

9“05

4“95

10195“81

11”32

6“68

l&90

11”10

19”10

12”90

21”29

1471

23”4616”54

28”87 34”24

21”13 25”76

39”58

30”4244”90

35”10

50”20

39-801500 7“90

4“10

l&51

11“49

20”85

15”1523”00

17”0028”35 33”67

21”65 26”332000 7“64

436

2500 7“474’53

3000 7“344“66

5000 7“044“96

8“77923

8“595“41

8“455“55

9906“10

9“70fY30

ll”QI699

10807“20

10%47’36

10”277“73

18”6813”32

38”9731”03

4*2435”76

49’50

40”50

l&2411-76

18”40

13”60

20”5515”45

22”6817-32

28’00 33”29

22”00 26”7138”5531”45

43’79

36”2149”024!)”98

9“55&45

9“206“80

16’0511“95

18-1913”81

20-3215”68

22-4517”55

27-74 33”0022-26 27”00

38-2431”76

37”51

32”49

43”4636-54

42”6837”32

48”6741”33

47”8542”15

8“125“88

15”5912”41

17”701P30

19”801620

21”9018”10

27”12 32-3222”88 27”68

17

IS 397 (Part 4) :2003

ANNEX A — Conld.

UCL AND LCL FOR CONTROL CHART ON NUMBER OF DEFECTS PER 100 UNITS

z+ 500 60’0 700 800 90”(J 10WO 12(VO 1400 IWO 1800 200@ 25(Yo 300”0 35f% 40(YO

$

]0 117”08 133°48 149”37 16*85 l&J”OO 19*87 223”92 252”25 280”00 307”28 33*16 400”00 464”32 527”48 589”74——

0“00 woo woo 0“00 0“00 5“13 l&08 27”75 40000 52”72 65”84 100”00 13$68 172”52 21026

20 97”43 111.96 12612 140”00 153”64 167”08 193”48 2 t9”37 24*85 270-80 29487 356”07 416”19 475.50 534162“57 804 13”88 20”00 26”36 32-92 46”52 60”63 75”15 90”00 105”13 143”93 183”81 22W50 265”84

30 88”73 10T43 115”83 128”99 141”96 15#77 180000 20$81 22928 253”48 277”46 336”60 394”87 452”47 5095411”27 17-57 2417 31”01 38”04 45”23 60”00 75”19 90”72 106”52 122”54 163-40 205”13 247”53 290”46

40 83”54 96.74 109”69 122-43 135”00 147”43 171”96 19fY12 220”00 243”64 267”08 325”00 382’16 438”74 4948716”46 23”26 30”31 37”57 -45”00 52”57 68”04 83”88 100”00 116”36 132”92 175”00 217-84 261”26 305”13

50 80.00 92”86 10Y5o 117”95 130”25 142”43 166”48 190”20 213”67 236”92 260”00 317”08 373”48 429-37 4848520”00 27”14 34”50 42”05 49”75 57-57 73”52 8!+80 106”33 123”08 140”00 182”92 226”52 270”63 315”15

60 77”39 90”00 102”40 114”64 126’74 138”73 162”43 185”83 208”99 231”96 25477 311”24 367”08 422”46 477”4622”61 3000 37”60 45”36 53”26 61”27 77”57 94”17 111’01 128”04 145”23 188”76 232”92 277”54 322-54

70 75”35 8777 100”00 112”07 124”02 135”86 159”28 182”43 205”36 228”11 250’71 306”69 362”11 417”08 471-7124”65 32”23 40”00 47”93 55”98 64’14 80”72 97”57 114”64 131”89 149’29 193”31 237”89 282”92 328”29

80 73”72 85”98 98’06 110’00 121”82 133”54 156”74 179”69 202-43 225-00 247”43 303”03 358”09 412”75 467”0826”28 34”02 41”94 50”00 58°18 66”46 83-26 10031 117”57 13!kO0 152”57 196”97 241”91 287”25 332’92

90 72”36 84”49 96”46 108”28 120-00 131”62 15464 177”42 200”00 222”43 24472 300”00 354”77 40SP16 463”2527’64 35”51 43”54 51”72 60”00 68”38 85”36 102”58 120”00 137”57 155”28 200”00 245”23 290”84 336”75

100 71’21 83-24 95”10 106”83 118”46 131% 152”86 175”50 197’95 220”25 242”43 297”43 351”96 406”12 460”0028”79 3676 W90 53”17 61-54 7@O0 87”14 104”50 122”05 13975 157’57 202”57 246”04 293’88 340”00

120 69”36 81’21 92”91 104”49 115“98 127”39 150”o0 ‘172”40 194”64 216”74 238”73 293”30 347”43 401”23 454°7730”64 38”79 4F09 55”51 6402 72”61 90”00 107”60 125”36 143”26 161”27 20670 252:57 298”77 345”23

140 67”93 79”64 91*2I 102+68 114”05 125”35 147”77 17VO0 192”07 21402 235’86 290”09 343”92 397”43 450”7132”07 40’36 48”79 57”32 65”95 74”65 92-23 110-00 127”93 145”98 16414 209”91 256”08 302”57 349”29

160 66”77 78”37 89”84 101”21 112”50 123”72 145”98 168’06 190”00 211”82 233”54 287”50 341”08 39#37 447”4333.23 41”63 50”16 58”79 67”50 76”28 9402 111“94 130”00 148”18 16&46 212”50 258”92 305”63 352”57

180 65”81 77”32 88”71 100”00 111”21 122”36 144”49 166”46 188”28 21000 231”62 285”36 338”73 391”83 444”7234.19 42”68 51“29 60”00 68”79 77”64 95”51 113”54 131”72 150”00 168”38 21464 261”27 308”17 355”28

200 65’00 76”43 87”75 98”97 110”12 121-21 143.24 165.10 186.83 208.46 23VO0 283.54 336.74 389.69 442.4335.00 43.57 52’25 61.03 69.83 78.79 9676 11#90 133.17 151.54 170.00 216’46 263.26 310.31 357.57

250 63”42 7v70 85.87 96.97 108.OO118.97 140078 -162.45 18400 205.46 22@83 280.00 332.86 385.50 437.9536.58 45”30 54.13 6Y03 72.00 81”03 99.22 117.55 13&O0 15*54 173.17 22@00 267’14 31450 362.05

300 62.25 73”42 84.49 95.49 106.43 117.32 138.97 160.49 181.91 203.24 224’49 277.39 330.00 382.40 4346437.75 46.58 55.51 64”51 73.57 82.69 101.03 119.51 13809 15&76 175”51 222.61 270.00 317.60 365”36

350 61.34 72.42 83.42 94.34 105”21 116”04 137.57 158.97 180.28 201.51 222’68 275.35 327.77 380.00 432.0738’66 47”58 56.58 65.66 74.79 83.96 102.43 ]21.03 139’72 158.49 177.32 22465 272.23 320.00 367.93

400 60.61 71.62 82.55 93.42 104.23 115.00 136’43 157.75 178.97 200”12 221.21 273.72 325.98 378”06 4300039.39 48”38 57.45 66”58 75.77 85.00 103.57 122.25 141.03 159.88 178.79 226.28 274.02 321.94 370”00

450 6000 70.95 81.83 92”65 103.42 114.14 135.49 156.73 177.89 198.97 220.00 272.36 324.49 376.46 428.2840.00 49.05 58.17 67.35 76.58 85.86 10451 123.27 142.11 161.03 180’00 227.64 275.51 323.54 37172

500 59.49 70.39 81.22 92”00 102.73 113.42 134.70 155.87 176.97 198.00 218.97 271.21 323.24 375.1O 426.8340’51 49.61 58.78 68.00 77.27 86.58 105.30 12413 143.03 162.00 181.03 228.79 276.76 324.90 373.17

600 58.66 69.49 80.25 90.95 101”62 112’25 133.42 154.49 175.49 196.43 217.32 269.36 321.21 372.91 424.4941.34 50.51 59.75 69.05 78”38 87.75 10.6.58 125.51 144.51 163.57 182’68 230”64 27&79 327.09 375”51

700 58.02? 68.78 79.49 90.14 100.76 111.34 132.42 153.42 174.34 195.21 216”04 267.93 319%4 371.21 422.6841.98 51”22 60”51 69.86 79.24 88.66 107.58 126.58 145”66 16*79 183.96 232.07 280.36 328.79 377.32

800 57.50 68.22 78.87 89.49 100.06 110.61 131”62 152”55 173.42 194”23 215.00 266”77 318.37 369.84 421.214~.50 51.78 61.13 70”51 79.94 89.39 108.38 127.45 146.58 165077 185.00 233.23 281.63 330.16 378.79

18

IS 397 (Part 4): 2003

ANNEX A — Concluded

UCL AND LCL FOR CONTROL CHART ON NUMBER OF DEFECTS PER 100 UNITS

d + 50@0 604)0 7000 8W80 WOO 100 1200 14&0 160-0 IWO 200”0 2500 3000 3W0 40W0n4

900 57”07 67”75 78”37 8&94 99”49 llO”oo 130”95 151”83 172”65 193”42 214”14 265-81 317”32 368-71 4W”O042-93 52”25 61”63 71-06 80’51 90”00 109”05 128”17 147’35 166”58 185”86 234”19 282”68 331”29 380’00

1000 56-71 67-35 77”94 88”49 99”00 109”49 13@39 151”22 172”09 192”73 213”42 265”00 316”43 367”75 413”9743”29 52”65 62W6 71“51 81-00 90’5[ 109”61 128’78 148”00 167”27 188”58 235”00 283”57 332”25 38] ’03

1500 5748 6600 76°48 86”93 97”35 107”75 128”49 149”17 169”80 190”39 218”95 262”25 313”42 364’49 415”4944-52 54”00 63”52 73”07 82”65 92-25 111“51 13083 150”20 169”61 189”05 237”75 28658 335’51 38451

2000 5474 65”20 ‘75”61 86”00 96”35 106”71 127’35 147”94 168”49 189”00 209-49 26061 311“62 362”55 413”4245”26 5480 6*39 74”00 83”64 93”29 112”65 132”06 151“51 171”oo 190”51 239”39 28838 337”45 386”58

2500 54”24 6465 7Y02 85”37 95”69 10600 12657 147”10 167”59 188”05 208”49 25949 31039 361”22 412”0045-76 5Y35 6498 74”63 8+31 9*OO 113”43 132-30 152”41 171”95 191”51 240”51 289”61 33878 38800

3000 53”87 6424 7*58 8490 S5”20 105”48 126”00 146”48 16693 187”35 207”75 258”66 30949 360”25 410”9546-13 55”76 .65”42 75”10 arao 9&52 11*OO 133”52 153”07 172”65 192”25 241-34 290’51 339”75 389’05

5000 53.00 63”29 73s55 83”79 94”02 10#24 12*65 145”02 16S37 185”69 2of3@3 256”71 307”35 357”94 408”4947”00 56”71 6645 76%!1 85”98 95”76 11Y35 13498 15*63 174”31 19400 243”29 292”65 342”06 391”51

19

IS 397 (Part 4) :2003 ,.-

ANNEX B

(Foreword)

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 sod 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, Malviya Nagar, New Delhi 110017)

In personal capacity (20/1, Krishna Nagar, Saf2arjung Enclave,New Delhi 110029)

BIS Directorate General

Representative(s)

PROFS. P. MUKHEJUEE(Chairman)

SHJUS. N. JHASHRIA. V. KJUSHNAN(Alternate)

DR NAWNKAPURSHRIVIPULGUPTA(Alternate)

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

DR ASHOKKUMAR

SHJUC. S. V. NARENDRA

SHRJK. VIJAYAMMA

DR S. D. SHAIUMADR A. K. SRIVASTAVA(Alternate)

DR B. DAS

PROFS. CHAKRABORTV

PROFS. R. MOHANPROFARVINDSETH(Alternate)

SHRJ Y. K. BHATSHRJG. W. DATSV(Ahernafe)

DR S. K. AGARWALSHRJD. Ctmrcwaorrw (Alternate)

SHRIA. SANJEEVARAOSHJUC, DESIGAN(Alternate)

SHRIS. K. KIMOTHISHruP. N. SRIKANTH(Alternate)

SHRIS. KUMARSHIUSHANTISARUP(Alternate)

PROFM. C. AGRAWAL

PROFA, N. NANKANA

SHIUD. R. SEN

SHRIP. K. GAMBHIF+Director & Head (MSD)[Representing Director General (Ex-o@cio)]

Member SecretarySHRI LALITKUMARMEHTA

Deputy Director (MSD), BIS

Basic Statistical Methods Subcommittee, MSD 3:1

KolkataUniversity,Kolkata PROF S. P. MUKHERJEE(Convener)

Laser Science and Technology Centre, DRDO, New Delhi DR ASHOK KUMAR

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

(Continued on page21 )

20

IS 397 (Part 4): 2003

(Conrirruedfrompage 20)

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

Impersonal capacity (B-109, Ma!viya Nagar, New Delhi l10017)

In personal capacity (20/1, Krishna Nagar, Safdaq”ungEnclave,New Delhi [10029)

Representative(s)

DR B. DASDRA. LAisnu(,41fernare)

PROFS. CHAKRABORTV

PROFS. R. MOHAN

SHRI Y. K. BHAT

Ssw G. W. DATSV(Aherrrale)

DR S. K. AGARWAL

.SHRI S. K. KIMOTHI

SHRI SHANTISARVP

DR A. INORAYAN

PROF M. C. AGRAWAL

PROF A. N. NANKANA

-SHFUD. R. SEN

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

In personal capacity (B-J 09, Malviya Nagar, New Delhi 110017) PROF A. N. NANKANA(Convener)

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

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

Standardization, Testing and Quality Certification Directorate, SHRI S. K. KiMOTHI

New Delhi

Tata Engineering and Locomotive Co Ltd, Pune SHRI SHANTISARUP

In personal capacity (20/[, Krishna Nagar, Sajiiarjung Enclave, SHIU D. R. SENNew Delhi 110029)

21

Bureau of Indian Standards

BIS is a statutory institution established under the Bureau of Indian Standards Act, 1986 to promoteharmonious development of the activities of standardization, marking and quality certification of goodsand attending to connected matters .in the country.

Copyright

BIS has the copyright of all its publications. No part of these publications may be reproduced in any form [without the prior permission in writing of BIS. This does not preclude the free use, in the course ofimplementing the standard, of necessary details, such as symbols and sizes, type or grade designations. )Enquiries relating to copyright be addressed to the Director (Publications), BES.

Review of Indian Standards

Amendments are issued to standards as the need arises on the basis of comments. Standards are also reviewedperiodically; a standard along with amendments is reaffirmed when such review indicates that no changes areneeded; if the review indicates that changes are needed, it is taken up for revision. Users of “Indian Standardsshould ascertain that they are in possession of the latest amendments or edition by referring to the latest issue of‘BIS Catalogue’ and ‘Standards: Monthly Additions’.

This Indian Standard has been developed from Doc : No. MSD 3 (220).

Amendments Issued Since Publication

Amend No. Date of Issue Text Affected

BUREAU OF INDIAN STANDARDS

Headquarters :

Manak Bhavan, 9 13ahadurShah Zafar Marg, New Delhi 110002 Telegrams : ManaksansthaTelephones :23230131,23233375,2323 9402 (Common to all offices)

Regional Offices : Telephone

Central :

Eastern :

Northern :

Southern :

Western :

Manak Bhavan, 9 Bahadur Shah Zafar Marg

{

23237617NEW DELHI 110002 23233841

1/14 C.I.T. Scheme VII M, V. I. P. Road, Kankurgachi

{

23378499,23378561KOLKATA 700054 23378626,23379120

SCO 335-336, Sector 34-A, CHANDIGARH 160022

{

603843609285

C.I.T. Campus, IV Cross Road, CHENNAI 600113

{

22541216,2254144222542519,22542315

Manakalaya, E9 MIDC, Marol, Andheri (East) ~2832 9295,28327858MUMBAI 400093 128327891,28327892

Branches : AHMEDABAD. BANGALORE. BHOPAL. BHUBANESHWAR. COIMBATORE. FARIDABAD.GHAZIABAD. GUWAHATI. HYDERABAD. JAIPUR. KANPUR. LUCKNOW. NAGPUR.NALAGARH. PATNA. PUNE. RAJKOT. THIRUVANANTHAPURAM. VISAKHAPATNAM.

-.—.- .— —._._

Printed at Prabhat Offset Press, New Delhi-2

—