unit iii control charts

8/13/2019 UNIT III Control Charts

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N.PandiarajanAssociate Professor/EEE

SSNCE


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Statistics is defined as the science that deals

with the collection, tabulation, analysis,interpretation, and presentation of

quantitative data.

Prepared By N.Pandiarajan Associate Professor/EEESSNCE 2


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A measure of central tendency of adistribution is a numerical value that

describes the central position of the data orhow the data tend to build up in the center.

There are three measures in common use inquality

(1) The Average,(2) The Median, and(3) The Mode.



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Find the average of 12,13,14,15,16

= 12+13+14+15+16/5 = 70/5 = 14



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Median, Md, is defined as the value thatdivides a series of ordered observations so

that the number of items above it is equal tothe number below it. When the number in the series is odd, the

median is the midpoint of the values,provided the data are ordered.

Thus the ordered set of numbers 3, 4, 5, 6, 8,8, and 10 has a median of 6 .



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When the number in the series is even, themedian is the average of the two middle

numbers. Thus, the ordered set of numbers 3, 4, 5, 6 ,8, and 8 has a median that is the average of5 and 6,which is (5 + 6)/2 = 5.5.



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The average is the most commonly-usedmeasure of central tendency.

It is used when the distribution issymmetrical or not appreciably skewed tothe right or left.When measures of dispersion, controlcharts, and so on, are to be computed basedon the average.



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The median becomes an effective measure ofthe central tendency when the distribution ispositively (to the right) or negatively (to the

left) skewed. The median is used when an exact midpoint ofa distribution is desired.

A control chart based on the median is user-friendly and excellent for monitoring quality.

The mode is used when a quick andapproximate measure of the central tendencyis desired.



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1. RANGE

2. STANDARD DEVIATION



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The range, which for a series of numbers isthe difference between the largest and

smallest values of observations.Symbolically, it is represented by theequation



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Determine the range of the series1.83, 1.91 .

1.78 , 1.80, 1.83, 1.85, 1.87

R = X h - X I = 1.91 - 1.78 = 0.13



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In symbolic terms, the standard deviation isrepresented by the equation



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The smaller the value of the standarddeviation, the better the quality, because the

distribution is more closely compactedaround the central value. The primary advantage of the range is in

providing a knowledge of the total spread ofthe data.

The standard deviation is used when amoreprecise measure is desired.



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Sample is smaller collection of data. Example Class average marks of TQM

It is Population is larger collection of data. Example Class average marks of TQM in

both A & B sections It is called as population mean . the symbol is (mu).



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The true population value may never beknown; therefore, the symbol and aresometimes used to indicate estimate of.

A sample frequency distribution is representedby a histogram, whereas a populationfrequency distribution is represented by asmooth curve.

To some extent, the sample represents the realworld and the population represents themathematical world.



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The primary objective in selecting a sample isto learn something about the population thatwill aid in making some type of decision.

The sample selected must be of such a naturethat it tends to resemble or represent thepopulation.

How successfully the sample represents thepopulation is a function of the size of thesample, chance, the sampling method, andwhether or not the conditions change.



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Although there are as many differentpopulations as there are conditions, they canbe described by a few general types.

One type of population that is quite common iscalled the normal curve, or Gaussiandistribution.

The normal curve is a symmetrical, uni modal,bell-shaped distribution with the mean,median, and mode having the same value.



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The normal distribution is fully defined bythe population mean and population

standard deviation. Also, as seen by Figures in last slides, thesetwo parameters are independent.In other words, a change in one parameterhas no effect on the other.



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A relationship exists between the standard deviation and thearea under the normal curve, is shown in Figure in next slide.

The figure shows that in a normal distribution, 68.26% of theitems are included between plus one sigma the limits of andminus one sigma,

95.46% of the items are included between the limits plus two sigma and minus two sigma and

99.73% of the items are included between plus three sigma andminus three sigma

One hundred percent of the items are included between the limi ts+00 and -00.

These percentages hold true regardless of the shape of thenormal curve.

The fact that 99:73% of the items are included between 3Sigma (6 Sigma) is the basis for variable control charts.



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No two objects are ever made exactly alike.The variation concept is a law of naturebecause no two natural items in anycategory are the same.When variations are very small, it mayappear that items are identical.

Three categories of variations are1. Within-piece variation2. Piece-to-piece variation3. Time-to-time variation



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The first source of variation is the equipment.This source includes tool wear, machinevibration, work holding-device positioning,and hydraulic and electrical fluctuations.The second source of variation is the material.Such material characteristics as tensile

strength, ductility, thickness, porosity, andmoisture content can be expected to contributeto the overall variation



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A third source of variation is theenvironment.

Temperature, light, radiation, particlesize, pressure, and humidity all cancontribute to variation in the product.

A fourth source is the operator.The operator's physical and emotionalwell-being, lack of training may contributeto the variation.



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A run chart is a very simple technique foranalyzing the process of variations.A picture is worth a thousand words.Plotting the data points is a very effectivewayof finding out the variations.



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The particular run chart shown in Figure in lastslide is referred to as an X bar chart and is used torecord the variation in the average value ofsamples.Other charts, such as the R chart (range) orp chart (proportion) would have also served forexplanation purposes.The horizontal X- axis is labeled "SubgroupNumber," which identifies a particular sampleconsisting of a fixed number of observations.



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Each small solid diamond represents theaverage value within a subgroup.

Thus, subgroup number 5 consists of. say,four observations, 3.46, 3.49, 3.45, and 3.44,and their average is 3.46 kg.This value is the one posted on the chart forsubgroup number 5.



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Averages are used on control charts rather thanindividual observations because average

values will indicate a change in variationmuch faster.Also, with two or more observations in asample, a measure of the dispersion can beobtained for a particular subgroup.



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The solid line in the center of the chart canhave three different interpretations, depending

on the available data. First, it can be the average of the plotted points, which in the case of an X chart is theaverage of the averages or "X- double bar.



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The control chart method for variables is ameans of visualizing the variations that occur

in the central tendency and dispersion of a setof observations. It is a graphical record of the quality of a

particular characteristic.It shows whether or not the process is in astable state by adding statistically determinedcontrol limits to the run chart.



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Figure in next slide, is the run chart of

previous slides with the control limits

added.

They are the two dashed outer lines and are

called the upper and lower control limits.



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The control limits are then established at 3 Sigma from the central line.

Recall, from the discussion on the normalcurve, that the number of items between+ 3Sigma and 3 Sigma equals 99.73%.

Therefore, it is expected that more than 997times out of 1,000 values of that subgroup willfall between the upper and lower limits.

unit iii control charts

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