overview of statistical quality control

7/24/2019 Overview of statistical quality control

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Text Book: Statistical Quality Control; a modern introducti

by Douglas C Montgomery


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If a product is to meet customer expectations, it should be produced by a stable

process (low variability)

Statistical Process Control (SPC) is a powerful collection of tools, useful in

achieving process stability and improving process capability through reducingvariability

Seven powerful statistical tools (the Magnificent seven)

-Histogram or stem-and-leaf plot

-Check sheet

-Pareto chart

-Cause and effect diagram

-Defect concentration diagrams

-Scatter diagrams

-Control charts (Shewhart control charts/ most technically sophisticated tool)

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Chance causes and assignable causes of quality variations

In any process, a certain amount of natural variability exists.

This is the cumulative effect of many small, unavoidable causes

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Chance causes (Background noise)

Mainly due to improperly controlled machines, operator errors or defectiveraw material

Assignable causes


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The objective of Statistical Process Control is to quickly detect the assignable

causes of process shifts so that investigation of process and corrective actionscan be taken before many nonconforming items are produced.

(The major objective of SPC is to eliminate variability in the process)

Basic Principles

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General model for a control chart

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When L = 3, then they are called three-sigma control limits

Example: Consider a process with a quality characteristic whose mean is 1.5and sample standard deviation is 0.0671. Determine 3-sigma control limits


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Choice of control limitsType I error a point falling beyond the control limits when there is no assignable

cause present (False alarm)

Type II error a point falling between the control limits when the process is

really out of control


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Two limits on control charts Three sigma limits for the outer limits/ actual limits

Two sigma limits for the inner limits/ warning limits

Warning limits increase the sensitivity of the control charts

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Example: Consider a process with a

quality characteristic whose mean is 1.5and sample standard deviation is 0.0671.

Determine warning limits


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Variable Control Charts

For quality characteristics that can be numerically measured

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x Control of process average quality level is done with control charts

Variability of the process is monitored by control charts for standard deviation (scontrol charts) or control charts for range (R control charts)


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If x is normally distributed with mean and standard deviation , then is

normally distributed with mean and standard deviationx

nx

Process standard deviation can be estimated by

WhereR=xmax-xmin and

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d

R

m

RRRR

m

.....

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Suppose samples of size m are taken randomly,

Then sample mean

m

xxxx

m.....

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Example 6.1 of Text

(Page 231)

Set up the andR contro

the data given

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x


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Control limits forRcharts

LCL = 0

CL= 0.32521

UCL= 0.68749

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Control limits for charts

LCL = 1.31795

CL= 1.5056

UCL= 1.69325

x

These are called trial control limits


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Trial control limits are used to determine whether the process has been

in control during the time in which the data were collected. This can be

done by plotting the sample means and range in the developed control

charts

If all the points lie inside the limits, then the process has been in control inthe past and trial control limits (now become actual limits) can be used for

the phase II applications where the future production is monitored

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If for any point lies outside the limits, should be investigated for assignablecauses. If any assignable cause is found, it should be eliminated and the limitsshould be re-calculated by excluding the corresponding points. This should be

repeated until reliable control limits are obtained.

Then new data should be collected and compared with these revised limits .

This should be repeated until reliable control limits are obtained.


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Exercise 6.23 of text book Page 276

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Given the following data of 20 samples, each with size 4.


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Instead of numerical representation, product classification is done as eitherdefective or non-defective (Conforming and non-conforming)

These are called attributes

Some examples: number of malfunctioning semi conductor chips, number of

errors made in filling a particular form etc

Four types of control charts ;

-pcharts (for fraction nonconforming)

- npcharts (for number of defects/ nonconforming items)

- ccharts (for nonconformities)

- charts (for nonconformities per unit)

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Control Charts for attributes


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The fraction nonconforming is defined as the ratio of the number of

nonconforming items to the total number of items in that population

In some cases, the true fraction non conforming pin the production process isknown or a standard value is given

If it is not known/ standard value is not given, then it should be estimated as

follows

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Where, is the fraction nonconforming in the ith sample

nis the size of each sample

mis the number of samples and it should be at least 20-25

Then,

Fraction nonconforming charts (p charts)


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Example 7.1 Page 292

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30 samples were selectedand sample size is 50


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npcharts for number of nonconforming

items

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Use the same data as in example 7.1 (Page 292) and developthe npcontrol charts


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Control charts for nonconformities ccharts

Sometimes it is possible for some items to have number of defects but stillclassified as a conforming item

Ex: Number of functional defects in an electronics device, Number of errors

on a document

Control charts are developed for the total number of nonconformities in aunit or average number of nonconformities per unit

In some cases, a standard value for number of nonconformities c is given orotherwise, it can be estimated as the observed average number of nonconformities in a preliminary sample

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Example 7.3 (Page 310- text book)

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Determine the trial control limits for number of nonconformities and revise thelimits if necessary, assuming that any out of control point has an assignable cause


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Control charts for average number of

nonconformities per unit ucharts

nis the sample size


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Example 7.4 (Page 315- text book)

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Determine the trial control limits fornumber of nonconformities and revise thelimits if necessary, assuming that any outof control point has an assignable cause

overview of statistical quality control

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