15- statistical quality control (1)

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15 Statistical Quality Control15-1 Quality Improvement & Statistics

15-1.1 Statistical quality control

15-1.2 Statistical process control15-2 Introduction to Control Charts

15-2.1 Basic principles

15-2.2 Design of a control chart

15-2.3 Rational subgroups

15-2.4 Analysis of patterns on control

charts15-3 X-bar& Ror SControl Charts

15-4 Control Chart for Individual

Measurements

15-5 Process Capability

15-6 Attribute Control Charts

15-6.1 P chart (Control chart for

proportions)15-6.2 U chart ( control chart for defects

per unit)

15-7 Control Chart Performance

15-8 Time-Weighted Charts

15-8.1 Cumulative sum control chart

18-8.2 Exponentially-weighted movingaverage control chart

15-9 Other SPC Problem-solving Tools

15-10 Implementing SPC

CHAPTER OUTLINE


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John Wiley & Sons, Inc. Applied Statistics and Probability for Engineers, by Montgomery and Runger.

Learning Objectives for Chapter 15

After careful study of this chapter, you should be able to do the

following:1. Understand the role of statistical tools in quality improvement.

2. Understand the different types of variability, rational subgroups, and how acontrol chart is used to detect assignable causes.

3. Understand the general form of a Shewhart control chart and how to applyzone rules (such as the Western Electric rules) and pattern analysis to detectassignable causes.

4. Construct and interpret control charts for variables such asX-bar, R, S, andindividuals charts.

5. Construct and interpret control charts for attributes such as Pand Ucharts.

6. Calculate and interpret process capability ratios.

7. Calculate the ARL performance for a Shewhart control chart.8. Construct and interpret a cumulative sum and exponentially-weighted

moving average control chart.

9. Use other statistical process control problem-solving tools.

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15-1: Quality Improvement and Statistics

Definitions of Quality

Qualitymeans fitness for use

- quality of design

- quality of conformance

Qualityis inversely proportional to

variability.

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15-1: Quality Improvement and Statistics

Quality Improvement

Quality improvementis the reduction of

variability in processes and products.

Alternatively, quali ty improvementis also

seen as waste reduction.

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15-1.2: Statistical Process Control

Statistical process controlis a

collection of tools that when usedtogether can result in process stability

and variance reduction

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15-1.2: Statistical Process Control

The seven major toolsare

1) Histogram

2) Pareto Chart

4) Cause and Effect Diagram

5) Defect Concentration Diagram

6) Control Chart7) Scatter Diagram

8) Check Sheet

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7/82 John Wiley & Sons, Inc. Applied Statistics and Probability for Engineers, by Montgomery and Runger.

15-2: Introduction to Control Charts

A process that is operating with onlychance causes of var iationpresent is said

to be in statistical control. A process that is operating in the presence

of assignable causesis said to be out of

control. The eventual goal of SPC is the eliminationof var iabi l i tyin the process.

15-2.1 Basic Principles

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A typical control chart has control limits set at values

such that if the process is in control, nearly all points

will lie within the upper control limit (UCL) and the

lower control limit (LCL).

Figure 15-1A typical control chart.


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Figure 15-2Processimprovement using the

control chart.


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where

k= distance of the control limit from the center linew= mean of some sample statistic, W.

w= standard deviation of some statistic, W.


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Important uses of the control chart

1. Most processes do not operate in a state of statistical

control

2. Consequently, the routine and attentive use of control

charts will identify assignable causes. If these causes

can be eliminated from the process, variability will be

reduced and the process will be improved3. The control chart only detects assignable causes.

Management, operator, and engineering action will be

necessary to eliminate the assignable causes.


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Types of control charts

Variables Control Charts

These charts are applied to data that follow acontinuous distribution.

Attributes Control Charts

These charts are applied to data that follow adiscrete distribution.


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Popularity of control charts

1) Control charts are a proven technique for improving

productivity.2) Control charts are effective in defect prevention.

3) Control charts prevent unnecessary process adjustment.

4) Control charts provide diagnostic information.

5) Control charts provide information about process

capability.


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15-2.2 Design of a Control Chart

Suppose we have a process that we assume the true

process mean is = 74 and the process standard

deviation is = 0.01. Samples of size 5 are takengiving a standard deviation of the sample average,

is

0045.05

01.0

nx


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Control limits can be set at 3 standarddeviations from the mean in both directions.

3-Sigma Control Limits

UCL = 74 + 3(0.0045) = 74.0135

CL= 74

LCL = 74 - 3(0.0045) = 73.9865


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Figure 15-3 X-barcontrol chart for piston ring diameter.

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Choosing the control limits is equivalent to

setting up the critical region for hypothesistesting

H0: = 74H1: 74


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15-2.3 Rational Subgrouping


Subgroups or samples should be selected

so that if assignable causes are present, thechance for differencesbetweensubgroups

will be maximized, while the chance for

differences due to these assignable causes

withina subgroup will be minimized.

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15-2.3 Rational Subgrouping


Constructing Rational Subgroups

Select consecutive units of production.

Provides a snapshot of the process. Good at detecting process shifts.

Select a random sample over the entire sampling

interval.

Good at detecting if a mean has shifted

out-of-control and then back in-control.

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15-2.4 Analysis of Patterns on Control Charts


Look for runs - this is a sequence of

observations of the same type (all above thecenter line, or all below the center line)

Runs of say 8 observations or more could

indicate an out-of-control situation.

Run up: a series of observations are increasing Run down: a series of observations are decreasing

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Figure 15-4 X-bar control chart.21





Figure 15-5 AnX-barchart with a cyclic pattern.

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Figure 15-6 (a) Variability with the cyclic pattern. (b) Variability with the cyclic pattern

eliminated. 23


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Western Electric Handbook Rules

A process is considered out of control if any of the

following occur:1)One point plots outside the 3-sigma control limits.

2)Two out of three consecutive points plot beyond the 2-sigma warning limits.

3)Four out of five consecutive points plot at a distance of1-sigma or beyond from the center line.

4)Eight consecutive points plot on one side of the centerline.

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Figure 15-7 The Western Electric zone rules. 25


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15-3: X-barand Ror SControl Charts

3-sigma control limits:

The grand mean:

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The average range:

An unbiased estimator of :

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Control Chart (from ):

RChart:

x R

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3-sigma control limits for S:

An unbiased estimator of :

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S Chart:

Control Chart (from ):x S

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Example 15-1

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Example 15-1

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Example 15-1

Figure 15-8 and Rcontrol

charts for vane opening.X

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Example 15-1

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b d l h


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Example 15-1

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3 b d S C l Ch


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Example 15-1

Figure 15-9The Scontrol chart for vane opening.

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15 3 X b d R S C l Ch


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Example 15-1

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15 3 X b d R S C l Ch


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Example 15-1

Figure 15-10

The X-bar

and Rcontrol charts

for vane opening.

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15 4 C t l Ch t f I di id l M t


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15-4: Control Charts for Individual Measurements

What if you could not get a sample size greater than 1(n =1)? Examples include

Automated inspection and measurement technologyis used, and every unit manufactured is analyzed.

The production rate is very slow, and it isinconvenient to allow samples sizes of N > 1 toaccumulate before analysis

Repeat measurements on the process differ onlybecause of laboratory or analysis error, as in manychemical processes.

The individual control charts are useful for samples of

sizes n = 1. 40



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The moving range(MR) is defined as theabsolute difference between two successive

observations:MRi= |xi- xi-1|

which will indicate possible shifts orchanges in the process from one observationto the next.

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Individuals Control Chart

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Interpretation of the Charts X Charts can be interpreted similar toX-barcharts. MR charts cannot be

interpreted the same asX-bar or R charts.

Since the MR chart plots data that are correlated with one another, then

looking for patterns on the chart does not make sense.

MR chart cannot really supply useful information about process variability. More emphasis should be placed on interpretation of the X chart.

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15 5 P C bilit


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15-5: Process Capability

Process capabilityrefers to the performance ofthe process when it is operating in control.

Two graphical tools are helpful in assessing

process capability: Tolerance chart(or tier chart)

Histogram

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15 5 Process Capability


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Tolerance Chart

Figure 16-12 Tolerance diagram of

vane openings.

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15 5: Process Capability


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Histogram

Figure 15-13 Histogram for vane openings.46



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Process Capability Ratio

PCRk

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Figure 15-14 Process Fallout and

the process capability ratio(PCR).

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Example 15-3

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Figure 15-15 Mean of a six-sigma process shifts by 1.5 standard deviations.

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15 6: Attribute Control Charts


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15-6: Attribute Control Charts

15-6.1 PChart (Control Chart for Proportions)

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Example 15-4

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Example 15-4

Figure 15-16 Pchart for a ceramic substrate.53



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Example 15-4

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15-6.2 UChart (Control Chart for Defects per Unit)

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Example 15-5

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Example 15-5

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Example 15-5

Figure 15-17 Uchart of defects per unit on printed circuit boards.58

15-7: Control Chart Performance


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15 7: Control Chart Performance

Average Run Length

The average run length(ARL) is a very important

way of determining the appropriate sample size

and sampling frequency. Letp= probability that any point exceeds the

control limits. Then,

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Figure 15-18 Process mean shift of 2.

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15-8: Time-Weighted Charts


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15 8: Time Weighted Charts

The cusum chartincorporates all information inthe sequence of sample values by plotting thecumulative sumsof the deviations of the sample

values from a target value. If 0is the target for the process mean, is the

average of the jth sample, then the cumulativesum control chart is formed by plotting the

quantity

jx

i

jji XS

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15-8.1 Cumulative Sum Control Chart

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Figure 15-19 Plot of the

cumulative sum for the

concentration data, Table15-7.

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Figure 15-20 The cumulative sum control chart. (a) The V-mask and scaling. (b) The cumulative

sum control chart in operation.65



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CUSUM Control Chart

15-8.1 Cumulative Sum Control Chart

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Example 15-6

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g

Example 15-6

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g

Example 15-6

Figure 15-21 The CUSUM

status chart for Example

15-6.

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g

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g

15-8.2 Exponential Weighted Moving Average

Control Chart

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g


Control Chart

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g


Control Chart

Figure 15-22 EWMAs with =0.8 and =0.2 show a compromise between a smooth curve

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g

EWMA Control Chart


Control Chart

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Example 15-7

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Control Chart

Figure 15-23 EWMA control chart for the Chemical Process Concentration Data from

Minitab.77

15-9: Other SPC Problem-Solving Tools


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Pareto Diagram

Figure 15-24 Pareto

diagram for printed circuit

board defects.

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Cause-and-effect Diagram

Figure 15-25 Cause-and-effect diagram for the printed circuit board flow solder

process.

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Defect Concentration Diagram

Figure 15-26 Defect concentration diagram for a printed circuit board.

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15-10: Implementing SPC


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Strategic Management of Quality

Demings 14 points

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Important Terms & Concepts of Chapter 15


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ARL

Assignable causes

Attributes control charts

Average run length

C chart

Cause-and-effect diagram

Center lineChance causes

Control chart

Control limits

Cumulative sum control

chart

Defect concentration

diagram

Defects-per-unit chart

Demings 14 points

Exponentially-weighted

moving average

control chart (EWMA)

False alarm

Fraction-defective control

chart

Implementing SPC

Individuals control chart

(Xchart)

Moving range

NP chart

P chart

Pareto diagram

PCR

PCRk

Problem-solving tools

Process capability

Process capability ratio

Quality control

RchartRational subgroup

Run rule

Schart

Shewhart control chart

Six-sigma process

Specification limits

15- statistical quality control (1)

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