Statistical Quality Control. Chapter 17. To accompany Quantitative Analysis for Management , Tenth Edition , by Render, Stair, and Hanna Power Point slides created by Jeff Heyl. © 2009 PrenticeHall, Inc. . Define the quality of a product or service
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Chapter 17
To accompanyQuantitative Analysis for Management, Tenth Edition,by Render, Stair, and Hanna
Power Point slides created by Jeff Heyl
© 2009 PrenticeHall, Inc.
Define the quality of a product or service
After completing this chapter, students will be able to:
17.1 Introduction
17.2 Defining Quality and TQM
17.3 Statistical Process Control
17.4 Control Charts for Variables
17.5 Control Charts for Attributes
Table 17.1
Target
Lower control limit
Statistical Process ControlFigure 17.1
One plot out above. Investigate for cause.
Normal behavior
One plot out below. Investigate for cause.
Target
Lower control limit
Upper control limit
Target
Lower control limit
Statistical Process ControlFigure 17.1
Two plots near upper control Investigate for cause.
Two plots near lower control. Investigate for cause.
Run of 5 above central line. Investigate for cause.
Run of 5 below central line. Investigate for cause.
Target
Lower control limit
Statistical Process ControlFigure 17.1
Erratic behavior. Investigate.
Trends in either direction 5 plots. Investigate for cause of progressive change.
The xchart (mean) and Rchart (range) are the control charts used for processes that are measured in continuous units
We often estimate and with the average of all sample means ( )
The Central Limit TheoremFigure 17.2 shows three possible population distributions, each with their own mean () and standard deviation ( )
Beta
Uniform
= (mean)
= (mean)
= (mean)
x = S.D.
x = S.D.
x = S.D.
99.7% of all x
fall within ±3x
95.5% of all x fall within ±2x

–3x

–2x

–1x

x =
(mean)

+1x

+2x

+3x
The Central Limit TheoremSampling Distribution of Sample Means (Always Normal)
Figure 17.2
= mean of the sample means
z = number of normal standard deviations
= standard deviation of the sampling distribution of the sample means =
Setting the xChart LimitsA large production lot of boxes of cornflakes is sampled every hour
= average of the samples
A2 = value found in Table 17.2
= mean of the sample means
Box Filling Example 16.01 + 0.144
16.154
16.01 – (0.577)(0.25)
16.01 – 0.144
15.866
Super Cola ExampleWe have determined upper and lower control limits for the process average
UCLR = upper control chart limit for the range
LCLR = lower control chart limit for the range
D4 and D3 = values from Table 17.2
Setting Range Chart Limits 112.042 pounds
(0)(53 pounds)
0
Range ExampleCollect 20 to 25 samples of n = 4 or n = 5 from a stable process and compute the mean and range of each
Compute the overall means ( and ), set appropriate control limits, usually at 99.7% level and calculate the preliminary upper and lower control limits. If process not currently stable, use the desired mean, m, instead of to calculate limits.
Graph the sample means and ranges on their respective control charts and determine whether they fall outside the acceptable limits
Five Steps to Follow in Using x and RChartsInvestigate points or patterns that indicate the process is out of control. Try to assign causes for the variation and then resume the process.
Collect additional samples and, if necessary, revalidate the control limits using the new data
= mean proportion or fraction defective in the sample
z = number of standard deviations
= standard deviation of the sampling distribution which is estimated by where n is the size of each sample
pChartsPercentage can’t be negative
0.12 –
0.11 –
0.10 –
0.09 –
0.08 –
0.07 –
0.06 –
0.05 –
0.04 –
0.03 –
0.02 –
0.01 –
0.00 –
UCLp = 0.10
Fraction Defective
LCLp = 0.00

1

2

3

4

5

6

7

8

9

10

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20
Sample Number
ARCO pChart ExampleFigure 17.3
Program 17.1A
In the previous example we counted the number of defective records entered in the database