Applied Statistics and Probability for Engineers

602 CHAPTER 16 STATISTICAL QUALITY CONTROL

experienced operator or engineer. This information allows the operator to implement

a change in the process that will improve its performance.

5. Control charts provide information about process capability.The control chart
   provides information about the value of important process parameters and their sta-
   bility over time. This allows an estimate of process capability to be made. This in-
   formation is of tremendous use to product and process designers.
   Control charts are among the most effective management control tools, and they are as
   important as cost controls and material controls. Modern computer technology has made it
   easy to implement control charts in any type of process, because data collection and analysis
   can be performed on a microcomputer or a local area network terminal in realtime, online at
   the work center.

16-4.2 Design of a Control Chart

To illustrate these ideas, we give a simplified example of a control chart. In manufacturing au-

tomobile engine piston rings, the inside diameter of the rings is a critical quality characteris-

tic. The process mean inside ring diameter is 74 millimeters, and it is known that the standard

deviation of ring diameter is 0.01 millimeters. A control chart for average ring diameter is

shown in Fig. 16-3. Every hour a random sample of five rings is taken, the average ring di-

ameter of the sample (say ) is computed, and is plotted on the chart. Because this control

chart utilizes the sample mean to monitor the process mean, it is usually called an con-

trol chart. Note that all the points fall within the control limits, so the chart indicates that the

process is in statistical control.

Consider how the control limits were determined. The process average is 74 millimeters,

and the process standard deviation is 0.01 millimeters. Now if samples of size n5 are

taken, the standard deviation of the sample average is

Therefore, if the process is in control with a mean diameter of 74 millimeters, by using

the central limit theorem to assume that is approximately normally distributed, we

would expect approximately 100(1)% of the sample mean diameters to fall between

74 z 2 (0.0045) and 74z 2 (0.0045). As discussed above, we customarily choose the

X

X

X



1 n



0.01

15

0.0045

X

X X

x x

1

73.9820

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

73.9865

73.9910

73.9955

74.0000

74.0045

74.0090

74.0135

74.0180

Sample number

LCL = 73.9865

UCL = 74.0135

Average ring diameter

x

Figure 16-3 con-

trol chart for piston

ring diameter.

X

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