Applied Statistics and Probability for Engineers

16-7 PROCESS CAPABILITY 619

(a) Using all the data, compute trial control limits for individ-

ual observations and moving-range charts. Construct

the control chart and plot the data. Determine whether

the process is in statistical control. If not, assume assigna-

ble causes can be found to eliminate these samples and

revisethe control limits.

(b) Estimate the process mean and standard deviation for the

in-control process.

16-12. The viscosity of a chemical intermediate is meas-

ured every hour. Twenty samples each of size n1, are in the

following table.

Sample Diameter

1 9.94

2 9.93

3 10.09

4 9.98

5 10.11

6 9.99

7 10.11

8 9.84

9 9.82

10 10.38

11 9.99

12 10.41

13 10.36

Sample Diameter

14 9.99

15 10.12

16 9.81

17 9.73

18 10.14

19 9.96

20 10.06

21 10.11

22 9.95

23 9.92

24 10.09

25 9.85

Sample Viscosity

1 495

2 491

3 501

4 501

5 512

6 540

7 492

8 504

9 542

10 508

11 493

12 507

13 503

14 475

15 497

16 499

17 468

18 486

19 511

20 487

(b) Estimate the process mean and standard deviation for the

in-control process.

16-11. The diameter of holes is measured in consecutive

order by an automatic sensor. The results of measuring 25

holes are in the following table.

Wafer x Wafer x

1 16.8 16 15.4

2 14.9 17 14.3

3 18.3 18 16.1

4 16.5 19 15.8

5 17.1 20 15.9

6 17.4 21 15.2

7 15.9 22 16.7

8 14.4 23 15.2

9 15.0 24 14.7

10 15.7 25 17.9

11 17.1 26 14.8

12 15.9 27 17.0

13 16.4 28 16.2

14 15.8 29 15.6

15 15.4 30 16.3

16-7 PROCESS CAPABILITY

It is usually necessary to obtain some information about the process capability,that is, the

performance of the process when it is operating in control. Two graphical tools, the toler-

ance chart(or tier chart) and the histogram,are helpful in assessing process capability.

(a) Using all the data, compute trial control limits for individ-

ual observations and moving-range charts. Determine

whether the process is in statistical control. If not, assume

assignable causes can be found to eliminate these samples

and revise the control limits.

(b) Estimate the process mean and standard deviation for the

in-control process.

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