Question

A company manufacturing oil seals wants to establish x and R control charts on the process. There are 25 preliminary samples of size 5 on the internal diameter of the seal. The summary data (in mm) are as follows:

6.1.

A manufacturer of components for automobile transmissions wants to use control charts to monitor a process producing a shaft. The resulting data from 20 samples of 4 shaft diameters that have been measured are:

20

∑ xi = 10.275, i=1

20

∑ Ri = 1.012 i=1

Subgroup x R

1 8.3 2

2 8.1 3

3 7.9 1

4 6.3 5

5 8.5 3

6 7.5 4

7 8.0 3

8 7.4 2

9 6.4 2

10 7.5 4

Subgroup x R

11 8.8 3

12 9.1 5

13 5.9 3

14 9.0 6

15 6.4 3

16 7.3 3

17 5.3 2

18 7.6 4

19 8.1 3

20 8.0 2

(a) Find the control limits that should be used on the x and R control charts.

the 20 preliminary samples plot in

25

∑ xi = 1,253.75, i=1

25

∑ Ri = 14.08 i=1

(b) Plot the preliminary data from the first 20 samples on the control charts that you set up in part (a). Is this process in statistical control?

6.6. Components used in a cellular telephone are manu- factured with nominal dimension of 0.3 mm and lower and upper specification limits of 0.295 mm and 0.305 mm respectively. The x and R control charts for this process are based on subgroups of size 3 and they exhibit statistical control, with the center line on the x chart at 0.3015 mm and the cen- ter line on the R chart at 0.00154 mm.

(a) Estimate the mean and standard deviation of this process.

(b) Suppose that parts below the lower specifica- tion limits can be reworked, but parts above the upper specification limit must be scrapped. Estimate the proportion of scrap and rework produced by this process.

(c) Suppose that the mean of this process can be reset by fairly simple adjustments. What value of the process mean would you recommend? Estimate the proportion of scrap and rework produced by the process at this new mean.

6.7. The data shown in Table 6E.2 are x and R values for 24 samples of size n = 5 taken from a process produc- ing bearings. The measurements are made on the

(a) Find the control limits that should be used on the x and R control charts.

(b) Assume that the 25 preliminary samples plot in control on both charts. Estimate the process mean and standard deviation.

Answer 1

6.1)

6.6)

6.7)