Chapter 16.3, Problem 19E

The accompanying table gives sample means and standard deviations, each based on n = 6 observations of the refractive index of fiber-optic cable. Construct a control chart, and comment on its appearance. [Hint: $\Sigma {\bar{x}}_i=2317.07$ and Σs_i = 30.34.]

Day	$\bar{x}$	s
1	95.47	1.3
2	97.38	0.88
3	96.85	1.43
4	96.64	1.59
5	96.87	1.52
6	96.52	1.27
7	96.08	1.16
8	96.48	0.79
9	96.63	1.48
10	96.5	0.8
11	97.22	1.42
12	96.55	1.65
13	97.02	1.28
14	95.55	1.14
15	96.29	1.37
16	96.8	1.4
17	96.01	1.58
18	95.39	0.98
19	96.58	1.21
20	96.43	0.75
21	97.06	1.34
22	98.34	1.6
23	96.42	1.22
24	95.99	1.18

12. Refer to Exercise 11. An assignable cause was found for the unusually high sample average refractive index on day 22. Recompute control limits after deleting the data from this day. What do you conclude?

19. Calculate control limits for an S chart from the refractive index data of Exercise 11. Does the process appear to be in control with respect to variability? Why or why not?