In the case of known u and o, what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .005?Consider the control chart based on control limits , + 2.81 or/v. a. What is the ARL when the process is in control? b. What is the ARL when n = 4 and the process mean has shifted to p = Up + 0? c. How do the values of parts (a) and (b) compare to the corresponding values for a 3-sigma chart?When S" is the sample variance of a normal random sample, $ has a chi-squared distribution with n - 1 di, so (# - 1)572 This suggests that an alternative chart for controlling process variation involves plotting the sample variances and using the control limits XML = 998 from which Xmeg Xmal =.998 A - I 1 - 1 Construct the corresponding chart for the data of Exercise 11. [Hint: The lower- and upper-tailed chi-squared critical values for 5 of are .210 and 20.515, respectively.] Reference exercise 11 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: Ex, = 2317.07 and Es, = 30.34.]and Day Day 95.47 1.30 13 97.02 1.28 97.38 88 14 WN 95.55 1.14 96.85 1.43 15 96.29 1.37 96.64 1.59 16 96.80 1.40 96.87 1.52 17 96.01 1.58 96.52 1.27 18 95.39 98 96.08 1.16 19 96.58 1.21 96.48 .79 20 96.43 .75 96.63 1.48 21 97.06 1.34 10 96.50 .80 22 98.34 1.60 11 97.22 1.42 23 96.42 1.22 12 96.55 1.65 24 95.99 1.18 Day Day 95.47 1.30 13 97.02 1.28 97.38 88 14 95.55 1.14 96.85 1.43 15 96.29 1.37 GUAWN- 96.64 1.59 16 96.80 1.40 96.87 1.52 17 96.01 1.58 96.52 1.27 18 95.39 .98 96.08 1.16 19 96.58 1.21 96.48 .79 20 96.43 75 96.63 1.48 21 97.06 1.34 10 96.50 .80 22 98.34 1.60 11 97.22 1.42 23 96.42 1.22 12 96.55 1.65 24 95.99 1.18