Consider the revised XÌ control chart in Exercise 15-8 with ÏÌ = 0.669, UCL = 7.443, LCL = 5.125, and n = 3. Suppose that

Consider the revised X̅ control chart in Exercise 15-8 with σ̂ = 0.669, UCL = 7.443, LCL = 5.125, and n = 3. Suppose that the mean shifts to 5.5.

(a) What is the probability that this shift is detected on the next sample?

(b) What is the ARL after the shift?

Exercise 15-8

The copper content of a plating bath is measured three times per day, and the results are reported in ppm. The xÌ… and r values for 25 days are shown in the following table:

Day Day 1.21 1 5.45 14 7.01 1.45 0.95 1.37 5.39 15 5.83 3 6.85 1.43 16 6.35 1.04 6.74 1.29 17 6.05 0.83 5 5.83 1.35 18 7.11 1.35 7.22 1.09 0.88 19 7.32 6.39 0.92 20 5.90 1.22 8. 6.50 1.13 21 5.50 0.98 1.25 22 9. 7.15 6.32 1.21 6.55 0.76 10 5.92 1.05 23 11 6.45 0.98 24 5.90 1.20 5.95 1.19 12 5.38 1.36 25 13 6.03 0.83