Consider a CUSUM with h = 5 and k = 1 / 2. Samples are taken every two hours from the process. The target value for the process is μ₀= 50 and σ = 2. Use Table 15-10.

Table 15-10

(a) If the sample size is n = 1, how many samples would be required to detect a shift in the process mean to μ = 51 on average?

(b) How does increasing the sample size to n = 4 affect the average run length to detect the shift to μ = 51 that you determined in part (a)?

h = 5 Shift in Mean (multiple of Og) h = 4 168 465 139 0.25 74.2 0.50 26.6 38 0.75 13.3 17 1.00 8.38 10.4 4.75 1.50 5.75 3.34 2.00 4.01 2.50 2.62 3.11 2.57 3.00 2.19 4.00 1.71 2.01