Consider an EMWA control chart. The target value for the process is μ₀= 50 and σ = 2. Use Table 15-11.

(a) If the sample size is n = 1, would you prefer an EWMA chart with λ = 0.1 and L = 2.81 or λ = 0.5 and L = 3.07 to detect a shift in the process mean to μ = 52 on average? Why?

(b) If the sample size is increased to n = 4, which chart in part (a) do you prefer? Why?

(c) If an EWMA chart with λ = 0.1 and L = 2.81 is used, what sample size is needed to detect a shift to μ = 52 in approximately three samples on average?

Table 15-11

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2 = 0.1 2 = 0.5 Shift in Mean (multiple of ) L= 3.07 L= 2.81 500 500 0.25 255 106 0.5 88.8 31.3 15.9 0.75 35.9 1 17.5 10.3 6.53 1.5 6.09 3.63 4.36 3 1.93 2.87