Suppose that the mean and standard deviation of a subgroup average are = 30 and /

Suppose that the mean and standard deviation of a subgroup average are

μ = 30 and σ/

√

n = 8, respectively, and consider the cumulative sum control chart with d = .5, B = 5. If the first eight subgroup averages are 29, 33, 35, 42, 36, 44, 43, 45 then the successive values of Yj = X j − 30 − 4 = X j − 34 are Y1 = −5, Y2 = −1, Y3 = 1, Y4 = 8, Y5 = 2, Y6 = 10, Y7 = 9, Y8 = 11 Therefore, S1 = max{−5, 0} = 0 S2 = max{−1, 0} = 0 S3 = max{1, 0} = 1 S4 = max{9, 0} = 9 S5 = max{11, 0} = 11 S6 = max{21, 0} = 21 S7 = max{30, 0} = 30 S8 = max{41, 0} = 41 Since the control limit is Bσ/
√
n = 5(8) = 40 the cumulative sum chart would declare that the mean has increased after observing the eighth subgroup average.