Statistical Details for Weighted Moving Average Charts

Control Limits for UWMA Charts

Control limits for UWMA charts are computed for each subgroup i as follows:

LCLi =

UCLi =

where:

w is the span parameter (number of terms in moving average)

ni is the sample size of the ith subgroup

k is the number of standard deviations

is the weighted average of the subgroup means

is the estimated process standard deviation

Control Limits for EWMA Charts

Control limits for EWMA charts are computed as follows:

LCL =

UCL =

where:

r is the EWMA weight parameter (0 < r ≤ 1)

xij is the jth measurement in the ith subgroup, with j = 1, 2, 3,..., ni

ni is the sample size of the ith subgroup

k is the number of standard deviations

is the weighted average of the subgroup means

is the estimated process standard deviation

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