A double-integral equation for the average run length of a multivariate exponentially weighted moving average control chart

Steven E. Rigdon

Statistics & Probability Letters, 1995, vol. 24, issue 4, 365-373

Abstract: The multivariate exponentially weighted moving average control chart is a control charting scheme that uses weighted averages of previously observed random vectors. This scheme, which is defined using Z0 = [mu]0, Zi = rXi + (1 - r)Zi - 1 (i [greater-or-equal, slanted] 1), where X1, X2, ... denote the vector-valued output of a process, can be used to detect shifts in the process mean vector more quickly, on the average, than the usual Hotelling T2 chart. We prove that for the special case [mu] = 0, [Sigma] = I, the average run length (ARL) depends on the initial value z0 for the MEWMA statistic only through its magnitude and the angle it makes with the mean vector. This theorem is then used to derive an integral equation of the ARL. This integral equation involves a double integral, and the unknown function is a function of two variables. ARLs can be obtained by approximating the solution to the integral equation. Previously, simulation was needed to approximate the ARLs.

Keywords: Multivariate; quality; control; Hotelling; T2; chart; Iterated; kernels (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (4)

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