A note on an average run length calculation for the EWMA and other charts

Abstract

In the last decade numerous papers have appeared in the statistical process monitoring literature where the in‐control and out‐of‐control average run length (ARL) profiles of the exponentially weighted moving average chart, and some of its variants, have been approximated under the assumption that the signal event can be represented by a sequence of independent Bernoulli random variables. In this short note we show that these approximations, presented in the literature as being exact, can be very inaccurate when compared with the true ARL values. Moreover, the use of these poor ARL approximations has led to many flawed articles, which should be either corrected or retracted.

A misuse of the EWMA‐type statistic in acceptance sampling applications

“…The methodology upon which these methods have been based is flawed in that the autocorrelation in the EWMA statistics and the resulting inertial effects were overlooked. Similar errors have been made in the statistical process monitoring literature as discussed by Haq and Woodall 26 …”

“…Similar errors have been made in the statistical process monitoring literature as discussed by Haq and Woodall. 26…”

A critique of the use of modified and moving average‐based EWMA control charts

“…Recently, Haq and Woodall 13 showed that the ARL approximations considered by Khan et al 6 . to justify the use of the mEWMA chart in comparison with the classical EWMA chart were seriously flawed because their ARL calculations were based on the false assumption that successive values of the EWMA and mEWMA statistics were independent over time.…”

“…The mEWMA chart triggers an out-of-control signal at the time 𝑡 when 𝐶 𝑡 > ℎ 2 or 𝐶 𝑡 < −ℎ 2 for indicating an upward or a downward shift in the process mean of 𝑍 𝑡 , respectively. Recently, Haq and Woodall 13 showed that the ARL approximations considered by Khan et al 6 to justify the use of the mEWMA chart in comparison with the classical EWMA chart were seriously flawed because their ARL calculations were based on the false assumption that successive values of the EWMA and mEWMA statistics were independent over time.…”

A study on inspection schemes in optimal design of control charts for deteriorating processes

“…We investigate both univariate and multivariate cases regarding the first category. See Khakifirooz et al 10 and Haq and Woodall 11 for more discussion.…”