The effect of measurement errors on the adaptive EWMA X¯ chart

Abstract

The AEWMA chart is an Adaptive EWMA (Exponentially Weighted Moving Average)–type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. Its performance has been studied under the assumption that there is no measurement error in the quality characteristic. In this paper, we investigate the performance of the AEWMA chart when measurement errors exist using a linearly covariate error model. The presence of measurement errors with a linearly increasing measurement error standard deviation is also investigated. It turns out that, with the existence of measurement errors, the efficiency of the AEWMA chart can be strongly affected, and the negative effect can be compensated by taking multiple measurements at each sample point. Comparisons with the classical EWMA scheme confirm the superiority of the AEWMA scheme in detecting a wide range of shifts even in the presence of measurement errors. An example is provided to illustrate the use of the AEWMA chart with measurement errors.