One-sided type schemes are known to be more appropriate for monitoring a process when the direction of a potential mean shift can be anticipated. Furthermore, if the magnitude of the potential mean shift is unknown, it is desired to design a control chart to perform well over a wide range of shifts instead of only optimizing its performance in monitoring a particular mean shift level. The one-sided adaptive truncated exponentially weighted moving average (ATEWMA) X scheme recommended in this paper is a control chart that combines a Shewhart X scheme and a new one-sided EWMA X scheme together in a smooth way for rapidly detecting the upward (or downward) mean shifts. The basic idea of the recommended one-sided ATEWMA X scheme is to truncate the observations (i.e., the sample means X) first, and then to dynamically weight the past observations according to a suitable function of the current prediction error. This helps to improve the sensitivity of the proposed one-sided ATEWMA X scheme for detecting both small and

In the application of control charts, most of the research in profile monitoring is based on accurate measurements. Measurement errors, however, often exist in many manufacturing and service environments. In this paper, we apply linear mixed models in the presence of measurement errors in fixed effects. We discuss three modified multivariate charts, namely Hotelling’s T2, multivariate exponential weighted moving average (MEWMA) control chart, and multivariate cumulative sum (MCUSUM) control chart. Performance comparisons are made in terms of the average run length (ARL) and average extra quadratic loss (AEQL). Finally, a real data example on healthcare expenditures is used to illustrate the implementation of the proposed monitoring schemes.

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