Monitoring of Linear Profiles Using Linear Mixed Model in the Presence of Measurement Errors

Abstract

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.

Keywords

• profile monitoring
• measurement errors
• linear mixed model
• MCUSUM
• MEWMA
• Hotelling’s <i>T</i>²