Linear profiles monitoring in the presence of nonnormal random errors

Chung I. Li, Tzong Ru Tsai

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Profile monitoring is a technique to test the stability of the relationship between a response variable and explanatory variables over time. The most relevant linear profile monitoring methods have been constructed using the normality assumption. However, the normality assumption could be violated in many quality control applications. In this study, we consider a situation in which the random errors in a linear profile model follow a skew-normal distribution. The skew-normal distribution is a generalized version of the normal distribution. A new Shewhart-type chart and exponentially weighted moving average (EWMA) chart, named the ShewhartR and EWMAR charts, respectively, are constructed based on residuals to monitor the parameters of linear profile model. The simulation results show that the multivariate EWMA chart is sensitive to the normality assumption and that the proposed ShewhartR and EWMAR charts have good ability to detect big and small-to-moderate process shifts, respectively. An example using photo mask techniques in semiconductor manufacturing is provided to illustrate the applications of the ShewhartR and EWMAR charts.

Original languageEnglish
Pages (from-to)2579-2592
Number of pages14
JournalQuality and Reliability Engineering International
Issue number8
Publication statusPublished - 2019 Dec 1

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


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