Quality and Reliability Engineering International

A robust control chart for simple linear profiles in two‐stage processes

Journal Article

Abstract In many manufacturing systems, the final product is the result of several dependent stages. In particular, in multistage processes, the quality characteristics of downstream stages are influenced by those in the earlier stages (upstream). This property is referred to as the cascade property, which, if disregarded in process monitoring, may bring about misleading results for the subsequent fault diagnosis. Considering the relationships among consecutive stages of the process, the U statistic is the most widely used method for monitoring multistage processes. Using this method, our paper deals with monitoring a two‐stage process where quality characteristics are represented as simple linear profiles. To guard against the detrimental effect of contaminated data in the phase I of statistical process control, two well‐known robust M‐estimators, including Huber's and bi‐square, are employed for estimation of the process parameters. Under different degrees of autocorrelation across stages of the process and also for different contamination rates, the performances of the proposed methods are compared with that of the conventional least‐square method. From the viewpoint of estimation performance measures, including unbiasedness and efficiency, along with the capability of the control chart in identifying the true source of variation, extensive simulation results reveal that robust estimators outperform the traditional method in a two‐stage process. Meanwhile, it should be noted when there is contamination only in the first stage of the process, the least‐square method performs slightly better.

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