Ameliorating the diagnostic power of combined shewhart-memory-type control chart strategies for mean

Abstract

A great deal of research in statistical process control (SPC) involves the integration of different ideas to achieve the optimal detection of anomalies in the location parameter of a process. Likewise, the prime rationale of the combined (Shewhart-Memory-type) strategies is to promptly detect the shift of any size: small, moderate or large. An effort, along the same lines, is made to detect shifts in the mean of a normally distributed process. The usual difference estimator of the process mean instead of the sample mean is employed in the Mixed EWMA-Crosier CUSUM Combined Shewhart Mixed EWMA-CUSUM and Combined Shewhart Mixed EWMA-Crosier CUSUM charts to make their upgraded versions. This enhances the sensitivity of these charts against any shift size. The performance of the charts is appraised and compared with some notable charts of the same ilk, with reference to the average run length (ARL), relative average run length, extra quadratic loss and performance comparison index. An illustrative example is also provided.

KEYWORDS:

• Memory-type charts
• combined Shewhart-CUSUM
• Crosier’s CUSUM
• statistical process monitoring

Disclosure statement

No potential conflict of interest was reported by the author(s).

Authors’ Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Aqeel ur Rehman, Javid Shabbir and Tahir Munir. The first draft of the manuscript was written by Aqeel ur Rehman. Illustrative example is handled by Shabbir Ahmad and Muhamma Riaz. Finally, all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.