Reliability and sensitivity comparisons and average run lengths of CUSUM scale chart

ABSTRACT

The cumulative sum (CUSUM) control chart is considered one of the best methods used to detect process shifts. It has been observed that there are certain studies which focused on the analysis and description of the distribution of run-length of CUSUM charts under shifts in process variance. Keeping this in view, an efficient and accurate algorithm based on the distribution of run length of CUSUM chart for examining the variance changes of normal process is developed in this research. Since one of the measures for evaluating the performance of control chart is average run length (ARL), therefore it is considered for comparing the reliability and sensitivity of CUSUM scale chart. Simulation studies have been carried out to generate the data through which both in-control and out-of-control ARLs are calculated by varying sample size, decision limits and reference values. The efficiency of the proposed control chart is shown in terms of ARLs. A numerical example is given to illustrate the practical application of the proposed scheme.

KEYWORDS:

• Control charts
• CUSUM
• Average Run Lengths (ARL)
• In-Control Average Run Length (ARL₀) and out-of control Average Run Length (ARL₁)

Acknowledgements

The authors are deeply thankful to editor and reviewers for their valuable suggestions to improve the quality of this manuscript. This article was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah. The author, Muhammad Aslam, therefore, acknowledge with thanks DSR technical and financial support.