New cumulative sum control charts for monitoring process variability

ABSTRACT

In this article, we propose new cumulative sum (CUSUM) control charts using the ordered ranked set sampling (RSS) and ordered double RSS schemes, with the perfect and imperfect rankings, for monitoring the variability of a normally distributed process. The run length characteristics of the proposed CUSUM charts are computed using the Monte Carlo simulations. The proposed CUSUM charts are compared in terms of the average and standard deviation of run lengths with their existing competitor CUSUM charts based on simple random sampling. It turns out that the proposed CUSUM charts with the perfect and imperfect rankings are more sensitive than the existing CUSUM charts based on the sample range and standard deviation. A similar trend is present when these CUSUM charts are compared with the fast initial response features. An example is also used to demonstrate the implementation and working of the proposed CUSUM charts.

KEYWORDS:

• Average run length
• control charts
• CUSUM
• ordered ranked set sampling
• ordered double ranked set sampling
• statistical process control

Acknowledgments

The authors are thankful to the associate editor and the two referees for some useful comments that led to an improved version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.