A new cumulative sum control chart for monitoring the process mean using varied L ranked set sampling

Abstract

Recently, a varied L ranked set sampling (VLRSS) scheme has been introduced in the literature for estimating the population mean. The VLRSS scheme is a cost-efficient alternative to the classical ranked-set sampling (RSS) and median RSS (MRSS) schemes. In this paper, we construct a new cumulative sum (CUSUM) control chart for efficiently monitoring the process mean using VLRSS, named the CUSUM-VLRSS chart. The CUSUM-VLRSS chart encompasses the existing CUSUM charts based on RSS and MRSS schemes, named the CUSUM-RSS and CUSUM-MRSS charts. We use extensive Monte Carlo simulations to compute the run length characteristics of the proposed CUSUM chart. It is shown that the CUSUM-VLRSS chart is able to perform uniformly better than the CUSUM-RSS and CUSUM-MRSS charts when detecting different kinds of shift in the process mean. A similar trend is observed when the proposed CUSUM chart is constructed under imperfect rankings. A real data-set is also used to explain the implementation of the CUSUM-VLRSS chart.

Keywords:

• Average run length
• cumulative sum
• control chart
• perfect and imperfect rankings
• statistical process control

Acknowledgements

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

Notes

No potential conflict of interest was reported by the authors.