Identifying the time of step change in process parameter for Maxwell distribution

Abstract

Due to the quick identification of the root causes for an out-of-control process, the estimation of exact time of a process change would be helpful thing for the process improvement. In contrast to the typical normal assumption, this study realizes that a process may follow a skewed Maxwell distribution. In this paper, using maximum likelihood estimation, a considerably efficient change point model is proposed for $V$ control chart which underlying distribution is Maxwell distribution. The required chart statistics are calculated with its distributional properties. The proposed method is used when $V$ control chart signals a change in a process parameter. The proposed method, when used with $V$ control chart would be helpful for process engineers both in controlling and identifying a permanent step change in a process scale parameter. An illustrative example is given to understand the use of the proposed method.

KEYWORDS:

• Change point estimation
• V control chart
• Maxwell distribution
• Maximum likelihood estimation (MLE)
• average run length

Acknowledgement

The authors would like to thank the Editor and anonymous referee for their comments on an earlier version of this manuscript that lead to an improved final version. The first author would like to acknowledge the support by Department of Science and Technology (DST), Government of India, for award of Inspire Fellowship under Grant number DST/INSPIRE Fellowship/2016/IF/60410.

Disclosure statement

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