Distribution-free precedence schemes with a generalized runs-rule for monitoring unknown location

Abstract

Nonparametric statistical process monitoring schemes are robust alternatives to traditional parametric process monitoring schemes, especially when the assumption of normality is invalid or when we do not have enough information about the underlying process distribution. In this paper, we propose to improve the well-known precedence scheme using the 2-of-(h + 1) supplementary runs-rules (where $h$ is a nonzero positive integer). The in-control and out-of-control performances of the proposed control schemes are thoroughly investigated using both Markov chain and simulation based approaches. We find that the proposed schemes outperform their competitors in many cases. A real-life example is given to illustrate the design and implementation of the proposed schemes.

Keywords:

• Nonparametric scheme
• precedence control scheme
• generalized 2-of-(h + 1) runs-rules schemes
• Markov chain approach
• simulations

Acknowledgments

The authors thank Mr. Sandile Shongwe from the University of Pretoria for his helpful comments and suggestions. They also thank the University of South Africa for the support.