One-sided precedence monitoring schemes for unknown shift sizes using generalized 2-of-(h+1) and w-of-w improved runs-rules

Abstract

Parametric monitoring schemes are expected to perform better than their nonparametric counterparts when the assumption of a specific form of a distribution such as the normal is met. In practice, such assumption is often violated. Consequently, the performance of parametric schemes deteriorates considerably. To solve this problem, more efficient and flexible monitoring schemes based on nonparametric tests are recommended. In this paper, efficient and robust one-sided monitoring schemes are developed using generalized {1-of-1 or 2-of-(h + 1)} and {1-of-1 or w-of-w} improved runs-rules (IRR) without any distributional assumption in the zero- and steady-states modes. Moreover, the zero- and steady-states run-length properties of the resulting one-sided IRR schemes are formulated and empirically evaluated using the Markov chain technique. Comparisons with other well-known one-sided Shewhart-type nonparametric schemes (e.g., basic precedence scheme and precedence scheme with standard runs-rules) indicate that the proposed schemes have a better performance. Real data are used to demonstrate the design and implementation of the one-sided improved runs-rules precedence schemes. Finally, a discussion on the two-sided IRR precedence schemes is also provided.

Keywords:

• Distribution-free
• order statistic
• precedence statistic
• runs-rules
• Case U
• Markov chain
• Phase I
• Phase II

Acknowledgements

The authors would like to convey their gratitude to the two reviewers as well as the editorial team for taking their valuable time to evaluate and give us constructive suggestions to improve the manuscript.