One-Sided and Two-Sided w - of - w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations

S. C. Shongwe, J.-C. Malela-Majika and E. M. Rapoo

Journal of Probability and Statistics, 2019, vol. 2019, 1-20

Abstract:

The one-sided and two-sided Shewhart w-of-w standard and improved runs-rules monitoring schemes to monitor the mean of normally distributed observations from independent and identically distributed (iid) samples are investigated from an overall performance perspective, i.e., the expected weighted run-length ( EWRL ), for every possible positive integer value of w . The main objective of this work is to use the Markov chain methodology to formulate a theoretical unified approach of designing and evaluating Shewhart w-of-w standard and improved runs-rules for one-sided and two-sided schemes in both the zero-state and steady-state modes. Consequently, the main findings of this paper are as follows: (i) the zero-state and steady-state ARL and initial probability vectors of some of the one-sided and two-sided Shewhart w-of-w standard and improved runs-rules schemes are theoretically similar in design; however, their empirical performances are different and (ii) unlike previous studies that use ARL only, we base our recommendations using the zero-state and steady-state EWRL metrics and we observe that the steady-state improved runs-rules schemes tend to yield better performance than the other considered competing schemes, separately, for one-sided and two-sided schemes. Finally, the zero-state and steady-state unified approach run-length equations derived here can easily be used to evaluate other monitoring schemes based on a variety of parametric and nonparametric distributions.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:6187060

DOI: 10.1155/2019/6187060

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