Side-sensitive synthetic and runs-rules charts for monitoring AR(1) processes with skipping sampling strategies

Sandile Charles Shongwe, Jean-Claude Malela-Majika, Philippe Castagliola and Thapelo Molahloe

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 17, 4248-4269

Abstract: Side-sensitive Shewhart-type designs have been shown in a variety of process monitoring contexts to increase the performance of traditional charts when the process observations are independent and identically distributed. In this paper, we investigate whether this is also the case when the observations are from an autocorrelated process. Thus, we propose a synthetic chart and a 2-of-(H + 1) runs-rules chart using a side-sensitive design approach and a skipping sampling strategy for monitoring correlated observations from a stationary first-order autoregressive process. The resulting schemes have an improved zero-state and steady-state OOC performance as compared to the currently available non-side-sensitive Shewhart-type synthetic, runs-rules and the basic X¯ monitoring schemes. A Markov chain technique is used to derive closed-form average run-length expressions for the proposed schemes and overall performance measures are used to evaluate the efficiency of these monitoring schemes.

Date: 2020
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DOI: 10.1080/03610926.2019.1596284

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