On monitoring the process mean of autocorrelated observations with measurement errors using the w‐of‐w runs‐rules scheme. (21st January 2020)

• Record Type: Journal Article
• Authors: Shongwe, Sandile C.; Malela‐Majika, Jean‐Claude; Castagliola, Philippe
• Is Part Of: Quality and reliability engineering international. Volume 36:Number 3(2020)
• Page Start: 1144
• Page End: 1160
• Publication Date: 2020-01-21
• Subjects: first‐order autoregressive model -- Markov chain -- measurement errors -- multiple measurements sampling strategy -- runs‐rules -- skip sampling strategy -- steady state -- zero state; Reliability (Engineering) -- Periodicals; Quality control -- Periodicals; High technology -- Periodicals; 620.00452
• DOI: 10.1002/qre.2622
• Languages: English
• ISSNs: 0748-8017

Abstract

Abstract: Runs‐rules have been widely used since the 1950s in industrial and nonindustrial process monitoring applications to improve the performance of basic and other traditional monitoring schemes. However, none of the studies on runs‐rules have accounted for a process with a combined effect of measurement errors and autocorrelation. Hence, in this paper, the use of the w‐of‐w runs‐rules to improve the performance of the Shewhart X ¯ scheme using an additive model with a constant variance and a first‐order autoregressive model is proposed. To reduce the combined negative effect of measurement errors and autocorrelation, we implement a sampling strategy based on rational subgroups in which (a) multiple measurements per item are taken (instead of a standard single measurement) and (b) non‐neighboring observations are gathered. Moreover, the latter sampling strategy is incorporated into the values of probability elements of a Markov chain matrix which is used to derive some closed‐form expressions for the zero‐ and steady‐state run‐length distribution. The main finding of this study is that, with respect to some overall performance measures, the proposed scheme outperforms the existing Shewhart X ¯ scheme by a significant margin. A real‐life example is used to illustrate the practical implementation of the proposed scheme.