One‐sided runs‐rules schemes to monitor autocorrelated time series data using a first‐order autoregressive model with skip sampling strategies

Sandile Charles Shongwe · Jean‐Claude Malela‐Majika · Thapelo Molahloe

25 citations0/0 files storedQuality and Reliability Engineering International

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

Abstract In some industrial or health‐related processes, it makes more practical sense to monitor either an increase only or a decrease only in the quality characteristic of interest. Consequently, in this paper, we propose four one‐sided Shewhart charts supplemented with runs‐rules to monitor the mean of autocorrelated normally distributed samples using a stationary first‐order autoregressive model. To counteract the negative effect of autocorrelation, we implement a sampling strategy which involves sampling of non‐neighboring observations to form rational subgroups. The Markov chain technique is used to derive zero‐state and steady‐state closed‐form expressions of the specific shift performance metric, ie, average run‐length (ARL). Moreover, we compute the expected ARL metric which evaluates each monitoring scheme based on all specified range of possible values of the shift parameter, or more specifically, from a global point of view and thus gives a different perspective from the specific shift ARL metric. We observed that the steady‐state improved w‐of‐w and the improved 2‐of‐(H + 1) schemes yield a better overall performance than their corresponding basic counterparts for all different levels of autocorrelation. A real‐life example is provided to illustrate the implementation of the monitoring schemes proposed here.

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References

2009Statistical quality control : a modern introduction 2013Introduction to Statistical Process Control 2007Statistical Process Control using Shewhart Control Charts with Supplementary Runs Rules 2007SPC Procedures for Monitoring Autocorrelated Processes 2008Optimization designs of the combined Shewhart-CUSUM control charts 2010Effect of measurement error and autocorrelation on theX¯chart 2004Control Charts for Time Series: A Review 2019Nonparametric Statistical Process Control

Cited by

2022Run rules schemes for statistical process monitoring: a literature review 2020On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes 2020A combined mixed- s -skip sampling strategy to reduce the effect of autocorrelation on the X scheme with and without measurement errors 2019Shewhart-type monitoring schemes with supplementary w-of-w runs-rules to monitor the mean of autocorrelated samples 2020On monitoring the process mean of autocorrelated observations with measurement errors using the w‐of‐w runs‐rules scheme

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