Improved Shewhart-Type Charts for Monitoring Times Between Events

Nirpeksh Kumar · S. Chakraborti · Athanasios C. Rakitzis

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

Abstract

In high-yield processes with a low defect rate, the recommendation is to monitor the times between events (TBE) with variables control charts in order to overcome the weaknesses of conventional attribute control charts. In this paper, we incorporate supplementary runs rules into one of the existing Shewhart-type TBE charts, namely the tr -chart, in order to improve its small to moderate size-shift detection ability. Moreover, because the existing tr -chart based on probability limits is biased, we provide a procedure for designing a tr -chart, with or without runs rules, that is unbiased. The performance of several tr -charts with runs rules is investigated, whereas comparisons with EWMA and CUSUM charts are also given. It is seen that some of the runs rules enhanced tr -charts perform substantially better. A real-data example is provided for illustration and some concluding remarks are given.

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References

1987An Introduction to Statistical Quality Control.1987Exact Results for Shewhart Control Charts With Supplementary Runs Rules 1985Counted Data CUSUM's 2002Some effective control chart procedures for reliability monitoring 1998Designs of One- and Two-Sided Exponential EWMA Charts 1985Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed 2000Cumulative quantity control charts for monitoring production processes 2000Two Alternatives to the ShewhartXControl Chart

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2020On the performance of the adaptive EWMA chart for monitoring time between events 2021A one-sided exponentially weighted moving average control chart for time between events 2019One‐sided runs‐rules schemes to monitor autocorrelated time series data using a first‐order autoregressive model with skip sampling strategies 2023An improved adaptive EWMA control chart for monitoring time between events with application in health sector 2019Design and implementation of qth quantile‐unbiased tr‐chart for monitoring times between events

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