Improved CUSUM charts for monitoring process mean

Abdul Haq · Waqas Munir

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Advanced Statistical Process Monitoring Fault Detection and Control Systems Survey Sampling and Estimation Techniques

Abstract

In this paper, we propose new cumulative sum (CUSUM) and Shewhart-CUSUM (SCUSUM) control charts for monitoring the process mean using ranked-set sampling (RSS) and ordered RSS (ORSS) schemes. The proposed CUSUM charts include the Crosier's CUSUM (CCUSUM) and Shewhart-CCUSUM (SCCUSUM) charts using RSS, and the CUSUM, CCUSUM, SCUSUM and SCCUSUM charts using ORSS. Moreover, fast initial response features are also attached with these CUSUM charts to improve their sensitivities for an initial out-of-control situation. Monte Carlo simulations are used to compute the run length characteristics of the proposed CUSUM charts. Upon comparing the run length performances of the CUSUM charts, it turns out that the proposed CUSUM charts are more sensitive than their existing counterparts. A real dataset is used to explain the implementation of the proposed CUSUM charts.

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References

1954CONTINUOUS INSPECTION SCHEMES 1959Control Chart Tests Based on Geometric Moving Averages 2000Control Chart Tests Based on Geometric Moving Averages 2007Introduction to Statistical Quality Control 1982Combined Shewhart-CUSUM Quality Control Schemes 2000Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start 1982Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start 2012Mixed Exponentially Weighted Moving Average–Cumulative Sum Charts for Process Monitoring

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2020An efficient approach of designing distribution-free exponentially weighted moving average schemes with dynamic fast initial response for joint monitoring of location and scale 2023A review of ranked set sampling and modified methods in designing control charts

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