EWMA Control Charts for the Smallest and Largest Observations

Raid Amin · Hans W. Wolff · W Besenfelder · Robert V. Baxley

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Advanced Statistical Process Monitoring Fault Detection and Control Systems Management Systems and Quality Improvement

Abstract

In this article, we propose an exponentially weighted moving average (EWMA) control chart based on the smallest (Min) and largest observations (Max) in each sample, which we call the MaxMin EWMA control chart. When there is a change in the process, the proposed control chart (and its modification) shows which parameters have increased or decreased. Also, the MaxMin EWMA may be viewed as smoothed tolerance limits, and it offers useful graphical guidance for monitoring processes and for trouble shooting. We give a design procedure and develop a two-dimensional Markov chain to approximate the average run length (ARL) for the proposed control chart. Our numerical results show that the MaxMin EWMA chart has good ARL properties for simultaneous changes in the mean and standard deviation. We provide a comparison with the combined use of X̄ and ℓn(S2) EWMA charts. We present an application with 100 multi-stream processes in which the MaxMin EWMA chart has already been successfully field tested and subsequently implemented.

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References

1990Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements 1972An Approach to the Probability Distribution of Cusum Run Length 1997Introduction to Statistical Quality Control 1992An EWMA for Monitoring a Process Standard Deviation 1993The Exponentially Weighted Moving Variance 1991Some Omnibus Exponentially Weighted Moving Average Statistical Process Monitoring Schemes 1995Joint Monitoring of Process Mean and Variance Using Exponentially Weighted Moving Average Control Charts 1995Statistical Process Control of Multiple Stream Processes

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