Graphical Representation of Run Length Distributions

Darrell Radson · Amy Hancock Boyd

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

Abstract

With the development of techniques to compute run length distributions for various types of control charts, numerous researchers have advocated using these distributions. However, it is unclear how practitioners are expected to use run length distributions in making decisions about control chart performance and chart design. To alleviate this problem, we present a graphical method of representing run length distributions. Our method allows for the easy comparison of several distributions which is not currently permitted with standard types of distribution plotting.

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References

1972An Approach to the Probability Distribution of Cusum Run Length 1959Control Charts and Stochastic Processes 1987A Simple Method for Studying Run – Length Distributions of Exponentially Weighted Moving Average Charts 1987Exact Results for Shewhart Control Charts With Supplementary Runs Rules 1989Design of Exponentially Weighted Moving Average Schemes 1974The Effect of Serial Correlation on the Performance of CUSUM Tests 1983The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables 1969Cusum Techniques for Quality Control

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2019On Designing Distribution-Free Homogeneously Weighted Moving Average Control Charts 2017In-control robustness comparison of different control charts 2020On developing an exponentially weighted moving average chart under progressive setup: An efficient approach to manufacturing processes 2021On the Development of Triple Homogeneously Weighted Moving Average Control Chart 2020Nonparametric progressive sign chart for monitoring process location based on individual data

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