Design of Optimal Exponential CUSUM Control Charts

Fah Fatt Gan

100 citations0/0 files storedJournal of Quality Technology

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

Abstract

Control charts are needed in many manufacturing processes for monitoring the rate of occurrences of events such as nonconforming items. This rate can usually be modeled by the interarrival times for a homogeneous Poisson process, which are independent and identically distributed exponential random variables. The monitoring of the exponential mean provides an alternative method for monitoring the rate of occurrences of events. An extensive numerical study indicates that the reference value k obtained from the sequential probability ratio test is the optimal chart parameter k for the exponential CUSUM chart. Graphs of chart parameters are given and these graphs can be used to easily obtain the chart parameters of an optimal exponential CUSUM chart. The relative performance of exponential CUSUM and Poisson CUSUM charts for monitoring the rate of occurrences of events is also assessed.

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References

1954CONTINUOUS INSPECTION SCHEMES 1987An Introduction to Statistical Quality Control.1985Counted Data CUSUM's 1989Design of Exponentially Weighted Moving Average Schemes 1989Statistical Quality Control 1982Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start 1985The Statistical Design of Quality Control Charts 1985Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed

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2003Robustness of the time between events CUSUM 2014Designing of a new monitoring t-chart using repetitive sampling 2006Design of exponential control charts using a sequential sampling scheme 2009Properties of the exponential EWMA chart with parameter estimation 2007A comparison of surveillance methods for small incidence rates 2019A Review of Some Sampling and Aggregation Strategies for Basic Statistical Process Monitoring

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