Economic, Statistical, and Economic-Statistical X Chart Designs

Thomas P. McWilliams

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Advanced Statistical Process Monitoring Management and Optimization Techniques Fault Detection and Control Systems

Abstract

A FORTRAN program that enables users to determine economic, statistical, or economic-statistical X̄ chart designs is presented. Economic designs are designs that minimize cost as measured by the Lorenzen-Vance cost function. Statistical designs are designs that satisfy a series of average run length constraints associated with various degrees of shift in the process mean. These two concepts are combined to find economic-statistical designs, where cost is minimized subject to average run length constraints.

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References

1956The Economic Design of X Charts Used to Maintain Current Control of a Process 1986The Economic Design of Control Charts: A Unified Approach 1989Economic Statistical Control-Chart Designs With an Application to and R Charts 1971The Economic Design of -Charts When There is a Multiplicity of Assignable Causes 1985The Statistical Design of Quality Control Charts 1982Economic Design of an X Control Chart 1989Determination of Optimal Design Parameters of JointXandRCharts 1993Economic Design of X Control Charts Assuming Weibull In-Control Times

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1995Economic, Statistical, and Economic-Statistical Design of Attribute Charts 2001Economic-Statistical Design ofXand R orXand S Charts 2010Economic statistical design for x-bar control charts under non-normal distributed data with Weibull in-control time 2003Economic statistical design of x ¥ control charts for systems with gamma ( 5 ,2) in-control times 2001Economic designs of constrained EWMA and combined EWMA-X¯ control schemes

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