Economically Optimum Design of a Synthetic Chart

Wai Chung Yeong · Michael B. C. Khoo · Zhang Wu · Philippe Castagliola

35 citations0/0 files storedQuality and Reliability Engineering International

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

Abstract

This paper proposes an economic model for the synthetic chart. The synthetic chart is an integration of the chart and the CRL chart. A simplified algorithm to obtain the optimal parameters of the synthetic chart which minimizes the expected cost function is introduced. Numerical examples based on different values of input parameters are given, and sensitivity analyses of the parameters are performed. The input parameters which have a significant impact on the cost and choice of optimal parameters of the synthetic chart are identified. The effect of incorrect estimation of the input parameters is also investigated, and it is found that the optimal design parameters are quite robust to changes in the input parameters, except the shift parameter. It is also shown that if the chart cannot be operated at the economically optimal level, there is still a large choice of parameters to choose from which does not result in a large increase in cost. All the above analyses and results are based on numerical examples and verified through simulation over a wide range of parameter values. Comparisons are also performed among the synthetic Shewhart and EWMA charts. Based on the numerical examples and simulation over a wide range of parameter values, it is shown that the synthetic chart has better economic performance than the other two control charts under most conditions. Copyright © 2011 John Wiley & Sons, Ltd.

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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 1956The Economic Design of | barX Charts used to Maintain Current Control of a Process 2000A Synthetic Control Chart for Detecting Small Shifts in the Process Mean 1985The Statistical Design of Quality Control Charts 1974A Simplified Scheme for the Economic Design of X-Charts 1968An Algorithm for the Determination of the Economic Design of -Charts Based on Duncan's Model 2010A synthetic double sampling control chart for the process mean

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