An Algorithm for the Determination of the Economic Design of -Charts Based on Duncan's Model

A. L. Goel · S. C. Jain · S. M. Wu

103 citations0/0 files storedJournal of the American Statistical Association

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

Abstract

An algorithm for the determination of the economic design of -charts based on Duncan's model is described in this paper. This algorithm consists of solving an implicit equation in design variables n (sample size) and k (control limit factor) and an explicit equation for h (sampling interval). The use of this algorithm not only yields the exact optimum but also provides valuable information so that the sensitivity of the optimum loss-cost (L*) can be evaluated. Loss-cost contours are used to discuss the nature of the loss-cost surface and the effect of the design variables. The effect of two parameters, the delay factor (e), and the average time for an assignable cause to occur (1/λ), on the optimum design is evaluated. Numerical examples are used for illustrations.

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References

1932Economic Control of Quality of Manufactured Product.1932Economic control of quality of manufactured product 1956The Economic Design of X Charts Used to Maintain Current Control of a Process 1952A Bayes Approach to a Quality Control Model 1963Control Charts and the Minimization of Costs

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