Summary
The present study incorporates an important practical entity in the study of economic\(\bar X\)-charts. The process model assumes, in addition to other things, that the in-control level has a prior probability distribution, instead of being fixed. The loss-cost function is derived as a main result. A numerical study is further made to investigate properties of the economic optimum control charts. It is found that complete knowledge about the shape of the prior distribution is not vital to the optimum solution provided that its mean and variance can be accurately determined. Optimum values of all the three control variables are substantially larger than those for the old process model with a fixed in-control level.
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References
Baker, K.R.: Two process models in the economic design of an\(\bar X\)-chart. AIIE Transactions3, 1971, 257–263.
Bather, J.A.: Control charts and the minimization of costs. J. Roy. Statist. Society., SeriesB 25, 1963, 49–70.
Chiu, W.K.: Comments on the economic design of\(\bar X\)-charts. J. Amer. Statist. Ass.68, 1973, 919–921.
—: The economic design of cusum charts for controlling Normal means. Applied Statistics23, 1974a, 420–433.
—: A new prior distribution for attributes sampling. Technometrics16, 1974b, 93–102.
—: The economic design of attribute control charts. Technometrics17 1975, 81–87.
—: On the estimation of data parameters for economic optimum\(\bar X\)-charts. Metrika23, 1976, 135–147.
Chiu, W.K., andK.C. Cheung: An economic study of\(\bar X\)-charts with warning limits. J. Qual. Tech.9, 1977, 166–171.
Chiu, W.K., andG.B. Wetherill: A simplified scheme for the economic design of\(\bar X\)-charts. J. Qual. Tech.6, 1974, 63–69.
Cohen, A.C.: Estimating the mean and variance of normal populations from singly truncated and doubly truncated samples. Ann. Math. Statist.21, 1950, 557–569.
Cowden, D.J.: Statistical Methods in Quality Control. New York 1957.
Duncan, A.J.: The economic design of\(\bar X\)-charts used to maintain current control of a process. J. Amer. Statist. Ass.51, 1956, 228–242.
—: Review of Cowden's Statistical Methods in Quality Control. J. Amer. Statist. Ass.52, 1957, 583–586.
—: The economic design of\(\bar X\)-charts when ther is a multiplicity of assignable causes. J. Amer. Statist. Ass.66, 1971, 107–121.
—: The economic design ofp-charts to maintain current control of a process: some numerical results. Technometrics20, 1978, 235–243.
Gibra, I.N.: Economically optimum determination of the parameters of\(\bar X\)-charts. Management Science17, 1971, 635–646.
Goel, A.L., S.C. Jain, andS.M. Wu: An algorithm for the determination of the economic design of\(\bar X\)-charts based on Duncan's model. J. Amer. Statist. Ass.63, 1968, 304–320.
Goel, A.L., andS.M. Wu: Economically optimum design of cusum charts. Management Science19, 1973, 1271–1282.
Grant, E.L., andR.S. Leavenworth: Statistical Quality Control, 4th ed. New York 1972.
Johnson, N.L., andF.C. Leone: Statistics and Experimental Design in Engineering and the Physical Sciences. Vol. 1. New York 1964.
Saniga, E.M., andL.E. Shirland: Quality control in practice, a survey. Quality Progress10, 1977, 30–33.
Shewhart, A.W.: Economic Control of Quality of Manufactured Product. Princeton 1931.
Taylor, H.M.: The economic design of cumulative sum control charts. Technometrics10, 1968, 479–488.
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Chiu, W.K., Leung, M.P.Y. A new Bayesian approach to quality control charts. Metrika 27, 243–253 (1980). https://doi.org/10.1007/BF01893602
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DOI: https://doi.org/10.1007/BF01893602