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A Bayesian Analysis of the Deming Cost Model with Normally Distributed Sampling Data
代写留学生论文Chiuh-Cheng Chyu and I-Chung Yu
Department of Industrial Engineering and Management, Yuan-Ze University, Chung-Li, Taiwan
This article studies the Deming cost model using a Bayesianapproach when the quality characteristic of items is assumedto have a normal distribution with unknown mean. Previously,researchers studied this model by the go=no-go data.Through a Bayesian approach, the model consists of a twostagedecision that minimizes the expected total cost: Thefirst stage decision is to determine the optimal sample size,and the second stage decision is to decide whether to stopinspection or continue to inspect the remaining items of thelot. Numerical integration is used to find an approximatesolution to the model. An illustrative example is given anda numerical analysis of this example is performed to realize
the effects of the model parameters. The cost differencebetween using the measurement data and the correspondinggo=no-go data under the same probability assumptions andcost structure is also investigated.
Keywords Bayesian decision analysis; Decision trees;Inspection sampling.
1. INTRODUCTION
Inspection procedure is often used as a tool forquality assurance in many manufacturing systems. Ifwe are not sure the components in need are high qualityor the quality of the process declines, then someprocedure should be taken. In such situations, acceptancesampling plans and 100% inspection plans arecommon short-term approaches. There are various
approaches in the determination of an inspection procedure,and the decision theoretic approach is probablythe most reasonable method to model thisproblem on the basis of economic considerations andsampling information (Fink and Margavio, 1994).To classify an item in the lot as either defective ornondefective (go=no-go) is an attribute samplinginspection problem. To measure the quality of an item
in the lot by a continuous scale is a variable samplinginspectionproblem. A variable sampling inspectionproblem can become an attribute sampling problemif the procedure only counts the number of items nonconformingto specification limit(s) in the sample and
uses this number to decide whether the remaining itemsof the lot are accepted. To design a variable samplingplan, we need to specify the sample size and the acceptancelimit(s). If the measured value from the samplingvariables falls within the acceptance limit(s), the lot isaccepted. Otherwise, the lot is rejected. Usually, theacceptance limit(s) will depend on the probabilityassumptions of the inspection model, the sample size,and the loss function. A step loss function implies thatthe customers are completely satisfied with the itemsconforming to the specifications and become completelyunsatisfied when the value of the performancevariable falls outside the specifications. A loss functionis polynomial if the loss is polynomial in the valuedeviated from an ideal (target) value for an accepteditem.
Moskowitz and Tang (1992) used the cost structureproposed by Schmidt et al. (1974) to develop aBayesian variables acceptance sampling model with
the following probability assumptions: The performancevariable has anormal distribution withunknown mean, which is assumed to be normally distributedas well. Tagaras (1994) studied a similar coststructure under the same probability assumptions butassumed that the inspection was destructive and th本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。