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ereforethe cost of inspection per unit was greater than thecost of rejection per unit. Yeh and Van (1997) developeda Bayesian double-variable sampling model withthe polynomial loss function under the same probabilityassumptions.
Deming (1982) discussed a (n, c) rectifyingattributes sampling plan relative to two different costAddress correspondence to Chiuh-Cheng Chyu, Departmentof Industrial Engineering and Management, Yuan-ZeUniversity, Chung-Li, Taiwan. E-mail: iehshsu@satrun.
yzu.edu.twQuality Engineering, 18:107–116, 2006
setups, ðk1; k2Þ, where n is the sample size, c is the acceptancenumber, k1 is the cost per unit to inspect an item,and k2 is the cost per unit of a nonconforming item thatis either placed in an assembly that fails or that entersthe stream of commerce and subsequently fails.Usually, the k2 cost is much higher than the k1 inspectioncost. By rectifying inspection, we mean a procedurewhereby a lot rejected by sampling inspection is 100%inspected and all nonconforming items discovered during
inspection are replaced with conforming units.After observing the sampling outcome, if the numberof nonconforming items in the sample of size n isgreater than the acceptance number c, the lot is rejected
and subject to 100% inspection. Otherwise, the lot isaccepted and all remaining items of the lot are sent toassembly without inspection. It is noted that any nonconformingitem found in the inspection stage and in
the assembly stage will be replaced with a perfect item.The perfect item is obtained by inspecting items of thesame quality from other resource. Depending on thecontract, the extra inspection cost to obtain a perfect
item can be charged to either the manufacturer or thesupplier. An application example of the model is themanufacture of implantable prosthetic medical devices(Kaminsky and Haberle, 1995). Another example
occurs in applying the surface mount technology(SMT) to printed circuit board (PCB) assembly, wherethe rework cost for replacing a non conforming electronicdevice mounted onto the board is cheaper than the
scrap cost of the board.Papadakis (1985), Burke et al. (1993), Vander Wieland Vardeman (1994), and Kaminsky and Haberle(1995) discussed the Deming cost model by attributesfrom a classical statistics point of view (i.e., the fractionof conforming items in the lot, p, is known).Rigdon (1995) discussed in detail the case where p isunknown. In such situations, one might consider usinga Bayesian approach to minimize total cost. Applyingthis approach will necessitate the need to describe pwith a probability or density function based on knowledgeand previous data. The book by Berger (1985)provides several methods for quantifying prior informationas a distribution.Lorenzen (1985) and Barlow and Zhang (1986)discussed the Deming cost model by attributes froma Bayesian point of view and provided computer codesfor the model using beta prior for the probability of anitem being conforming. In this article, we extend theBayesian approach study of this model to the variablesampling plan, where the quality characteristic of itemshas a normal distribution with unknown mean butknown standard deviation. An item is conforming if
the value of its performance variable falls within atwo-sided specification interval. Meanwhile, we arealso interested in learning how much cost can be savedfor this model when the variable measurement data isused as compared with the derived go=no-go type data.The rem