The Optimum Mean for Processes with Normally Distributed Measurement Error

Abstract

This paper investigates the effect of measurement errors on the optimum process mean for a filling process. In this filling process, containers are filled with an expensive ingredient and containers weighing above a specified limit are sold in a regular market for a fixed price, while the underfilled containers are reprocessed at a cost. It is assumed that the quantity of the ingredients in the container and the observed weight of the container are normally distributed. A profit model is constructed which involves the selling price, the cost of the ingredients, the reprocessing cost, and the cost of accepting an underfilled container. Methods for finding the optimum process mean and cutoff value of the observed weight are presented, and a numerical example is given.

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