Determination of the Optimal Process Mean and the Upper Limit for a Canning Problem

Abstract

A method of determining the optimal process mean and upper fill weight limit for a canning process where the ingredient is expensive is presented. Underfilled (below a specified limit) and overfilled (above a controllable upper limit) cans are emptied and refilled. We assume that the fill weight is normally distributed with known variance. Using a reasonable cost structure, optimal values for the process mean and the upper limit are obtained. Simple approximate analytical expressions relating these optimal values to fundamental process parameters are given. An explicit measure is given for the value of being able to impose an upper limit on the fill.