Quality Selection under Sampling Inspection with an Exponential Production Cost Function

Abstract

A quality selection model consists of three parts; economy (prices and costs), production (variability, dependency and distribution of the quality characteristic) and the customer's quality requirements. The main use of quality selection models has earlier been to determine the process level(s) of the quality characteristic(s) which maximize(s) the expected profit. Recently, the interest has been more focused on sensitivity analysis mainly of the economic impact of changes in variability, and such a study could be an early part of a quality improvement program. In this paper, a general quality selection model is derived from a study of a Swedish pulp mill. The customer's quality requirements are assumed to be given by a capability index, which includes tolerance limits and means. The number of quality classes are allowed to be more than two and the production cost function is assumed to be exponential (including a linear cost function). When working with a non-linear cost function, two different cases have to be considered-the output case and the input case. The first (second) case covers production processes where the production cost depends on the real (intended) outcome of the production process. The equation for the optimal process level is derived and an explicit approximation of the optimal process level is given. The economic impact of changes in process variability is demonstrated in the case study and emphasized throughout the discussions. It is also shown by an example that a classification into more than two classes has a negligible effect on the optimal process level and on the optimal expected profit. Finally, it is shown that an exponential production cost function can be approximated with a properly chosen linear production cost function.