The development and analysis of a multi-attribute quality control cost model

Abstract

A multi-attribute quality control cost model is presented in this thesis. The mathematical model expresses the expected total cost of the quality system per lot as a function of the decision variables, nᵢ and cᵢ, i = 1, 2, . . . , m, where

nᵢ is the sample size for the ith attribute.

cᵢ is the acceptance number for the ith attribute.

m is the number of attributes.

The expected total cost is denoted by C_T and can be expressed as

C_T = E (cost of sampling inspection).

E (cost of accepting the lot).

E (cost of rejecting and scrapping the lot).

E (cost of rejecting and screening the lot).

An optimal sampling plan can be obtained by determining the nᵢ and cᵢ, i = 1, 2, …, m, that minimizes C_T. The nᵢ and cᵢ are found by means of a search technique that has proved useful in attribute quality control systems.

In addition to the model development and optimization, a sensitivity analysis is performed on the use of the gallllla distribution as an estimate of the true process distribution for single and triple attribute systems. Also, a model sensitivity analysis is performed on errors in the estimation of the Cₐᵢ, the cost of accepting a defective unit.