Projeto Econômico da Carta de Controle X : um modelo com custos dependentes dos desvios

Abstract

Due to the difficulty in estimating the operating costs associated to the statistical monitoring of the process described in the literature, this paper aims to propose a model of economic optimization for the _X control chart that considers the uncertainties in relation to the variable costs and dependent on the deviation in relation to the average of the process. The literature review performed supported the understanding of how the uncertainty in relation to costs in the use of control charts is treated. The treatment of the costs as well as the parameter of deviation of the process in relation to the _ average were indicated as discrete variables and that impacted on the chart. The proposal presented here consists of treating not only the deviation from the mean but also two costs associated with the operation of the _X control chart as random variables of continuous distribution, thus inserting a component of uncertainty in its estimation. A new formulation for the optimization problem was developed. Instances for optimization were chosen and the results were compared with those obtained by authors described in the literature. The results were obtained through simulated annealing metaheuristics. As a result, the method proved to be efficient, showing that the level of dependence between the process change parameter and the cost, as well as the uncertainty regarding the defined operating cost values impact on the total cost of operation of the SPC. The main contribution of this research work is the presentation of a mathematical formulation of optimization of the _X control chart that treats not only the deviation in relation to the average of the process but also the operating costs of the SPC as random variables. The originality of the formulation is to consider costs linearly dependent on the size of the process deviation in relation to its mean.