Complex production systems' performance measurement: Estimation of aggregate indices under uncertainty

Abstract

The paper deals with approaches utilized for adjustment of well known Method of Aggregate Indices (MAI) to uncertainty conditions. The necessity for such adjustments occurs because of the shortage of numeric information. It appears at any stage of estimation of the aggregate quality index for operating electricity units when respective measure (index) integrates a system of object's parameters. Each parameter is required for ultimate quality appraisal, and taken together they are supposed to be sufficient for estimating quality level of the analyzed unit. The Baye's uncertainty randomization procedure is proposed as a tool to simulate the shortage of numeric information. Through this procedure separate indices, weight coefficients and aggregated indices are transformed into correspondent random magnitudes. Then, comparing the qualities of any two objects is converted in the problem of revealing a certain type of stochastic dominance between respective randomized aggregate indices. The software implementation of described above method of Randomized Aggregated Indices Method (RAIM) is based on discrete model of weight coefficients, which allows for generation of all their possible meanings by directed calibration of all feasible bundles of the coefficients. The software implementation of full calibration of possible values for the aggregate indices permits consideration of additional information supplied by experts. It is shaped as a system of inequalities for feasible values of the weight coefficients. Such nonnumeric information from experts substantially increases the accuracy and reliability of constructed randomized estimates of the objects' aggregate quality indices.