Capability analysis of the variable measurement system with fuzzy data

The aim of this paper is to propose an approach to analyze capability of the variable measurement system in fuzzy environment, where the data acquired from the measurement process under study are assumed fuzzy numbers. To accomplish this goal, a pair of non-linear programming problems is formulated based on Zadeh’s extension principle to compute αα-level cuts of assessment criteria, which are frequently used to analyze capability of the variable measurement system in practice. The membership functions of these criteria are then constructed analytically by numerating different values of αα. The capability assessment criteria discussed in this paper include repeatability, reproducibly, GRR  % and CgkCgk. In the next step, a method for ranking fuzzy numbers is exploited to evaluate whether capability of the variable measurement system is satisfactory in fuzzy environment or not. Since fuzzy measures are gathered from the measurement system in a more realistic situation in which all variations and unexpected conditions are taken into account, it is shown using an empirical example that incorporating fuzziness into measurement data results in a more accurate capability analysis.