Economic design of Hotelling’s T 2 control chart on the presence of fixed sampling rate and exponentially assignable causes

Abstract

Control charts are extensively used in manufacturing contexts to monitor production processes. This article illustrates economical design of a variable sample size and control limit Hotelling’s T2 control chart based on a novel cost model when occurrence times of the assignable causes are exponentially distributed. The proposed nonlinear cost model is an extension of Duncan’s (J Am Stat Assoc 51: 228–242, 1956) model which was employed for univariate cases. Applying genetic algorithm to find optimum parameter values and using an L33 orthogonal array in sensitivity analysis on the model parameters is investigated through a numerical example to illustrate the effectiveness of the proposed approach.