Economic statistical design of ARMA control chart through a Modified Fitness-based Self-Adaptive Differential Evolution

Abstract

In this paper the economic statistical design of an Auto-Regressive Moving Average (ARMA) control chart for autocorrelated data has been investigated. In particular, the total cost of the chart subject to a constraint on the minimum in-control average run length has been taken into account. Due to the autocorrelation of the data, a simulation approach was adopted to assess both in-control and out-of-control average run lengths as the charting parameters change. In order to select the optimal parameters of the ARMA chart a Modified Fitness-based Self-Adaptive Differential Evolution algorithm, named MF-SADE, has been developed. To validate the effectiveness of MF-SADE in solving the proposed control chart design problem, an extensive comparison campaign involving four different metaheuristics from the relevant literature was arranged. Once the obtained numerical results confirmed the outperformance of SADE, it was used to carry out a sensitivity analysis including parameters of the cost model and those concerned with the underlying process, denoted as u and v. Among the numerous findings, the sensitivity analysis put in evidence the relationship between u, v and the variables of the economical statistical issue under investigation.