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

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