Economic-statistical design of adaptive arma control chart for autocorrelated data

• Published in: Journal of statistical computation and simulation Vol. 91; no. 3; pp. 623 - 647
• Main Authors: Costa, A., Fichera, S.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 11.02.2021; Taylor & Francis Ltd
• Subjects: Adaptive control; Algorithms; Auto-regressive; Autocorrelation; Constraints; control chart; Control charts; Cost function; Economics; evolutionary algorithms; Evolutionary computation; moving-average; Parameter sensitivity; Sensitivity analysis; simulation
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2020.1825716

To the best of our knowledge, no literary contribution addressed the design of adaptive ARMA control charts with autocorrelated data, so far. This paper aims to provide an original research contribution to the statistically constrained economic design of ARMA control charts with variable sampling interval (VSI). Due to the autocorrelation of data, a simulation approach has been used to compute the objective function, which consists of the well-known Lorenzen and Vance cost function subject to a constraint on the minimum ARL0. The main novelty is attributable to the simulation-based charting process as well as to an improved self-adaptive differential evolution for minimizing the charting cost. Subsequently, the proposed algorithm was employed to statistically demonstrate the outperformance of the VSI approach over the standard one with fixed charting parameters. Finally, a comprehensive sensitivity analysis was carried out with the aim of detecting the most influencing factors under economical and statistical viewpoints.