Comparative analysis between FAR and ARL based control charts with runs rules

Authors : Rashid MEHMOOD, Muhammad Hisyam LEE, Iftikhar ALİ, Muhammad RIAZ

Pages : 275-288

Doi:10.15672/hujms.758925

View : 26 | Download : 7

Publication Date : 2021-02-04

Article Type : Research Paper

Abstract :In this study, we have conducted comparative analysis between false alarm rate insert ignore into journalissuearticles values(FAR); and average run length insert ignore into journalissuearticles values(ARL); based control charts with runs rules. In this regard, we have considered various univariate and multivariate control charts which include mean, standard deviation, variance, Hotelling, and generalized variance. For evaluation purpose, we have used actual false alarm rate, power, in-control actual average run length, and out-of-control average run length as performance indicators. Furthermore, the performance indicators are calculated through Monte Carlo simulation procedures. Results revealed that performance order of runs rules with FAR based control charts are persistent whereas, performance order of runs rules with ARL based control charts are dependent on the circumstances, that is, sample size, size of shift, type of control chart, and side of control limit insert ignore into journalissuearticles values(upper-sided and lower-sided);. Besides, we have provided a real life example using the data on electrical resistance of insulation. In this approach, we have determined that behavior of FAR and ARL based control charts using the real data is recorded similar to the behavior using the statistical performance indicators.
Keywords : Average run length, control chart, false alarm rate, performance indicators, power, probability of single point, runs rules