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15. Uluslararası Ekonometri, Yöneylem Araştırması ve İstatistik Sempozyumu (15.Eyi), Isparta, Turkey, 22 - 25 May 2014, pp.1, (Full Text)
Average Run Length (ARL) calculations in Statistical Process Control (SPC) plays an important role not only for evaluating the performance of conventional control charts, but also designing new ones on the purpose of some special requirements. Run length distribution is supported and used by so many quality researchers for numerous studies on various types of control charts. However, ARL is a confusing concept and in some cases it would not be the proper or correct measure for the quality process evaluation. This type of inconvenience may generally be caused of the non-normality character of data, the unequal sample sizes used or the existence of correlation. In this study, ARL calculation and utilization areas in statistical quality control are mentioned initially. Then some recommendations are done after emphasizing the limitations for the usage of run length distribution depending upon the characteristics of charting statistics or some other properties of control charts. A representative example, which gives an early signal, contradicts with its in- control ARL is also proposed. The application is done on R statistical programming language. The data is generated randomly normal distributed and equal sample sizes are particularly used to show the impact of the existence of autocorrelation within the bounds of 95% significance level.