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Classical control charts were developed with the assumption that the quality characteristics being monitored are independent. However, observations from several time‐dependent processes, such as industrial or manufacturing, are bound to be autocorrelated such that their autocorrelations decay gradually (long memory) rather than exponentially (short memory). Runs rules monitoring schemes have been proposed in Statistical Process Control literature to monitor processes in the presence of autocorrelation by incorporating the autoregressive integrated moving average (ARIMA) class of models which can only handle autocorrelation with a short memory. This paper therefore incorporates the autoregressive fractionally integrated moving average (ARFIMA (1,d,1)) model into four one‐sided runs rules schemes to monitor the mean of an autocorrelated process with long memory. The performance of these four one‐sided schemes was assessed using average run length (ARL) and expected ARL (EARL) metrics. Based on the ARL and EARL of the improved runs rules (IRR) schemes, the IRR5‐of‐5 and IRR2‐of‐7 were found to issue an out‐of‐control signal faster than the corresponding standard runs rules (RR) schemes, RR5‐of‐5 and RR2‐of‐7, respectively. Also, the four one‐sided schemes IRR5‐of‐5, IRR2‐of‐7, RR5‐of‐5, and RR2‐of‐7 in their steady state condition perform better than their corresponding zero state condition. We further observed that as the fractional parameter d increases, the detection ability of the monitoring schemes reduces. The application of the four one‐sided schemes was demonstrated on the diameter of cable production. [ABSTRACT FROM AUTHOR]

Orthogonal‐array composite designs (OACDs) and orthogonal‐uniform composite designs (OUCDs) are orthogonal composite designs that combine two‐level full or fractional factorial and three‐level orthogonal‐array/uniform designs for estimation of the linear, bilinear, and quadratic effects in a second‐order response surface model. In this study, the effects of missing one observation in the various design portions (factorial (f) axial (a) and center (c)), on the precision of parameter estimates, prediction variance and design efficiency of OACDs and OUCDs for 5 ≤ k ≤ 9 factors at different values of α (the distance of a non‐zero co‐ordinate in an additional design point from the center) are evaluated. The results showed that missing a factorial and an axial point have adverse effect on the precision of parameter estimates of OACDs and OUCDs, while missing a center point has little effect. Missing an axial point caused the highest effect on the prediction variance and design efficiencies. The FDS plots showed OACDs to be better designs for k ≤ 7 and OUCDs for k = 8 and 9 factors. [ABSTRACT FROM AUTHOR]