Mean control chart based on ranked set schemes for unknown skewed probability distribution and parameters

Abstract

Several structures of mean control chart based on ranked set schemes are available in literature. These structures involve assumptions, that is, process distribution is known and sufficient amount of samples is available in estimating unknown parameters. It is a fact that the restricted assumptions do not fulfill in several processes.In such situation, the actual false alarm rate of mean control chart under ranked set schemes is deviated from true level. This issue has taken as one of the motivations of present study. In this study, we have designed a skewness correction mean control chart for managing the situations where skewed probability distribution and process parameters are unknown. The proposed skewness correction mean control chart depends on known skewness level of a process characteristics rather than the restricted assumption of known probability distribution. Furthermore, proposed skewness correction and usual mean control charts are assessed using actual false alarm rate. The outcomes revealed that actual false alarm rate of proposed skewness correction mean control chart remains close to true level when assumption(s) is violated compared to usual mean control chart. To explain the implementation procedure as well as advantages of the proposed control chart over usual, simulated and real data examples are considered. The real data example from agriculture field is included in which proposed control chart is implemented to monitor calcium + magnesium contents of irrigation water.

An adaptive EWMA control chart based on Hampel function to monitor the process location parameter

“…The μ 1 illustrates diverged value of the μ 0 such as $${\mu }_1 > \mu $$ or $${\mu }_1 < \mu $$. For a fair analysis or comparison, the ARL 0 is at least same or greater of a benchmark CC relative to other CCs, and the ARL 1 should be less at a specific δ (i.e., shift) in contrast to other CCs and detailsare discussed elsewhere (Riaz et al 29 . and Khan et al 30 …”