Median and interquartile range control charts based on quantiles of Marshall-Olkin inverse log-logistic distribution

Abstract

The presence of outliers makes process data deviate from normality and reduces the sensitivity of control charting procedures. This paper proposed a robust method of determining the control limits of X̄ and R charts in the presence of outliers when the data deviates from normality. The quantile of Marshall-Olkin inverse log-logistic distribution (MOILLD) is derived. The quantiles of the distribution are then used to estimate the process location and dispersion for the construction of control limits of median and interquartile range control charts. Control limit interval, false alarm rate, and average run length were used to compare the performance of the proposed control charts with similar control charts in the literature. The results showed that the proposed method detects out-of-control faster than the classical Shewhart control chart and robust control charts whose control limits were based on raw data.