Proposed ̃ and S control charts for skewed distributions

This paper proposes a weighted variance method to compute the limits of the X ¿ and S charts for skewed distributions. The proposed charts extend the weighted variance X ¿ and R charts in by enabling a process from a skewed distribution with moderate and large sample sizes to be monitored efficiently, hence producing more favourable Type-I and Type-II error rates than the charts in. Note that the charts in are only intended to be used for small sample sizes. The Type-I and Type-II error rates computed show that the proposed charts outperform the existing heuristic charts, as well as those in for moderate and large sample sizes, involving cases with known and unknown parameters, when the distribution of a process is skewed.