XandRControl Charts for Skewed Populations

Abstract

This paper proposes a heuristic method based on a weighted variance concept of setting up control limits of X̄ and R charts for skewed populations. It provides asymmetric control limits in accordance with the direction and degree of skewness estimated from the sample data, by using different variances in computing upper and lower control limits. For symmetric populations, however, these control limits are equivalent to those of Shewhart control charts. The new heuristic control charts are compared by Monte Carlo simulation with Shewhart charts and the geometric control charts of Ferrell. When the underlying population is Weibull or Burr's, the heuristic charts are found to perform better than Shewhart or geometric charts as the skewness increases.

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