Non-normal populations in quality applications: A revisited perspective

Much research effort has recently been focused on methods to deal with non-normal populations. While for weak non-normality the normal approximation is a useful choice (as in Shewhart control charts), moderate to strong skewness requires alternative approaches. In this short communication, we discuss the properties required from such approaches, and revisit two new ones. The first approach, for attributes data, assumes that the mean, the variance and the skewness measure can be calculated. These are then incorporated in a modified normal approximation, which preserves these moments. Extension of the Shewhart chart to skewed attribute distributions (e.g. the geometric distribution) is thus achieved. The other approach, for variables data, fit a member of a four-parameter family of distributions. However, unlike similar approaches, sample estimates of at most the second degree are employed in the fitting procedure. This has been shown to result in a better representation of the underlying (unknown) distribution than methods based on four-moment matching. Some numerical comparisons are given.