Data transformation for geometrically distributed quality characteristics

Abstract

Recently there has been an increasing interest in techniques of process monitoring involving geometrically distributed quality characteristics, as many types of attribute data are neither binomial nor Poisson distributed. The geometric distribution is particularly useful for monitoring high-quality processes based on cumulative counts of conforming items. However, a geometrically distributed quantity can never be adequately approximated by a normal distribution that is typically used for setting 3-sigma control limits. In this paper, some transformation techniques that are appropriate for geometrically distributed quantities are studied. Since the normal distribution assumption is used in run-rules and advanced process-monitoring techniques such as the cumulative sum or exponentially weighted moving average chart, data transformation is needed. In particular, a double square root transformation which can be performed using simple spreadsheet software can be applied to transform geometrically distributed quantities with satisfactory results. Simulated and actual data are used to illustrate the advantages of this procedure.