Data Transformation for Geometrically Distributed Quality Characteristics

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