Data transformation for geometrically distributed quality characteristics

Recently there has been an increasing interest in techniques of process mon itoring involving geometrically distributed quality characteristics, as man y 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 geomet rically distributed quantity can-never be adequately approximated by a norm al distribution that is typically used for setting S-sigma control limits. In this paper, some transformation techniques that are appropriate for geom etrically 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 transfo rmation which can be performed using simple: spreadsheet:software can be ap plied to transform geometrically distributed quantities with satisfactory r esults, Simulated and actual data are used to illustrate the advantages of this procedure. Copyright (C) 2000 John Wiley Br Sons, Ltd.