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August 31, 2006

14

Data Transformation for

Geometrically Distributed

Quality Characteristics

T. N. Goh, M. Xie and X. Y. Tang

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 3σ
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.

14.1 INTRODUCTION

The geometric distribution is commonly found in process control data, and control
charts based on such a distribution have received increasing attention recently. The

This chapter is based on the article by M. Xie. T. N. Goh, X. Y. Tang, ‘Data transformation for geometrically
distributed quality characteristics’, Quality and Reliability Engineering International, 16(1), 2002, pp. 9--15, and
is reproduced by the permission of the publisher, John Wiley & Sons, Ltd
Six Sigma: Advanced Tools for Black Belts and Master Black Belts L. C. Tang, T. N. Goh, H. S. Yam and T. Yoap
C 2006 John Wiley & Sons, Ltd
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