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6

Process Variations and

Their Estimates

L. C. Tang and H. S. Yam

The key to successful statistical analysis is the identification of variations, their sources
and their estimates. Variation is inherent in almost everything. In order to achieve a
given business target, the capabilities and variability of the process must be well es-
tablished and controlled. In this chapter the sources of variation will be discussed,
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followed by the basic statistical properties of the process variability σ and its unbi-
ased estimator. A short review of the nested design with variance components is then
presented to illustrate how various sources of variation can be estimated.

6.1 INTRODUCTION

Business growth depends on how well companies meet customer expectations in
terms of quality, price and delivery. Their ability to satisfy these needs with a known
degree of certainty is controlled by process capability, and the amount of variation
in their processes. Variation has a direct impact on business results in terms of cost,
cycle time, and the number of defects that affect customer satisfaction. No two units
of product produced by a manufacturing process (or two services provided by a ser-
vice provider) are identical. Variation is inherent in all processes and measurements,
natural or human-made. Figure 6.1 shows two main sources of variation, which are
process variation and measurement variation.

6.1.1 Process variation
Process variation is important in the Six Sigma methodology, because the customer is
alwaysevaluatingtheservices,productsandprocessesprovidedtothem,todetermine

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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