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21

Establishing Cumulative

Conformance Count Charts

L. C. Tang and W. T. Cheong

The cumulative conformance count (CCC) chart has been used for monitoring high
yield processes with very low process fraction nonconforming. Current work has yet
to provide a systematic treatment for establishing the chart, particularly when the
process fraction nonconforming parameter is estimated. We extend the results from
the recent studies by Tang and Cheong and by Yang et al. to enable engineers to
construct the CCC chart under different sampling and estimation conditions. We first
outline the statistical properties of the CCC chart. We then give new insights into the
behavior of CCC chart when the parameter is estimated. We propose some procedures
for constructing the CCC chart when the process fraction nonconforming is given,
when it is estimated sequentially, and when it is estimated with a fixed sample size.
The proposed steps are implemented using data from a high-yield process in order to
demonstrate the effectiveness of the scheme.

21.1 INTRODUCTION

Attribute Shewhart charts (such as the p chart) have proven their usefulness, but are
1
ineffective as the level of nonconformance improves to low levels. This has led to the
development of new methods of process monitoring, one of which is the cumulative
conformance count (CCC) chart. CCC charts track the number of conforming items
produced between successive nonconforming ones. This type of chart has been shown

This chapter is based on the article by L. C. Tang and W. T. Cheong, “On establishing cumulative conformance
charts”, International Journal of Performability Engineering, 1(1), 2005, pp. 5--22, and is reproduced by the
permission of the publisher, the RAMS Consultants.
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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