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24

Cumulative Sum Charts with

Fast Initial Response

L. C. Tang and O. O. Atienza

In this chapter, we give a short review of the two types of cumulative sum (CUSUM)
chart, namely the tabular CUSUM and V-mask CUSUM, and highlight their head-start
features,alsocalledfastinitialresponse(FIR)forCUSUM.Amoredetailedexploration
of FIR for V-mask CUSUM is presented as this is its first appearance in a textbook. Its
underlying working principle is explained and two variants are presented.

24.1 INTRODUCTION

In conventional Shewhart control charts, only information contained in the last sample
observation is used in process monitoring. As a result they are insensitive to small
(about 1.5σ or less) but persistent shifts. To mitigate this deficiency, sensitizing rules,
also called ‘supplementary run rules’, have been used in conjunction with Shewhart
1
charts. However, Champ and Woodall showed that, even with such run rules, the
Shewhart chart is not as sensitive as the cumulative sum (CUSUM) control chart in
detecting small, sustained shifts in the process mean.
2
The CUSUM chart was first introduced by Page , and has been studied by many
authors. 3−5 Inthischapter,theapplicationoftheCUSUMchartformonitoringchanges
in the process mean with fast initial response (FIR) is presented. The results can be
extended to enable CUSUM charts to be used to monitor other parameters. To detect
shifts in the process mean, the CUSUM chart is implemented by summing deviations
from the nominal or target value. When this sum exceeds a specified threshold value,
one concludes that there has been a change in process mean. There are two ways
to represent CUSUMs, the tabular (sometimes called algorithmic) CUSUM, and the
V-mask, which is the original form of the CUSUM.

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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