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False Alarm Probability Function of Cusum Charts
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Ken Nishina
Published/Copyright:
March 10, 2010
Abstract
In this paper, standard Cusum charts with head start value zero are compared with fast initial response (FIR) Cusum charts proposed by Lucas and Crosier (Technometrics 24: 199–205, 1982) from the viewpoint of the false alarm probability function. The focus in this comparison is conservativeness. The concept of conservativeness is based on the relationship between the in-control ARL and the false alarm probability function by regarding the Cusum statistic as a Markov process. The comparison shows that standard Cusum charts are conservative in contrast to FIR Cusum charts. Moreover, the concept of false alarm probability function provides an easy probabilistic interpretation of the in-control ARL.
Published Online: 2010-03-10
Published in Print: 2003-April
© Heldermann Verlag
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Articles in the same Issue
- On the Distribution of the Estimated Process Capability Index Cpmk
- Nonparametric Capability Indices
- Statistical Inference from Boyles' Capability Index
- Time Dependent Availability of K-out-of-N:G Systems with Exponential Failures and General Repairs
- A Note on Monotonic Probability Distributions
- A Note on the Murthy-Sarma Estimators of the Mean of the Normal Distribution for Small Samples
- Charts for Detecting Small Shifts
- False Alarm Probability Function of Cusum Charts
- The Validation of the Human Contribution to Quality: A Case Study at Lockheed Martin Aeronautics - Fort Worth
