The Effect of Parameter Estimation on Upper‐sided Bernoulli Cumulative Sum Charts

Abstract

The Bernoulli cumulative sum (CUSUM) chart has been shown to be effective for monitoring the rate of nonconforming items in high-quality processes where the in-control proportion of nonconforming items (p 0 ) is low. The implementation of the Bernoulli CUSUM chart is often based on the assumption that the in-control value p 0 is known; therefore, when p 0 is unknown, accurate estimation is necessary. We recommend using a Bayes estimator to estimate the value of p 0 to incorporate practitioner knowledge and to avoid estimation issues when no nonconforming items are observed in phase I. We also investigate the effects of parameter estimation in phase I on the upper-sided Bernoulli CUSUM chart by using the expected value of the average number of observations to signal (ANOS) and the standard deviation of the ANOS. It is found that the effects of parameter estimation on the Bernoulli CUSUM chart are more significant than those on the Shewhart-type geometric chart. The low p 0 values inherent to high-quality processes imply that a very large, and often unrealistic, sample size may be needed to accurately estimate p 0 . A methodology to identify a continuous variable to monitor is highly recommended when the value of p 0 is low and the required phase I sample size is impractically large.

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