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Comparisons of the Performance with Bayes Estimator and MLE for Control Charts Based on Geometric Distribution

기하분포에 기초한 관리도에서 베이즈추정량과 최대우도추정량 사용의 성능 비교

  • Hong, Hwiju (Department of Applied Statistics, Chung-Ang University) ;
  • Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University)
  • 홍휘주 (중앙대학교 응용통계학과) ;
  • 이재헌 (중앙대학교 응용통계학과)
  • Received : 2015.06.05
  • Accepted : 2015.09.21
  • Published : 2015.10.31

Abstract

Charts based on geometric distribution are effective to monitor the proportion of nonconforming items in high-quality processes where the in-control proportion nonconforming is low. The implementation of this chart is often based on the assumption that in-control proportion nonconforming is known or accurately estimated. However, accurate parameter estimation is very difficult and may require a larger sample size than that available in practice for high-quality process where the proportion of nonconforming items is very small. An inaccurate estimate of the parameter can result in estimated control limits that cause unreliability in the monitoring process. The maximum likelihood estimator (MLE) is often used to estimate in-control proportion nonconforming. In this paper, we recommend a Bayes estimator for the in-control proportion nonconforming to incorporate practitioner knowledge and avoid estimation issues when no nonconforming items are observed in the Phase I sample. The effects of parameter estimation on the geometric chart and the geometric CUSUM chart are considered when the MLE and the Bayes estimator are used. The results show that chart performance with estimated control limits based on the Bayes estimator is generally better than that based on the MLE.

Acknowledgement

Supported by : 한국연구재단

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