Improvement on the Natural Estimators for Process Capability Indices

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  • 工程能力指数の点推定の改良について
  • コウテイ ノウリョク シスウ ノ テン スイテイ ノ カイリョウ ニ ツイテ

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Abstract

Process capability indices (PCI) are widely used in the activities of quality control. This paper discusses the improvement on the natural estimators for the basic PCI's, Cp, CpL, CpU and CpK. <br>Under the squared error loss function, Nagata (1995) showed that the natural estimator for Cp can be uniformly improved on by the estimator which is multiplied by some constant, and gave the degrees of improvement numerically. He also suggested by numerical calculations that the natural estimator for CpK cannot be improved on by the simple estimator which is multiplied by some constant.<br> In this paper it is shown that the natural estimator for CpU and CpL can be uniformly improved on by the estimators which are multiplied by some constant, and the degrees of improvement are given numerically. Furthermore, it is mathematically shown that the natural estimator for CpK cannot be improved on by any simple estimators which are multiplied by some constant when the sample size is larger than or equal to 7.

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