Weibull分配產品的壽命績效指標在逐 步型Ι區間下之檢定程序的檢定力分析

The power analysis of the testing procedure for the lifetime performance index of products with Weibull distribution under progressive type I interval censoring

吳奇翰(Chi-Han Wu)

指導教授 ： 吳淑妃

淡江大學/商管學院/統計學系碩士班/碩士(2018年)

https://doi.org/10.6846/TKU.2018.00525

摘要

近年來，隨著科技的進步，許多電子資訊產品像是平板、智慧型手機等等越來越普及，而消費者對這類產品除了價格要低，品質也要求越高，因此如何提升產品製程的能力是品管上很重要的工作。目前，已經發展了許多方法評估產品的品質能力，而製程能力指標(process capability indices, PCIs) 已經被廣泛地應用在評估製程的績效，進而提升產品品質及製程能力。
　　本研究假設產品壽命服從Weibull分配時，在逐步型I區間設限下，計算出壽命績效指標CL之最大概似估計量並求其漸近分配。在規格下限L已知的情況下，使用此估計量及兩種拔靴法發展三個檢定程序以判定壽命績效指標是否達到預期的要求水準。最後，用一個數值例子和一個模擬例子說明如何使用本研究所提出的檢定程序。

關鍵字

逐步型I 區間設限 ； Weibull 分配 ； 最大概似估計量 ； 拔靴法 ； 製程能力指標 ； 檢定程序

並列摘要

In recent years, with the advancement of science and technology, many electronic information products such as tablets, smart phones, etc. have become more and more popular, and consumers are demanding more and more quality in addition to the price, so how to improve The ability to manufacture products is an important part of quality control. At present, many methods have been developed to evaluate the quality capabilities of products. Process capability indices (PCIs) have been widely used to evaluate the performance of processes and improve product quality and process capability.　　
This research is focusing on the lifetime of products following the Weibull distribution. The maximum likelihood estimator is used to estimate the lifetime performance index (CL) based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also investigated. We use this estimator and two kinds of bootstrap methods to develop three kinds of hypothesis testing algorithmic procedure in the condition of known lower specification limit L. Finally, we give one practical example and one simulation example to illustrate the use of the proposed testing algorithmic procedure to determine whether the process is capable.

並列關鍵字

progressive type I interval censoring ； Weibull distribution ； maximum likelihood estimator ； bootstrap ； process capability index ； testing procedure

參考文獻

[1]Boyles, R. A. (1991), The Taguchi capability index, Journal of Quality Technology, 23(1), pp. 17–26.

[2]Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988), A new measure of process capability: Cpm, Journal of Quality Technology, 20(3), pp. 162-175.

[3]Cohen, A. C. (1963), Progressively Censored Samples in Life Testing,Technometrics, 5(3), pp. 327–339.

[4]Efron, B. (1982), The Jackknife, the Bootstrap and Other Re-sampling Plans, CBMS-NSF Regional Conference Series in Applied Mathematics, 38, SIAM, Philadelphia, PA.

[5]Hall, P. (1988), Theoretical comparison of bootstrap confidence intervals, Annals of Statistics, 16, pp. 927–953.