Weibull分配產品的壽命績效指標在逐步型I區間設限下之統計檢定程序

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

林孟儒(Meng-Ju Lin)

指導教授 ： 吳淑妃

淡江大學/商管學院/統計學系碩士班/碩士(2014年)

https://doi.org/10.6846/TKU.2014.00905

摘要

最近幾年來，由於高科技產品，例如:智慧型手機和平板電腦等的盛行，消費者對於產品的品質要求越加嚴格，在產業高度競爭的時代，廠商該如何提升製程能力，是品管上很重要的工作。在實務上，製程能力指標(process capability indices, PCIs)被廣泛應用在評估製程的績效，進而不斷地提升產品品質及製程能力。
本研究假設產品的壽命服從Weibull分配時，在逐步型I區間設限下，計算出壽命績效指標 之最大概似估計量，並探討其漸近分配與檢定力函數，在規格下限L已知的情形下，利用此估計量及兩種拔靴法，發展出三個新的假設檢定程序，以判定壽命績效是否達到預期的能力水準。最後，我們用兩個數值實例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, due to the prevalence of smart phones and tablet PCs, the consumers require more stringent product quality in the highly competitive commercial market. In practice, process capability indices (PCIs) has been widely used to assess the performance of the process, and then continues to be employed to improve the 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 (C_L) 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 new hypothesis testing algorithmic procedure in the condition of known lower specification limit L. Finally, two practical examples are given to illustrate the use of this 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

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