指數分配產品的壽命績效指標在逐步型I區間設限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 Exponential distribution under progressive type I interval censoring

鄭竣哲(Jyun-Jhe Jheng)

指導教授 ： 吳淑妃

淡江大學/商管學院/統計學系碩士班/碩士(2017年)

https://doi.org/10.6846/TKU.2017.00074

摘要

近年來，科技的進步，許多高科技產品像是平板、智慧型手機等等，皆為消費者喜愛，而消費者對產品的品質要求則更加嚴格，因此提升產品製程的能力是品管上很重要的工作。在實務上，已經發展了很多方法來評估產品的品質能力，製程能力指標(process capability indices, PCIs)就是其中一種方法。
本研究假設產品的壽命服從指數分配時，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求得其漸近分配。在規格下限L已知的情形下，使用此估計量及兩種拔靴法發展出三個假設檢定程序以判定壽命績效是否達到預定的能力水準。最後，我們用兩個數值實例和一個模擬例子去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 ； 指數分配 ； 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, consumers are in the pursuit of more stringent product quality requirements for many high-tech products such as tablet, smart mobile phones, etc. In practice, many researchers have developed a variety of methods to assess the quality of the product and the method of process capability indices (PCIs) is one of them.
This research is focusing on the lifetime of products following the Exponential 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, two practical examples and a simulation example 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 ； exponential distribution ； maximum likelihood estimator ； bootstrap ； process capability index ； testing procedure

參考文獻

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