利用逐步加速壽命試驗資料評估Rayleigh產品的壽命績效指標

Assessing the Lifetime Performance Index of Rayleigh Products Based on Step-Stress Accelerated Life-Testing Data

葉廷軒(Tin-Shiuan Yeh)

指導教授 ： 李秀美

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.2018.00794

摘要

製程能力指標在現今已被廣泛使用在產品品質的監控，藉由指標值評估製程能力是否達到要求。在進行多數的製程能力指標時，都是假設產品的壽命服從常態分布，然而在實務上，產品的壽命並非服從常態分布，而可能是指數分布、韋伯分布或是Rayleigh分布等等。此外，由於產品的高可靠度，經過長時間的觀察仍不易觀察到失效產品，為了能更快速的收集到失效資料，因此本文使用逐步加速壽命試驗的方法，可以更快速的取得產品的失效資訊。
本研究假設產品的壽命服從Rayleigh分布，使用逐步加速壽命試驗資料，建立壽命績效指標之最大概似估計量C ̂_L並求得其漸近分布。在壽命規格下界L已知的情形下，應用信賴區間建立假設檢定程序來判斷壽命績效是否達到預定的能力水準，並使用兩個模擬範例說明如何應用本文所提出的信賴區間進行假設檢定程序。最後，本研究使用蒙地卡羅模擬程序生成資料，計算信賴區間的涵蓋率、最大概似估計量的均方誤 (MSE) 和平均試驗時間以評估本文所提方法的成效。

關鍵字

逐步加壽命試驗 ； Rayleigh分布 ； 最大概似估計量 ； 曝露模型 ； 產品合格率 ； 壽命績效指標 ； 信賴區間 ； 統計假設檢定

並列摘要

Process capability indices are commonly used to measure process potential and performance. Most of the process capability indices assume the lifetime of products are normally distributed. However, the lifetime of products generally may possess an exponential, Weibull or Rayleigh distribution. Additionally, high reliability makes it difficult to obtain failure products. Accelerate life- testing has often been used to yield information quickly.
In this paper, we assume the lifetime of products are Rayleigh distributed, using step-stress accelerated life-testing to obtain failure products to construct the maximum likelihood of lifetime performance index, C ̂_L, and the asymptotic distribution of C ̂_L. Given the lower specification limit, L, using the confidence interval of C ̂_L to construct hypothesis tests process to determine whether the lifetime performance reaches the expected level. Two examples are simulated to explain how the method in this paper work. Finally, Monte Carlo method are used to simulate the lifetime of products, calculating the coverage rate of the confidence interval of C_L, mean square error of C ̂_L and the average testing time to assess the result.

並列關鍵字

step-stress accelerated life-testing ； Rayleigh distribution ； maximum likelihood estimator ； exposure model ； product percent of pass ； lifetime performance index ； confidence interval testing procedure

參考文獻

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