用無母數迴歸的方法推估逐步應力加速衰變試驗資料的壽命分布

Abstract

為了節省時間及成本，工程師常使用逐步應力加速衰變試驗來研究高可靠度產品的壽命。本文針對逐步應力加速衰變試驗資料，提出一個加速衰變試驗模型，並假設應力的大小只會影響產品衰變的速度，並不會影響產品衰變的路徑。利用加速因子與應力間的關係，我們將逐步應力加速衰變試驗模型轉換成最大應力下的加速衰變試驗模型，並提出一個演算法來估計加速因子。最後，藉由Shiau and Chien (2000)的作法以推估產品的壽命分布。我們利用發光二極體的加速衰變試驗資料及已知的加速因子產生一組的逐步應力加速衰變試驗資料，並針對估計出的加速因子以驗證模型的合適度。此外，我們也利用已知函數來模擬出逐步應力加速衰變試驗資料，一方面驗證模型的合適度，另一方面也驗證推估壽命分布的方法。

In order to reduce time and the cost, engineers gradually adopt step-stress accelerated degradation tests (SSADT) to study the lifetime distribution of highly-reliable products. We propose a nonparametric regression stochastic process model for SSADT data. We assume that different stress levels only affect the degradation rate of the product characteristic, but not the degradation trend. With the relationship between the acceleration factors and the stress levels, we transform the SSADT data into a set of accelerated degradation test (ADT) data under the largest stress* level, and propose an algorithm to estimate the acceleration factors. Then, we can obtain the lifetime distribution of the product under usual use according to the method described in Shiau and Chien (2000). We generate a set of SSADT data by a set of ADT data of an LED (light emitting diode) product and a given set of acceleration factors to check the adequacy of the method. In addition, we also simulate two sets of SSADT data with known functions to check the adequacy of the method and the lifetime distribution estimate.