非線性隨機衰變模型之最適設計

Optimal Design of a Non-linear Degradation Test

10.29973/JCSA.200406.0002

曾勝滄(Sheng-Tsaing Tseng)；彭健育(Chien-Yu Peng)；劉家銘(Chia-Ming Liu)

高可靠度產品 ； 衰變試驗 ； 非線性隨機衰變模型 ； 最佳衰變試驗 ； 終止時間 ； Highly reliable products ； non-linear degradation model ； optimal degradation test

中國統計學報

42卷2期（2004 / 06 / 01）

115 - 130

繁體中文

針對高可靠度產品，如何選用適當的衰變模型(degradation model)來描述產品之衰變路徑，進而推估產品壽命是工業界十分重要之研究課題。本文採用非線性隨機衰變莫型來描述產品衰變路徑，同時在試測試成本不超過給定上限之前提下，以產品的(方程式省略)(p(上標th) percentile)及MTTF之估計量的變異數達極小化為目標，來決定衰變試驗所需的最適樣本數(sample size)、觀測頻率(ob-served frequency)以及終止時間(termination time)。文中以light emitting diode (LED)模擬次料為例，說明如何決定最佳衰變試驗及其敏感度分析。

Degradation tests are widely used to assess the lifetime distribution of highly re-liable products that are not likely to fail under a traditional life test. To conduct a degradation test, three key variables, observed frequency, sample size and termination time shall be given a special consideration. Tseng & Liao (1998) proposed a method to design a degradation test. Under the constraint that the total experimental cost does not exceed a pre-determined budget, the optimal decision variables are obtained by minimizing the variance of (abbreviate equation) (the estimated p(superscript th) percentile) of the product's lifetime istribution. The quasi-linear degradation path proposed by Tseng & Liao (1998); how-ever, may lead Var (abbreviate equation) to be extremely large. To overcome this difficulty, motivated from a real light emitting diode (LED) data, we propose a nonlinear diffusion process to model the degradation path and the corresponding optimal design can be solved successfully. Finally, we also use an example to illustrate the difference between these two approaches.

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