在這產品可靠度非常高的時代，為了提升產品競爭力，製造商必須對自身產品的可靠度資訊有十足的掌握。對於收集可靠度訊息的方式有很多，若產品存在一品質特徵值與壽命有相關，且會隨著時間而漸漸衰退，此時便可實驗收集其衰退路徑來推估其產品壽命相關資訊，稱之為衰退實驗。因此，對製造商而言，在衰退實驗中如何建構衰退模型及如何在有限的資源下提升估計產品壽命的效率，已成為製造商重要的課題之一。文獻上有關衰退模型的建構，大都以Wiener過程或Gamma過程之衰退模型來描述，近年來的文獻Inverse Gaussian過程也常被用來做衰退模型的建構。故本論文主要針對Inverse Gaussian衰退模型探討當Inverse Gaussian模型與Wiener模型之間發生錯置，對於產品平均壽命之估計準確度及精確度的影響、當Inverse Gaussian模型與Wiener模型之間發生錯置，對於壽命分配之第p百分位數的估計準確度及精確度的影響及如何以一實驗設計的手法，使得在模型錯置的衰退實驗下，二者估計的精確度能為最佳。本研究以Tsai et al. (2011)為基礎，討論了不同的模型錯置會有何不同的影響，並更進一步探討如何透過實驗設計來使此影響最小化。
本研究找出模型錯置下之估計準確度無法以實驗設計控制其影響，但可設計一演算法對精確度進行實驗設計使得精確度最佳並找出最佳衰退實驗計畫。故本研究在資源有限下針對平均壽命之估計精確度及壽命分配之第p百分位數的估計精確度進行最佳實驗設計，結果可看出此演算法可有效提升精確度，由敏感度分析發現對最佳衰退實驗計畫有一定影響程度之成本。
關鍵字：Inverse Gaussian過程、Wiener過程、模型錯置、衰退實驗設計

In this era of high reliability, in order to enhance product competitiveness, manufacturers must have a good understanding of the reliability information of their products. There are many ways to collect reliability information. If there is a quality characteristic related to the life of the product, and it will gradually decline with time, then you can collect its degradation data from the experiment to estimate the life-related information of the product. This is called degradation experiment. Therefore, it has become an important issue for manufacturers to construct a degradation model in a degradation experiment and how to improve the efficiency of estimating product’s MTTF(mean-time-to-failure) under limited resources. The degradation models, Wiener degradation process or gamma degradation process, are mostly used to describe the degradation path in the literature. In recent years, inverse Gaussian process has also been used to construct the degradation model. Therefore, this paper focuses on the model mis-specification between inverse Gaussian degradation process and Wiener degradation process. We investigate the impact on the accuracy and the precision of the product's MTTF and the pth percentile of the lifetime distribution of the product. Furthermore, we show how to conduct a degradation experiment through experimental design to make the precision of the estimation can be optimal under the model mis-specification. Based on Tsai et al. (2011), this study discusses the effect of model mis-specification and further explores how experimental design can minimize this impact.
The result of this study is that the accuracy of the estimation of the model mis-specification cannot be controlled by experimental design, but an algorithm can be designed to conduct a degradation experiment to optimize the precision and carry out the optimal test plan. Therefore, this study reveals the optimal design of degradation experiment for the precision of the estimation of the product’s MTTF and the precision of the estimation of the pth percentile of the lifetime distribution under the limited resources. The results show that the algorithm can effectively improve the precision. By sensitivity analysis, there are some costs that will have some impact on optimal test plan.

Key words: inverse Gaussian process, Wiener process, model mis-specification, the
design of a degradation experiments

中文文獻
[1] 許雅宣（2019）。模型錯置下預估產品平均壽命的影響分析─以Inverse Guassian process 與Wiener process為例（未出版碩士論文）。國立成功大學，台南市。

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