隨著產品可靠度之提升，傳統可靠度試驗已經不再有效，學者發現，當產品存在一品質特性，此品質特性與產品壽命高度相關時，則可利用此品質特性之衰退路徑來估計產品之可靠度，包括：產品平均壽命、產品剩餘可用壽命…等，此方法稱為衰變分析。
在衰變分析之相關文獻中，學者會選擇一衰退模型來配似產品之衰退資料，但是，衰退模型不一定跟此筆資料吻合，此時，就發生模型錯置，當發生模型錯置時，模型參數與產品平均壽命之估計會產生估計誤差。本研究即針對此類模型錯置問題，探討當模型錯置時，對模型參數估計與產品平均壽命估計產生之影響。
本研究以逆高斯過程模型與Wiener過程模型為例，假設當產品實際衰退路徑為逆高斯過程，卻用Wiener過程去配似時，以White(1982)與Pawitan(2001)之理論，推導模型參數與產品平均壽命估計之期望與變異，以此來計算模型錯置下之估計誤差效果，並以(Meeker and Escobar, 1998)範例中之雷射資料，證實用不同模型去配似資料，其產品平均壽命之估計值結果不同，及模型錯置下之估計誤差效果。
在後續敏感度分析章節中，驗證了前面所推導之模型參數與產品平均壽命估計之理論在大樣本下成立，並探討了實際衰退模型參數之增減對產品平均壽命估計之相對偏誤及相對變異產生之影響。結果顯示，模型參數a增加，產品平均壽命估計之相對變異會跟著增加；而當模型參數b增加，產品平均壽命估計之相對偏誤會減少，產品平均壽命估計之相對變異也會跟著降低。

In recent years, degradation analysis has widely used to access lifetime of highly reliable products. If there exists quality characteristics whose degradation paths can be related to the reliability of the product, then collecting degradation data can help with evaluating product reliability and lifetime. In this paper, motivated by laser data, we investigate the mis-specification effect on the prediction of product’s MTTF (mean-time-to-failure) when the wrong degradation model is fitted to data.
On the basis of the maximum likelihood under a wrong model theory, we first derive mean and variance of the product’s MTTF when the true degradation model comes from inverse Gaussian process, but is wrongly assumed to be Wiener process. In addition, laser data are used to illustrate the model mis-specification effect. A simulation study is carried out to evaluate the bias of the model mis-specification, using which we show that the simulation results are quite close to the theoretical ones. The result reveals that the effect on the accuracy of the product’s MTTF prediction depends on the value of critical value and the parameter of the inverse Gaussian process. In addition, the effects on the precision of the product’s MTTF prediction are influenced by the parameters of the inverse Gaussian process.

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