摘要
高可靠度的時代為了提升產品競爭力，製造商必須即時地提供顧客有關產品可靠度的訊息，唯高可靠度產品之壽命推論，即使利用加速壽命試驗，亦很難在有限的測試時間內獲得產品失效資料。此時，若存在與壽命相關之品質特徵值 (quality characteristics, QC) 且會隨時間逐漸衰變，則可藉由衰變路徑來推估產品壽命相關資訊。因此，對於生產製造商而言，如何建構衰變模型及推論產品壽命分配，將顯得格外重要。文獻上有關衰變模型之建構，大都以隨機效應 (random effect) 或維納 (Wiener) 過程之衰變模型來描述之。然而對於產品的衰變路徑為單調遞增，如金屬疲勞，此時可以考慮伽瑪 (Gamma) 過程及逆高斯 (Inverse Gaussian) 過程來描述產品衰變路徑。故本論文主要針對逆高斯衰變模型探討以下兩個研究主題：
1. 當衰變路徑為逆高斯過程時，如何推導出產品壽命的分配及產品平均壽命。
2. 探討當逆高斯衰變模型與伽瑪衰變模型之間發生誤判，對於產品平均壽命 (mean-time-to failure, MTTF) 之估計準確度 (accuracy) 與精確度 (precision) 的影響。
具體來說，本文在大樣本下，探討當衰變路徑為逆高斯過程，卻被誤判為伽瑪過程時，逆高斯過程的平均 (mean) 參數太大或形狀 (shape) 參數太小時，對於產品平均壽命之估計準確度與精確度的影響皆是不容忽視的。另一方面，當衰變路徑為伽瑪過程，卻被誤判為逆高斯過程時，伽瑪過程的尺度 (scale) 參數太大或形狀參數太小，亦對產品平均壽命之估計準確度與精確度的影響頗巨。 此外，在小樣本或較短測試時間下，本文以模擬方式探討誤判對於產品平均壽命估計值之影響，其模擬結果與大樣本下的結論是差異不大。

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