本論文探討四個有關低不良率產品之統計問題, 最終目地在提升這些產品之品質。

第一個課題探討如何在工程管制的機制下, 同時呈現統計製程管制圖。
本課題的困難在於若每個製程批次採用了工程管制的方式來調整參數, 未調整前的原始數據已不存在。本研究藉由估計相關參數, 進而估計原始數據, 以還原工程管制調整前的製程數據。

第二個課題探討如何估計樹酯式變壓器的壽命分配。 本課題的困難在於目前沒有足夠的樹酯式變壓器壽命資料。本研究分析樹酯式變壓器的核心部分 -- 樹酯。 以 Generalized Gamma - Arrhenius 作為壽命與壓力模式來估計樹酯壽命。

第三主題探討如何估計高可靠度的電子傳輸二元資料之傳位元錯誤率。傳統的模擬法沒有效率, 因為在高可靠度的電子傳輸設備中, 位元錯誤率的機率很小,
因此在有限的時間內無法得到足夠的錯誤訊息資料。本研究結合模擬方式與重點抽樣去降低模擬的時間或樣本數, 所估計出的位元錯誤率有比較好的統計特性。

第四個課題探討如何建立在參數 p 值很小時之伯努力分配參數 p 之信賴區間。 本課題的特例是探討第一個課題中高可靠度的電子傳輸二元資料之傳輸錯誤率之信賴區間。本課題的困難在於伯努力分配的二元離散性, 使得傳統的信賴區間之覆蓋率不穩定。

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