對於第二個最佳設計的問題，我們結合逐步設限與第一失敗設限，提出以逐步第一失敗設限方法所收集的設限資料來設計可靠度抽樣計畫。在給定生產者風險、消費者風險與實驗成本預算限制下，提出三個不同的最佳化準則來得到最適的實驗配置與允收臨界值，並做數值研究、蒙地卡羅模擬與敏感度分析之討論。 In traditional censoring schemes, type-I and type-II censoring are often used in life-testing. To shorten experiment time and reduce experiment cost, failures are collected only before the censoring time. There are many scenarios that we cannot avoid removing some surviving units early from the life test. Such a life test that allows units removed before the termination of the experiment is called progressive censoring. In this dissertation, we consider the progressive censoring and assume the lifetime data are from a Weibull distribution. Based on this type of censored data, we discuss two important optimal design problems in practice: length of warranty and reliability sampling plan.
In an intensely competitive market, one way by which manufacturers attract consumers to their products is to provide warranties on the products. Consumers are willing to purchase a high-priced product only if they can be assured about the product''s reliability. A longer warranty period usually indicates better reliability. However, offering an unlimited warranty is unrealistic because maintaining such a policy needs very high cost. We first derive the maximum likelihood estimator and Bayes estimator for the parameters of the Weibull distribution and then obtain the one-sample and two-sample prediction interval. For the optimal design problem, we consider a combined warranty which is a combination of free-replacement and pro-rata policies. We propose a utility function to determine the optimal warranty length which maximizes the expected value of the utility function. Two examples are discussed to illustrate the application of the proposed method.
For the second problem, we combine the progressive censoring and first-failure censoring to develop a progressive first-failure censoring. Under the progressive first-failure censoring, we propose an approach to establish reliability sampling plans which minimize three different objective functions under the constraint of total cost of experiment and given consumer''s and producer''s risks. Some numerical examples, Monte Carlo simulation and the sensitivity analysis are performed to demonstrate the proposed approach.