抽樣檢查是品質管制問題中主要研究的議題，如何決定壽命實驗的配置與允收臨界值將會影響整個抽樣實驗的結果，我們將在給定生產者風險與消費者風險下，建立一允收抽樣計畫使得整個實驗總成本小，並做數值的模擬分析與討論。 In traditional censoring schemes, surviving units can only be removed at the end of the life tests. However, in some practical situations, one has to remove surviving units at the points other than the final termination point. A life test of this type is called progressive censoring. Besides, in some life tests, we can only record whether a test unit fails in an interval instead of measuring failure time exactly. Hence, the test units are inspected intermittently. This type of inspection is called interval censoring. In this thesis, we combine progressive censoring and interval censoring to develop a progressive type-I interval-censoring scheme. We will focus on two designing problems of progressive type-I interval-censoring life test with exponential failure time distribution.
The first problem is how to design an appropriate life test that would result in the optimal estimation of the mean life. Simply put, more test units, more test time, and more number of inspections will generate more information, which improves the precision of estimates. However, one practical problem arising from designing a life test is the restricted budget of experiment. The size of budget always affects the decisions of number of test units, number of inspections and length of inspection intervals and hence, affects the precision of estimation. In this study, we will use the nonlinear mixed integer programming to obtain the optimal settings of a progressive type-I interval-censored life test by minimizing the asymptotic variance of mean life under the constraint that the total experimental cost does not exceed a pre-determined budget. An example is discussed to illustrate the proposed method and sensitivity analysis is also studied.
The second problem is to establish the acceptance sampling plans with cost consideration. We will construct acceptance sampling plans which have the minimum experimental cost under given consumer''s and producer''s risks. Some numerical examples and studies are performed to illustrate the proposed approach.
