| 摘要: | 本計畫將探討關於一次性(或破壞性)試驗資料之貝氏可靠度分析。所謂一次性試驗或破壞 性試驗是指欲取得產品壽命資訊必須將產品予以破壞性的測試方能取得資料，如電火工品或 安全性產品等。此類產品經測試後均無法再度使用，且無法得知其確實壽命，因此傳統的壽 命試驗為這類產品將很難得到精確的壽命評估。但由於高生產成本和一次性使用特性，其可 靠度評估在控制產品品質上更具重要性。另一方面，經由觀察與壽命息息相關且隨時間漸減 的產品特徵值—即產品的衰變資料—在壽命資料無法取得時或許仍能提供相當的訊息。同樣 的在一次性產品中，衰變資料的取得也必須先將產品進行破壞測試，此即所謂的一次性或破 壞性衰變試驗。衰變分析之最終目的是得到產品失效時間的統計推論，通常藉由衰變模型與 失效時間的關係，推導相對應失效時間分布並建構所謂的虛擬壽命以探討其適合度分析。然 而在一次性試驗中由於各測試產品分別只有一筆觀測資料，在文獻上只著重其資料分析，對 其破壞性衰變模型適合性的評估卻付之闕如，原因不外乎是可辨別性之問題造成模型參數多 過資料本身，此時結合來自資料以外的其他先驗資訊的貝氏統計方法應是最為可行的分析方 式。本三年期子計畫即將探討關於一次性或破壞性衰變試驗資料之貝氏可靠度推論和適合度 檢定問題。 本子計畫第一年，擬由最簡單的線性衰變模型出發，但其中每一測試單位只有單筆觀測 資料。藉由貝氏方法調整未知參數之先驗分布的超參數來預測各測試產品的虛擬壽命，進而 提出一合理的適合度檢定。另外，加速破壞衰變試驗能更有效的收集與到較有意義的衰變資 料，因此本計畫的第二年，預期將第一年的研究結果推廣至加速破壞衰變試驗模型中。而計 畫的第三年將考慮把結果應用到更一般化的非線性衰變路徑中，除了基本的貝氏可靠度分析 中關於失效分布的推估外，適合度檢定是最終的目標。 ;In this proposal, we will discuss the Bayesian reliability inference for the destructive device (or so called the one-shot device) that can be tested only once and can never be used anymore after the test. Since we cannot adjudge failure of the units from their exterior, traditionally, we can observe the conditions only by testing them in order to accrue inference on reliability. After successful testing, the device cannot be used any further; while if the test fails, it is not known when the device failed either. As a result, it is uneasy to collect useful data to make accurate reliability inference from conventional life tests. On the other hand, useful reliability information is available from degradation data when there are few or even no failures. Similarly, degradation measurement process destroys or changes the physical/mechanical characteristics of destructive devices and thus only one meaningful measurement can be taken on each test unit. In typical degradation analysis, a specified statistical model is an essential assumption to formulate and analyze the observed data. The ultimate life time distribution of the device is obtained by converting from the degradation model, and used to construct the pseudo-failure time of each test unit for goodness of fit. However, in destructive tests, since each test unit can only provide one observation, none of the research has discussed on the issue of goodness of fit in addition to data analysis due to the model identifiability problem. Bayesian analysis is therefore a reasonable alternative for such concern. In this three-year subproject, we will discuss the Bayesian reliability inference in destructive degradation analysis, not only to make general statistical inference, but also to focus on the issue of goodness of fit. In the first year, we will begin with the simplest linear degradation model while each unit only has one observation. By adjusting the hyperparameters of the prior distributions, pseudo-failure time of each test unit will be developed and tested for goodness of fit. Degradation tests are often accelerated by testing at higher than usual levels of accelerating variables like temperature to receive more meaningful data. Therefore, we will extend our first year’s results to the accelerated destructive models (ADDT) in the second year. In the last year of this subproject, nonlinear Bayesian ADDT models will be considered to complete this project. In all cases, Bayesian inference on the failure time distribution should be developed as well as the tests for goodness of it. |
