運用層級貝氏方法建構以失效測量為基礎的可靠度預測模式

Construction of Reliability Prediction Model by Using the Hierarchical Bayesian Approach

隨著現今科技的快速發展，顧客對產品品質的要求亦隨之不斷的提升，生產者必須在有限的時間內，評估並改善產品的可靠度，是以如何選擇一個適當的可靠度量測方法，對業界而言，是一個相當重要的問題。截至目前為止不管是業界或學界在進行資料分析時，大多採用傳統的統計分析技術，在本研究中，我們嘗試提出一個更一般化的資料分析技術－－層級貝氏模式（Hierarchical Bayesian Model）－－來量測產品衰退的過程。而在模式建構的過程中，我們利用 Markov Chain Monte Carlo （MCMC）來進行模式參數的估計。此外，論文中亦將 針對可靠度模式的失效時間分配型態進行建構並驗證該分配之適合度及其產品壽命預測值的準確性。

The reliability for some devices with few or no failures in their life tests becomes very hard to access if a traditional life test which records only time-to-failure was utilized. To solve this problem, the analysis of the over time degradation processes is always considered in the practical cases. In this paper, a degradation model was constructed by hierarchical Bayesian approach to represent the realization of the degradation processes. Based on the developed model, the failure times and the time-to-failure distribution can be estimated. For finding the appropriate estimates of model’s parameters, the Markov Chain Monte Carlo (MCMC) algorithm is applied. A fatigue crack growth data is used as an example for illustrating the modeling procedure. By specifying the coefficients, we successfully identify the heterogeneity varying across individual products. Moreover, the time-to-failure distribution is further estimated and the reliability bounds were constructed.