層級貝氏類神經網路方法在建構可靠度預估模式上之應用

Reliability Prediction Based on Degradation Measurements Using Hierarchical Bayesian Neural Network Approach

邱志洲(Chih-Chou Chiu) ； 廖子毅(Chih-Yi Liaw) ； 高淩菁(Ling-Jing Kao) ； 鐘振聲(Chen-Sheng Chung)

《品質學報》 13卷3期 (2006/09) Pp. 221-240

摘要

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，而為了滿足消費者對產品品質日益著重的要求，許多廠商開始致力於製造出更好、更具可靠性的產品。由於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，而在這樣統計模式和動態過程建構程序中，通常都會先假設參數估計的抽樣分配，或是參數檢定的統計量是在資料屬性為隨機或者是資料乃根據某一機率模式所產生的前提下所建構而成的。換言之，傳統的分析方法是在尚未得到樣本觀察值之前，就已經將參數的樣本分配假設為某一種機率分配，而沒有真正針對實際觀察值進行考慮，因此也造成在這樣假設下所進行的所有推論必須架構在大樣本或是樣本趨近於無限大的限制條件下始能成立。
在本研究中，我們嘗試提出一個更一般化的資料分析技術－層級貝氏類神經網路模式(Hierarchical Bayesian Neural Networks model, HBNN)-來進行失效時間的預測。而在模式建構的過程中，我們利用近年來廣為人採用的模擬方法Markov Chain Monte Carlo(MCMC)來進行模式中參數的估計。此外，為了更進一步驗證所提模式的有效性以及比對模式的預測能力，我們也分別使用了層級貝氏方法(Hierarchical Bayesian Model, HBM)及類神經網路(Neural Networks, NN)來進行失效時間預測模式的建構。最後本研究也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。

關鍵字

層級貝氏類神經網路模式 ； 衰退過程 ； 失效時間 ； 馬可夫鏈蒙地卡羅

並列摘要

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. The realization of the degradation processes is expected to be represented by the constructed degradation model. Based on the developed models, the failure times for devices and the time-to-failure distribution can be estimated. In this paper, a hierarchical Bayesian neural networks model (HBNN) with autocorrelated residuals is proposed to construct a broad class of degradation models. Markov Chain Monte Carlo (MCMC) algorithm is used to estimate the proposed model. A fatigue crack growth data is used as an example for illustrating the modeling procedure of HBNN. By specifying the random effect distribution of the coefficients in the HBNN, we successfully identify the heterogeneity varying across individual products. In additions, the prediction intervals of future degradation processes for evaluating the prediction accuracy are provided. To demonstrate the effectiveness of the proposed HBNN model, two alternative models constructed by Hierarchical Bayesian (HB) and neural network (NN) approaches are applied to conduct the failure time prediction. The results show that our proposed HBNN model can not only identify the heterogeneity across various paths successfully, but also make an effective failure time prediction. Moreover, the time-to-failure distribution is further estimated and the reliability bounds have been constructed.

並列關鍵字

Hierarchical Bayesian Neural Network Model ； Degradation Process ； Failure Time ； Markov Chain Monte Carlo

參考文獻

Akama M.(2002).Bayesian analysis for the results of fatigue test using full-scale models to obtain the accurate failure probabilities of the Shinkansen vehicle axle.Reliability Engineering and System Safety.75,321-332.

Bernardo, J. M.,Smith, A. F. M.(1994).Bayesian Theory.John Wiley & Sons.

Bishop, C. M.(1993).Curvature-driven smoothing: A learning algorithm for feed-forward networks.IEEE Transactions on Neural Networks.4(5),882-884.

Bogdanoff, J.L.,Kozin, F.(1984).Probabilistic Models of Cumulative Damage.New York:John Wiely.

Breiman, Leo(2001).Statistical Modeling: The Two Cultures.Statistical Science.16(3),199-231.