類神經網路於完備與型Ⅱ設限資料之韋伯與對數常態分配判定的應用

Discrimination between Weibull and lognormal distributions for complete and type II censored data via artificial neural network

黃耿輝(Geng-Huei Huang)

指導教授 ： 于鴻福

國立虎尾科技大學/管理學院/工業工程與管理研究所/碩士(2006年)

https://doi.org/10.6827/NFU.2006.00010

摘要

韋伯 (Weibull) 分配與對數常態 (lognormal) 分配，兩者極為相似，於資料分析時常造成分配的誤判，而導致後續可靠度推估時的嚴重偏差。因此，如何正確選擇適當的壽命分配，是可靠度工程師常需面對的問題。本研究針對完備資料 (complete data) 和型Ⅱ (type Ⅱ) 設限資料 (censored data)，利用類神經網路 (artificial neural network) 來探討此二種分配之模型判别問題。其中關於型II設限的部份，本研究亦提出一種資料的修補方法，將設限資料補成「虛擬完備資料 (pseudo-complete data)，再針對虛擬完備資料進行判別，以探討在不同樣本設限比例下的判別正確率。在四種不同樣本組數 (N=5000, 10000, 20000, 30000) 之訓練資料庫，與八種不同樣本數 (n=15, 20, 25, 30, 40, 60, 80, 100) 的組合下進行模擬分析。模擬結果顯示：(a) 在完備資料方面，本研究提出兩種模擬程序，在小樣本 (n=15, 20, 25) 時，兩種方法之正確辨識率互有優劣，約介於0.72~0.81之間；在n=30, 40時的辨識正確率介於0.81~0.89；至於大樣本高達0.92~0.89。(b) 在設限資料方面，在樣本數 (n=60, 80, 100) 時的正確辨識率大都在0.8以上；n=30, 40 時的辨識正確率約介於0.70~0.81；然對於小樣本 (n=15, 20, 25) 且觀測比例在0.7以下者，正確辨識率有些甚至會低於0.6。

關鍵字

韋伯分配 ； 對數常態分配 ； 型 II 設限資料 ； 類神經網路 ； 模型判别

並列摘要

Weibull and lognormal distributions are two of the most appropriate lifetime distributions for highly reliable productions, especially for electronic production. In practical applications, Weibull and lognormal distributions are much alike and may fit the lifetime data well. However, their predictions may lead to a significant difference. The main purpose of this paper is to deal with model discrimination between these two distributions for complete and type II censored data via artificial neural network. As to type II censored data, we propose a remedial method to remedy the censored data as a “pseudo-complete” data. Then model discrimination is conducted by treating the “pseudo-complete” data as a “real” complete data. The simulation results appear: (1) For complete data, the percentages of correct discrimination for small sample sizes are about 0.72~0.81, those for adequate sample sizes are about 0.81~0.89, and those for large sample sizes almost achieve 0.92~0.98. (2) For type II censored data, the percentages of correct discrimination for large sample sizes are almost greater than 0.8, those for adequate sample sizes are about 0.70~0.81; while some of those for small sample sizes with observed rates equal to or less than 0.7 are smaller than 0.6.

並列關鍵字

Weibull distribution ； lognormal distribution ； model discrimination ； artificial neural network ； type II censored data

參考文獻

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