類神經網路於完備資料之韋伯與對數常態分配之判定

Discrimination between Weibull and Lognormal Distributions for Complete Data via Artificial Neural Network

于鴻福(Hong-Fwu Yu) ； 黃耿輝(Geng-Huei Huang)

《高雄師大學報：自然科學與科技類》 24期 (2008/06) Pp. 43-56

https://doi.org/10.7060/KNUJST.200806.0043

摘要

韋伯(Weibull)分配與對數常態(lognormal)分配，可用以描述大多數電子產品之壽命，惟兩者極為相似，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，在資料分析時，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。本研究擬針對完備資料(complete data)，利用類神經網路(artificial neural network)來探討此二種分配之判定問題。模擬結果顯示，在大樣本(n=60, 80, 100)下的正確辨識率幾乎都在0.92以上，而在中樣本(n=30, 40)時，正確辨識率約介於0.81~0.88之間，然而在小樣本(n=15, 20, 25)時其正確辨識率約介於0.72~0.81之間。此外，本文亦針對上述八種樣本數所得之模擬結果與以最大概似比(ratio of maximized likelihood; RML)所得的結果進行比較。數值結果顯示，在樣本數n=25, 40, 60, 80, 100時，本研究所提出的方法較RML法的辨識效率為佳；而當n=15, 20, 30時，則是RML法的辨識效率為佳。由此可知：本研究所提出之方法並不比RML法遜色。

關鍵字

分配的誤判 ； 韋伯分配 ； 最大概似比 ； 對數常態分配 ； 類神經網路

並列摘要

Weibull and lognormal distributions are two of the most appropriate lifetime distributions for electronic products. In practical applications, these two distributions are much alike and may fit the lifetime data well. However, this usually results in mis-discrimination between these two distributions in lifetime data analysis and then leads to a significant difference between their reliability predictions. The main purpose of this paper is to deal with model discrimination between there two distributions for complete data via an artificial neural network. The simulation results appear that the percentages of correct discrimination for large sample sizes (n=60, 80, 100) are greater than 0.92, those for adequate sample sizes (n=30, 40) are about 0.81~0.88, but those for small sample sizes (n=15, 20, 25) are about 0.72~0.81. Besides, to evaluate the efficiency of the proposed method, a comparison of the proposed method to the ratio of maximized likelihood (RML) method is made with respect to the eight sample sizes mentioned above. It is observed, from the numerical results, that the proposed method has a better performance in discrimination efficiency for n=25, 40, 60, 80, 100 than the RML method, but has a worse performance for n=15, 20, 30. This indicates that the proposed method is not inferior to the RML method.

並列關鍵字

mis-discrimination ； Weibull distribution ； lognormal distribution ； artificial neural network ； ratio of maximized likelihood

參考文獻

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