韋伯分配參數估計法的比較與探討

A Comparison Study on Parameter Estimation Methods of Weibull Distribution

李佩熹(Pei-Hsi Lee) ； 童超塵(Chau-Chen Torng) ； 廖翊亨(Yi-Heng Liao) ； 鍾承利(Cheng-Li Jung)

《智慧科技與應用統計學報》 7卷2期 (2009/12) Pp. 25-36

https://doi.org/10.29807/JTITAS.200912.0002

摘要

在可靠度試驗中，韋伯分配為最常用的產品壽命分配，韋伯機率紙(WPP)和最大概似估計法(MLE)是韋伯分配常用的兩種參數估計方法。本研究探討這兩種方法評估估計的準確性，並透過模擬方法來分析樣本數與設限比例對於參數估計影響。從模擬結果發現，完整資料時建議採用WPP估計，當觀測資料為嚴重設限時，建議採用MLE來估計參數，而WPP法誤差太大，不建議使用。最後以TFT液晶顯示器模組壽命試驗的實際案例，說明本研究的結果的實際應用。

關鍵字

韋伯分配 ； 最大概似估計法 ； 韋伯機率紙

並列摘要

In reliability testing, weibull distribution is widely used to analyze the lifetime of electronic products. Weibull Probability Plot (WPP) and Maximum Likelihood Estimator (MLE) were often applied to estimate the weibull parameters. In this study, we focus on the accuracy evaluation of parameter estimation of WPP and MLE, then we use simulation approach to examine the estimating performance for different sample sizes and censoring ratios. From the simulation results, we suggest that WPP is a better choice in this complete data case. In the censoring data cases, MLE can obtain more accurate weibull parameter estimations than WPP. If the serious censoring ratio was occur, WPP would have higher estimating error, and we do not suggest WPP is used in this case. Finally, an accelerated testing example of TFT LCD module is illustrated the application of this study result.

並列關鍵字

Weibull distribution ； maximum likelihood Estimator ； Welbull probability plot