兩參數(shù)BS疲勞壽命分布的擬合檢驗以及環(huán)境因子的近似區(qū)間估計

王蓉華 顧蓓青 徐曉嶺

摘 要： 兩參數(shù)BirnbaumSaunders（BS）疲勞壽命分布是概率物理方法中的一個重要的失效模型，它比常用的壽命分布，如威布爾分布、對數(shù)正態(tài)分布，更適合描述某些由疲勞引起失效的產(chǎn)品的壽命規(guī)律，其主要應(yīng)用于對疲勞失效以及電子產(chǎn)品性能退化失效的分析研究.在全樣本場合，利用徐曉嶺等的研究中刻度參數(shù)的對數(shù)矩估計的性質(zhì)，構(gòu)造了兩參數(shù)BS疲勞壽命分布擬合檢驗的檢驗統(tǒng)計量，并通過3個實(shí)例說明擬合檢驗方法的應(yīng)用性.給出了兩種求兩參數(shù)BS疲勞壽命分布環(huán)境因子近似區(qū)間估計的新方法，通過Monte Carlo模擬與原有的方法進(jìn)行了比較，發(fā)現(xiàn)利用對數(shù)正態(tài)近似的方法優(yōu)勢明顯，并通過一個算例說明方法的應(yīng)用性.

關(guān)鍵詞： 兩參數(shù)BirnbaumSaunders（BS）疲勞壽命分布; 刻度參數(shù); 形狀參數(shù); 對數(shù)矩估計; 擬合檢驗; 環(huán)境因子

中圖分類號： O 213? 文獻(xiàn)標(biāo)志碼： A? 文章編號： 10005137（2019）04033908

Abstract： Twoparameter BirnbaumSaunders （BS） fatigue life distribution is an important failure model in the probability physical methods.It is more suitable for describing the life rules of fatigue failure products than common life distributions such as Weibull distribution and Lognormal distribution.Besides，it is mainly applied to analytical research about fatigue failure and degradation failure of electronic product performance.Based on the full sample，the test statistics are constructed for fitting test of twoparameter BirnbaumSaunders fatigue life distribution by using the property of logarithmic moment estimation of scale parameter proposed in XUs reseaching.Three examples are given to illustrate the application of fitting test method.Besides，two new methods of approximate interval estimation of environmental factor are given for twoparameter BS fatigue life distribution，which is compared with the original method through Monte Carlo simulations.We find that the advantage of logarithmic normal approximate method is obvious，and the example is given to illustrate the application of the method.

Key words： twoparameter BirnbaumSaunders （BS） fatigue life distribution; scale parameter; shape parameter; logarithmic moment estimation; fitting test; environmental factor

參考文獻(xiàn)：

[1] BIRNBAUM Z W，SAUNDERS S C.A new family of life distribution[J].Journal Applied Probability，1969，6（2）：319-322.

[2] WANG B X，WANG L L.Estimation for the BirnbaumSaunders fatigue life distribution [J].Journal of East China Normal University （Natural Science），1996 （4）：10-15.

[3] WANG B X，WANG L L.Statistical analysis for the BirnbaumSaunders fatigue life distribution under censored testing [J].Chinese Journal of Applied Probability and Statistics，1996，12（4）：369-375.

[4] WANG R H，F(xiàn)EI H L.Statistical analysis for the BirnbaumSaunders fatigue life distribution under type II bilateral censoring and multiply type II censoring [J].Chinese Quarterly Journal of Mathematics，2004，19（2）：126-132.

[5] SUN Z L.The confidence intervals for the scale parameter of the BirnbaumSaunders fatigue life distribution [J].Acta Armamentar II，2009，30（11）：1558-1561.

[6] SUN Z L.Confidence limits for the environment factor of the BirnbaumSaunders distribution [J].Structure & Environment Engineering，2012，39（4）：51-55.

[7] WANG B X.Generalized interval estimation for the BirnbaumSaunders distribution [J].Computational Statistics and Data Analysis，2012，56：4320-4326.

[8] XU X L，WANG R H，GU B Q.Two notes of statistical analysis about twoparameter BirnbaumSaunders fatigue life distribution [J].Journal of Zhejiang University （Science Edition），2016，43（5）：539-544.

[9] SUN Z L.Regression estimation of the parameters of the BirnbaumSaunders fatigue life distribution [J].Acta Armamentar II，2010，31（9）：1259-1262.

[10] SUN Z L.Statistical inference of variation coefficinet for fatigue life distribution [J].Quality and Reliability，2013（1）：13-15.

[11] XU X L，WANG R H，GU B Q.Statistical analysis of twoparameter BirnbaumSaunders fatigue life distribution under full sample [J].Journal of Zhejiang University （Science Edition），2017，44（6）：692-704.

[12] XU X L，WANG R H.Probability and Mathematical Statistics [M].Shanghai：Shanghai Jiao Tong University Press，2013：278-279.

[13] BALAKRISHNAN N，KANNAN N，KUNDU D.On the hazard function of BirnbaumSaunders distribution and associated inference [J].Computational Statistics and Data Analysis，2008，52：2692-2702.

[14] BALAKRISHNAN N，KUNDU K，NG H K T.Modified moment estimation for the twoparameter BirnbaumSaunders distribution [J].Computational Statistics and Data Analysis，2003，43：283-298.

[15] LEMONTE A J，CORDEIRO G M.The exponentiated generalized BirnbaumSaunders distribution [J].Applied Mathematics and Computation，2014，247：762-779.

[16] ZHOU Y Q，WENG Z X，YE X T.Study on accelerated factor and condition for constant failure methanism（I）：the case for lifetime is a random variable [J].Journal of Systems Engineering and Electronics，1996 （1）：55-67.

[17] SUN Z L.A condition for constant failure methanism [J].Electronic Product Reliability and Environmental Testing，2008，26（4）：6-8.

（責(zé)任編輯：馮珍珍）