两参数Birnbaum-Saunders疲劳寿命分布图像特征的拓展分析
|
摘要
研究了两参数BS疲劳寿命分布BS(α,β)密度函数f (t)和失效率函数λ(t)顶峰点的位置以及在中位数β左右侧的图像特征,并给出了判断失效率函数图像特征的更为一般的结论 .
The image features of density function f(t) and failure rate function λ(t) at the peak and around the median βare studied for two-parameter BS fatigue life distribution.Meanwhile,a general conclusion for identifying image feature of failure rate function is proposed.
The image features of density function f(t) and failure rate function λ(t) at the peak and around the median βare studied for two-parameter BS fatigue life distribution.Meanwhile,a general conclusion for identifying image feature of failure rate function is proposed.
引文
[1]BIRNBAUM Z W,SAUNDERS S C.A new family of life distribution[J].Journal of Applied Probability,1969,6(2):319-327.DOI:10.2307/3212003
[2]DESMON A.Stochastic models of failure in random environments[J].The Canadian Journal of Statistics,1985,13(3):171-183.DOI:10.2307/3315148
[3]DESMOND A F.On the relationship between two fatigue-life models[J].IEEE Transactions on Reliability,1986,35(2):167-169.DOI:10.1109/TR.1986.4335393
[4]BIRNBAUM Z W,SAUNDERS S C.Estimation for a family of life distribution[J].Journal of Applied Probability,1969,6(2):328-347.
[5]MAX E,BAIN L J,WRIGHT F T.Inferences on the parameters of the birnbaum saunders fatigue life distribution based on maximum likelihood estimation[J].Technometrics,1981,23(3):251-256.
[6]RIECK J R,NEDELMAN J R.A log-linear model for the Birnbaum Saunders distribution[J].Technometrics,1991,33(1):51-60.DOI:10.2307/1269007
[7]NG H K T,KUNDU D,BALAKRISHNAN N.Modified moment estimation for the two-parameter Birnbaum-Saunders distribution[J].Computational Statistics and Data Analysis,2003,43(3):283-298.
[8]DUPUIS D,MILLS J E.Robust estimation of the Birnbaum-distribution[J].IEEE Transactions on Reliability,1998,47(1):88-95.DOI:10.1109/24.690913
[9]CHANG D S,TANG L C.Reliability bounds and critical time for the Birnbaum-Saunders distribution[J].IEEE Transactions on Reliability,1993,42(3):464-469.DOI:10.1109/24.257832
[10]RIECK J R.Parametric estimation for the BirnbaumSaunders distribution based on symmetrically censored samples[J].Communications in Statistics-Theory and Methods,1995,24(7):1721-1736.DOI:10.1080/03610929508831581
[11]OWEN W J,PADGETT W J.A Birnbaum-Saunders accelerated life model[J]IEEE Transactions on Reliability,2000,49(2):224-229.
[12]OWEN W J,PADGETT W J.Acceleration models for system strength based on Birnbaum-Saunders distribution[J].Lifetime Data Analysis,1999,5(2):133-147.
[13]OWEN W J,PADGETT W J.Power-law accelerated Birnbaum-Saunders life models[J].International Journal of Reliability,Quality and Safety Engineering,2000,7(1):1-15.DOI:10.1142/S021853930000002X
[14]KUNDU D,KANNNAN N,BALAKRISHNAN N.On the hazard function of Birnbaum-Saunders distribution and associated inference[J].Computational Statistics&Data Analysis,2008,52(5):2692-2702.DOI:10.1016/j.csda.2007.09.021
[15]王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布的参数估计[J].华东师范大学学报,1996(4):10-15.WANG B X,WANG L L.Estimation for the BirnbaumSaunders fatigue life distribution[J].Journal of East China Normal Universty(Nature Science),1996(4):10-15.
[16]王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布在截尾试验情形的统计分析[J].应用概率统计,1996,12(4):369-375.WANG B X,WANG L L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under censored testing[J].Chinese Journal of Applied Probability and Statistics,1996,12(4):369-375.
[17]王蓉华,费鹤良.双边截尾场合下BS疲劳寿命分布的参数估计[J].上海师范大学学报(自然科学版),1999,28(2):17-22.WANG R H,FEI H L.Statistical analysis of Birnbaum-Saunders fatigue life distribution[J].Journal of Shanghai Teachers University(Nature Sciences),1999,28(2):17-22.
[18]WANG R H,FEI H L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under multiply type II censoring[J].Chin Quart J of Math,2006,21(1):15-27.
[19]WANG R H,FEI H L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under type II bilateral censoring and multiply type II censoring[J].Chin Quart J of Math,2004,19(2):126-132.
[20]孙祝岭.Birnbaum-Saunders疲劳寿命分布尺度参数的区间估计[J].兵工学报,2009,30(11):1558-1561.SUN Z L.The confidence intervals for the scale parameter of the Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2009,30(11):1558-1561.
[21]孙祝岭.Birnbaum-Saunders疲劳寿命分布参数的回归估计方法[J].兵工学报,2010,31(9):1260-1262.SUN Z L.Regression Estimation of the parametrs of the Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2010,31(9):1260-1262.
[22]孙祝岭,Birnbaum-Saunders分布环境因子的置信限[J].强度与环境,2012,39(4):51-55.DOI:10.3969/j.issn.1006-3919.2012.04.011SUN Z L.Confidence limits for the environment factor of the Birnbaur-Saunders distribution[J].Structure&Environment Engineening,2012,39(4):51-55.DOI:10.3969/j.issn.1006-3919.2012.04.011
[23]WANG B X.Generalized interval estimation for the Birnbaum-Saunders distribution[J],Computational Statistics and Data Analysis,2012,56:4320-4326.DOI:10.1016/j.csda.2012.03.023
[24]NIU C Z,GUO X,XU W L,et al.Comparison of several Birnbaum-Saunders distributions[J].Journal of Statistical Computation and Simulation,2014,84(12):2721-2733.
[25]周磊,孙玲玲,严晓浪,等.一种基于概率解释的新型互连线时延Slew模型[J].电路与系统学报,2009,14(2):7-10.DOI:10.3969/j.issn.1007-0249.2009.02.002ZHOU L,SUN L L,YAN X L,et al.A novel interconneet delay and slew model based PDFinterpretation for qunm technology[J].Journal of Circuits and Systems,2009,14(2):7-10.DOI:10.3969/j.issn.1007-0249.2009.02.002
[26]赵建印,孙权,彭宝华,等.基于加速退化数据的BS分布的统计推断[J].电子产品可靠性与环境试验,2006,24(1):11-14.DOI:10.3969/j.issn.1672-5468.2006.01.004ZHAO J Y,SUN Q,PENG B H,et al.Inferences for the BS life model from accelerated degradation tests[J].Eletronic Product Reliability and Environmental Testing,2006,24(1):11-14.DOI:10.3969/j.issn.1672-5468.2006.01.004
[27]BALAKRISHNAN N,ZHU X J.On the existence and uniqueness of the maximum likelihood estimates of the parameters of Birnbaum-Saunders distribution based on Type-I,Type-II and hybrid censored samples[J].Statistics,2014,48(5):1013-1032.DOI:10.1080/02331888.2013.800069
[28]徐晓岭,王蓉华,顾蓓青.关于两参数BirnbaumSaunders疲劳寿命分布统计分析的2个注记[J].浙江大学学报(理学版),2016,43(5):539-544.DOI:10.3785/j.issn.1008-9497.2016.05.008XU X L,WANG R H,GU B Q.Two notes of statistical analysis about two-parameter BirnbaumSaunders fatigue life distribution[J].Journal of Zhejiang University(Science Edition),2016,43(5):539-544.DOI:10.3785/j.issn.1008-9497.2016.05.008
[29]徐晓岭,王蓉华,顾蓓青.全样本场合下两参数Birnbaum-Saunders疲劳寿命分布的统计分析[J].浙江大学学报(理学版),2017,44(6):692-704.DOI:10.3785/j.issn.1008-9497.2017.06.008XU X L,WANG R H,GU B Q.Statistical analysis of two-parameter Birnbaum-Saunders fatigue life distribution under full sample[J].Journal of Zhejiang University(Science Edition),2017,44(6):692-704.DOI:10.3785/j.issn.1008-9497.2017.06.008
[30]GLASER R E.Bathtub and related failure rate characterizations[J].Journal of the American Statistical Association,1980,75(371):667-672.DOI:10.2307/2287666
[2]DESMON A.Stochastic models of failure in random environments[J].The Canadian Journal of Statistics,1985,13(3):171-183.DOI:10.2307/3315148
[3]DESMOND A F.On the relationship between two fatigue-life models[J].IEEE Transactions on Reliability,1986,35(2):167-169.DOI:10.1109/TR.1986.4335393
[4]BIRNBAUM Z W,SAUNDERS S C.Estimation for a family of life distribution[J].Journal of Applied Probability,1969,6(2):328-347.
[5]MAX E,BAIN L J,WRIGHT F T.Inferences on the parameters of the birnbaum saunders fatigue life distribution based on maximum likelihood estimation[J].Technometrics,1981,23(3):251-256.
[6]RIECK J R,NEDELMAN J R.A log-linear model for the Birnbaum Saunders distribution[J].Technometrics,1991,33(1):51-60.DOI:10.2307/1269007
[7]NG H K T,KUNDU D,BALAKRISHNAN N.Modified moment estimation for the two-parameter Birnbaum-Saunders distribution[J].Computational Statistics and Data Analysis,2003,43(3):283-298.
[8]DUPUIS D,MILLS J E.Robust estimation of the Birnbaum-distribution[J].IEEE Transactions on Reliability,1998,47(1):88-95.DOI:10.1109/24.690913
[9]CHANG D S,TANG L C.Reliability bounds and critical time for the Birnbaum-Saunders distribution[J].IEEE Transactions on Reliability,1993,42(3):464-469.DOI:10.1109/24.257832
[10]RIECK J R.Parametric estimation for the BirnbaumSaunders distribution based on symmetrically censored samples[J].Communications in Statistics-Theory and Methods,1995,24(7):1721-1736.DOI:10.1080/03610929508831581
[11]OWEN W J,PADGETT W J.A Birnbaum-Saunders accelerated life model[J]IEEE Transactions on Reliability,2000,49(2):224-229.
[12]OWEN W J,PADGETT W J.Acceleration models for system strength based on Birnbaum-Saunders distribution[J].Lifetime Data Analysis,1999,5(2):133-147.
[13]OWEN W J,PADGETT W J.Power-law accelerated Birnbaum-Saunders life models[J].International Journal of Reliability,Quality and Safety Engineering,2000,7(1):1-15.DOI:10.1142/S021853930000002X
[14]KUNDU D,KANNNAN N,BALAKRISHNAN N.On the hazard function of Birnbaum-Saunders distribution and associated inference[J].Computational Statistics&Data Analysis,2008,52(5):2692-2702.DOI:10.1016/j.csda.2007.09.021
[15]王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布的参数估计[J].华东师范大学学报,1996(4):10-15.WANG B X,WANG L L.Estimation for the BirnbaumSaunders fatigue life distribution[J].Journal of East China Normal Universty(Nature Science),1996(4):10-15.
[16]王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布在截尾试验情形的统计分析[J].应用概率统计,1996,12(4):369-375.WANG B X,WANG L L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under censored testing[J].Chinese Journal of Applied Probability and Statistics,1996,12(4):369-375.
[17]王蓉华,费鹤良.双边截尾场合下BS疲劳寿命分布的参数估计[J].上海师范大学学报(自然科学版),1999,28(2):17-22.WANG R H,FEI H L.Statistical analysis of Birnbaum-Saunders fatigue life distribution[J].Journal of Shanghai Teachers University(Nature Sciences),1999,28(2):17-22.
[18]WANG R H,FEI H L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under multiply type II censoring[J].Chin Quart J of Math,2006,21(1):15-27.
[19]WANG R H,FEI H L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under type II bilateral censoring and multiply type II censoring[J].Chin Quart J of Math,2004,19(2):126-132.
[20]孙祝岭.Birnbaum-Saunders疲劳寿命分布尺度参数的区间估计[J].兵工学报,2009,30(11):1558-1561.SUN Z L.The confidence intervals for the scale parameter of the Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2009,30(11):1558-1561.
[21]孙祝岭.Birnbaum-Saunders疲劳寿命分布参数的回归估计方法[J].兵工学报,2010,31(9):1260-1262.SUN Z L.Regression Estimation of the parametrs of the Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2010,31(9):1260-1262.
[22]孙祝岭,Birnbaum-Saunders分布环境因子的置信限[J].强度与环境,2012,39(4):51-55.DOI:10.3969/j.issn.1006-3919.2012.04.011SUN Z L.Confidence limits for the environment factor of the Birnbaur-Saunders distribution[J].Structure&Environment Engineening,2012,39(4):51-55.DOI:10.3969/j.issn.1006-3919.2012.04.011
[23]WANG B X.Generalized interval estimation for the Birnbaum-Saunders distribution[J],Computational Statistics and Data Analysis,2012,56:4320-4326.DOI:10.1016/j.csda.2012.03.023
[24]NIU C Z,GUO X,XU W L,et al.Comparison of several Birnbaum-Saunders distributions[J].Journal of Statistical Computation and Simulation,2014,84(12):2721-2733.
[25]周磊,孙玲玲,严晓浪,等.一种基于概率解释的新型互连线时延Slew模型[J].电路与系统学报,2009,14(2):7-10.DOI:10.3969/j.issn.1007-0249.2009.02.002ZHOU L,SUN L L,YAN X L,et al.A novel interconneet delay and slew model based PDFinterpretation for qunm technology[J].Journal of Circuits and Systems,2009,14(2):7-10.DOI:10.3969/j.issn.1007-0249.2009.02.002
[26]赵建印,孙权,彭宝华,等.基于加速退化数据的BS分布的统计推断[J].电子产品可靠性与环境试验,2006,24(1):11-14.DOI:10.3969/j.issn.1672-5468.2006.01.004ZHAO J Y,SUN Q,PENG B H,et al.Inferences for the BS life model from accelerated degradation tests[J].Eletronic Product Reliability and Environmental Testing,2006,24(1):11-14.DOI:10.3969/j.issn.1672-5468.2006.01.004
[27]BALAKRISHNAN N,ZHU X J.On the existence and uniqueness of the maximum likelihood estimates of the parameters of Birnbaum-Saunders distribution based on Type-I,Type-II and hybrid censored samples[J].Statistics,2014,48(5):1013-1032.DOI:10.1080/02331888.2013.800069
[28]徐晓岭,王蓉华,顾蓓青.关于两参数BirnbaumSaunders疲劳寿命分布统计分析的2个注记[J].浙江大学学报(理学版),2016,43(5):539-544.DOI:10.3785/j.issn.1008-9497.2016.05.008XU X L,WANG R H,GU B Q.Two notes of statistical analysis about two-parameter BirnbaumSaunders fatigue life distribution[J].Journal of Zhejiang University(Science Edition),2016,43(5):539-544.DOI:10.3785/j.issn.1008-9497.2016.05.008
[29]徐晓岭,王蓉华,顾蓓青.全样本场合下两参数Birnbaum-Saunders疲劳寿命分布的统计分析[J].浙江大学学报(理学版),2017,44(6):692-704.DOI:10.3785/j.issn.1008-9497.2017.06.008XU X L,WANG R H,GU B Q.Statistical analysis of two-parameter Birnbaum-Saunders fatigue life distribution under full sample[J].Journal of Zhejiang University(Science Edition),2017,44(6):692-704.DOI:10.3785/j.issn.1008-9497.2017.06.008
[30]GLASER R E.Bathtub and related failure rate characterizations[J].Journal of the American Statistical Association,1980,75(371):667-672.DOI:10.2307/2287666