当前对于无失效数据和极少失效数据的处理方法，不能同时得到参数的点估计和置信区间估计。在具体应用中，如果基于不同方法得到点估计和置信区间估计，则造成结果的可信度降低。针对这一问题，在威布尔分布下，对当前广泛应用的配分布曲线法的各个环节进行详细分析并加以改进，使得计算结果既包含点估计，也包含置信区间估计，从而增强了结果的可信度。经过对3组不同产品的寿命数据的分析计算，并与其他方法得到的结果相对比，发现根据所提出的方法计算得到的结果更为合理。这证明了这一方法的有效性和合理性。
For zero-failure data and very few failure data, the current methods fail to obtain both the estimate and confidence interval of parameters. If the estimate and confidence interval of parameters are obtained based on different methods, the results seem to be unconvincing. In this case, the match distribution curve (MDC) method is analyzed and improved to be able to compute both the estimate and confidence interval of parameters for Weibull distribution. And the improved method could make the results more convincing. After calculation for three examples, the estimate and confidence interval of parameters based on the proposed method are better than the results by other methods. It demonstrates the effectiveness and rationality of this method.
[1] 陈家鼎, 孙万龙, 李补喜. 关于无失效数据情形下的置信限[J]. 应用数学学报, 1995, 18(1)：90-100. CHEN Jiading, SUN Wanlong, LI Buxi. On the confidence limits in the case of no failure data[J]. Acta Mathe-maticae Applicatae Sinica, 1995, 18(1)：90-100.
[2] 韩明. Weibull分布可靠性参数的置信限[J]. 机械强度, 2009, 31(1)：59-62. HAN Ming. Confidence limits of reliability parameters for Weibull distributionJournal[J]. Journal of Mechanical Strength, 2009, 31(1)：59-62.
[3] 王凭惠, 范本尧, 傅惠民. 卫星推力器可靠性评估和寿命预测[J]. 航空动力学报, 2004, 19(6)：745-748. WANG Pinghui, FAN Benyao, FU Huimin. Reliability assessment and life prediction for satellite engine[J]. Journal of Aerospace Power, 2004, 19(6)：745-748.
[4] 韩明. 无失效数据下液体火箭发动机的E-Bayes可靠性分析[J]. 航空学报, 2011, 32(12)：2213-2219. HAN Ming. E-Bayes reliability analysis for liquid rocket engine with zero-faiure data[J]. Acta Aeronauticaet Astronautica Sinica, 2011, 32(12)：2213-2219.
[5] 峁诗松, 罗朝斌. 无失效数据的可靠性分析[J]. 数理统计与应用概率, 1989, 4(4)：489-506. MAO Shisong, LUO Chaobin. The reliability analysis for zero-failure data[J]. Mathematical Statistics And Applied Probability, 1989, 4(4)：489-506.
[6] 茆诗松, 夏剑锋, 管文琪. 轴承寿命试验中无失效数据的处理[J]. 应用概率统计, 1993, 9(3)：326-331. MAO Shisong, XIA Jianfeng, GUAN Wenqi. The reliability analysis of zero-failure data for bearing life test[J]. Chinese Journey of Applied Probability and Statistics, 1993, 9(3)：326-331.
[7] 茆诗松, 汤银才, 王玲玲. 可靠性统计 [M]. 北京：高等教育出版社, 2008. MAO Shisong, TANG Yincai, WANG Lingling. Reliability statistics [M]. Beijing：High Eucation Press, 2008.
[8] 傅惠民, 岳晓蕊, 张勇波. 极少失效数据的可靠性评估和寿命预测[J]. 航空动力学报, 2010, 25(8)：1855-1859. FU Huimin, YUE Xiaorui, ZHANG Yongbo. Reliability assessment and life prediction for very few failure data[J]. Journal of Aerospace Power, 2010, 25(8)：1855-1859.
[9] 张志华. 正态分布场合下只有一个失效数据的统计分析[J]. 应用概率统计, 1998, 14(2)：185-190. ZHANG Zhihua. Satistical analysis of data only one failure under normal case[J]. Chinese Journal of Applied Probability and Statistics, 1998, 14(2)：185-190.
[10] 陈文华, 崔杰, 樊晓燕. 单失效数据的可靠性统计分析[J]. 机械工程学报, 2003, 39(9)：44-48. CHEN Wenhua, CUI Jie, FAN Xiaoyan. Reliability statistical analysis of data only one failure[J]. Chinese Journal of Mechanical Engineering, 2003, 39(9)：44-48.
[11] 宁江凡. 液体火箭发动机无失效条件下的可靠性评估方法研究 [D]. 长沙：国防科学技术大学, 2005. NING Jiangfan. Study on reliability assessment method for liquid rocket engine in the case of zero-failure data [D]. Changsha：National University of Defense Technology, 2005.
[12] 贾祥, 蒋平, 郭波. 威布尔分布场合无失效数据的失效概率估计方法[J]. 机械强度, 2015, 37(2)：288-294. JIA Xiang, JIANG Ping, GUO Bo. The estimation to failure probability for zero-failure data in Weibull distribution[J]. Journal of Mechanical Strength, 2015, 37(2)：288-294.
