Abstract

The problem of testing the scale parameter (γ) of the power-law process for a single system is taken into account when dealing with incomplete failure data. In this study, the modified signed log-likelihood ratio test is introduced as a method for testing parameter γ. The accuracy of the proposed method is evaluated in the literature. For incomplete failure data, the modified signed log-likelihood ratio test is satisfactory and preferable to the signed log-likelihood ratio test for most situations in terms of controlling type I errors, and this method works well like the generalized variable test which is the exact method since it yields the empirical type I errors close to the nominal level 0.05. In terms of empirical powers, the modified signed log-likelihood ratio test performs satisfactorily and seems to be superior to the generalized variable test when the ratio of ${\gamma }_1/{\gamma }_0$ is small even for small number of failures and large missing ratios.

摘要

在处理不完整的失效数据时，考虑了对单个系统的幂律过程的尺度参数（ γ ）进行检验的问题。在本研究中，引入了改进的带符号对数似然比检验作为测试参数γ的方法. 在文献中评估了所提出方法的准确性。对于不完整的失效数据，修正的有符号对数似然比检验在控制 I 类错误的大多数情况下是令人满意的并且优于有符号对数似然比检验，并且该方法与广义变量检验一样有效，是精确的方法，因为它产生的经验类型 I 误差接近标称水平 0.05。就经验能力而言，修正的有符号对数似然比检验表现令人满意，并且似乎优于广义变量检验，当${\gamma }_1/{\gamma }_0$即使对于少量的故障和大的缺失率，它也很小。