Trend analysis of the power law process using Expectation-Maximization algorithm for data censored by inspection intervals
Trend analysis of the power law process using Expectation-Maximization algorithm for data censored by inspection intervals
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DOI：
10.1016/j.ress.2011.03.018
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发表时间：
2011-10
期刊：
影响因子：
--
通讯作者：
S. Taghipour;D. Banjevic
中科院分区：
文献类型：
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作者：
S. Taghipour;D. Banjevic
趋势分析是一种常用的统计方法，用于研究可修系统随时间的运行和变化。该方法采用一个系统或一组类似系统的历史故障数据，并确定重复故障是否呈现增加或减少的趋势。文献中提出的大多数趋势分析方法假设故障时间是已知的，因此故障数据在统计上是完整的;然而，在许多情况下，例如隐藏故障，故障时间会受到删失。本文假设一组相似的独立可修部件的失效过程服从强度函数为幂律的非齐次泊松过程。此外，失效数据受到左、区间和右删失。本文提出使用似然比检验来检查故障数据的趋势。它使用期望最大化（EM）算法来找到参数，在零假设和备择假设的情况下最大化数据可能性。采用递归方法解决了期望步骤中期望值计算的主要技术问题。所提出的方法被应用到一家医院的维修数据的趋势分析的一般输液泵的组件。
Trend analysis is a common statistical method used to investigate the operation and changes of a repairable system over time. This method takes historical failure data of a system or a group of similar systems and determines whether the recurrent failures exhibit an increasing or decreasing trend. Most trend analysis methods proposed in the literature assume that the failure times are known, so the failure data is statistically complete; however, in many situations, such as hidden failures, failure times are subject to censoring. In this paper we assume that the failure process of a group of similar independent repairable units follows a non-homogenous Poisson process with a power law intensity function. Moreover, the failure data are subject to left, interval and right censoring. The paper proposes using the likelihood ratio test to check for trends in the failure data. It uses the Expectation–Maximization (EM) algorithm to find the parameters, which maximize the data likelihood in the case of null and alternative hypotheses. A recursive procedure is used to solve the main technical problem of calculating the expected values in the Expectation step. The proposed method is applied to a hospital's maintenance data for trend analysis of the components of a general infusion pump.