Trend analysis of the power law process using Expectation–Maximization algorithm for data censored by inspection intervals

• Published in: Reliability engineering & system safety Vol. 96; no. 10; pp. 1340 - 1348
• Main Authors: Taghipour, Sharareh, Banjevic, Dragan
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2011; Elsevier
• Subjects: Algorithms; Applied sciences; Censoring; EM algorithm; Exact sciences and technology; Failure; Failure times; Intervals; Mathematics; Maximum likelihood; Medical infusion pump; Operational research and scientific management; Operational research. Management science; Parametric inference; Power law; Power law process; Probability and statistics; Queuing theory. Traffic theory; Reliability theory. Replacement problems; Sciences and techniques of general use; Statistical methods; Statistics; Trend analysis; Trend test; Trends; Trend test; Maximum likelihood; Medical infusion pump; Censoring; Power law process; EM algorithm; Recurrence; Data analysis; Statistical analysis; Censored sample; Censorship; Maintenance; Failures; Poisson process; Pump; Break up time; Likelihood ratio test; Trend analysis; Recursive method; Hospital; Repair; Power law; Repairable system
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2011.03.018

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.