Trend analysis of the power law process with censored data

In this paper we assume that the failures of a system follow a non-homogenous Poisson process (NHPP) with a power law intensity function. NHPP is a model commonly used to describe a system with minimal repairs. In many situations, such as hidden failures, failure times of a system are subject to censoring. Current trend analysis methods in the literature for NHPP consider only right censoring and do not address recurrent failure data with left or interval censoring and periodic or non-periodic inspections. We use the likelihood ratio test to check for trend in the failure data. We use the EM algorithm and a recursive method to calculate the likelihood for estimating the parameters of the power law process in the case of null and alternative hypotheses (no trend and trend assumptions). As an example, the proposed method is applied to the failures of a medical infusion pump. It was found that the likelihood ratio test and the proposed recursive method can be applied successfully to censored data, although the method may be computationally intensive for larger datasets. We also compared the likelihood method to an ad-hoc method using the mid points of censoring intervals instead of unknown failure times. The comparison showed that using the midpoints is not reliable and may result in incorrect conclusion about the trend. The proposed method can be applied to other repairable systems used in industry.