Abstract
We propose an algorithm for estimating the effectiveness of maintenance on both age and health of a system. One of the main contributions is the concept of virtual health of the device. It is assumed that failures follow a nonhomogeneous Poisson process (NHPP) and covariates follow the proportional hazards model (PHM). In particular, the effect of maintenance on device’s age is estimated using the Weibull hazard function, while the effect on device’s health and covariates associated with condition-based monitoring (CBM) is estimated using the Cox hazard function. We show that the maintenance effect on the health indicator (HI) and the virtual HI can be expressed in terms of the Kalman filter concepts. The HI is calculated from Mahalanobis distance between the current and the baseline condition monitoring data. The effect of maintenance on both age and health is also estimated. The algorithm is applied to the case of railway point machines. Preventive and corrective types of maintenance are modelled as different maintenance effect parameters. Using condition monitoring data, the HI is calculated as a scaled Mahalanobis distance. We derive reliability and likelihood functions and find the least squares estimates (LSE) of all relevant parameters, maintenance effect estimates on time and HI, as well as the remaining useful life (RUL).
Highlights
Introduction and backgroundMaintenance is critical for the longevity, reliability and availability of a vast majority of industrial, consumer and specialised systems and devices
We show that the maintenance effect on the health indicator (HI) and the virtual HI can be expressed in terms of the Kalman filter concepts
A common approach found in the literature on complex maintenance models of various industrial systems divides maintenance actions into four categories: worse repairs, minimal repairs (do not change the age when applied, leaving the system in the as-bad-as-old (ABAO) state), imperfect repairs and perfect repairs (effectively reduce the age to 0, amounting to as-good-as-new (AGAN) state) (Pulcini, 2003; Wu & Zuo, 2010)
Summary
Maintenance is critical for the longevity, reliability and availability of a vast majority of industrial, consumer and specialised systems and devices. Furthering the framework of Kijima (Kijima, Some results for repairable systems with general repair, 1989) and Doyen and Gaudoin (Doyen & Gaudoin, Classes of imperfect repair models based on reduction of failure intensity or virtual age, 2004), in the present paper, virtual age and virtual health indicator are used, and the effects of maintenance are considered simultaneously on both intensity and age. Said and Taghipour further expanded this by considering three maintenance types for PM events and minimal repair for CM events (Said & Taghipour, 2016) They derive the likelihood function for estimating the parameters of the failure process and the effects of preventive maintenance, as well as provide the conditional reliability and the expected number of failures between two consecutive PM types (Said & Taghipour, 2016). The present article is structured as follows: Section 2 contains the relevant background; Section 3 presents the model; Section 4 contains reliability and likelihood functions; Section 5 illustrates the models by providing numerical examples; lastly, Section 6 summarises the conclusions
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