Modelling maintenance and repair costs using stochastic point processes for life cycle costing of repairable systems

Abstract

The objective of this article is to present a methodology based on reliability and maintainability (R & M) parameters for effective implementation of life cycle costing in design and procurement of repairable systems. For this purpose, a number of life cycle cost models developed over the years have been reviewed, the important life cycle stages for repairable systems are identified and a generalised model for life cycle cost analysis is first proposed. The mathematical equations have been formulated for the life cycle stages, such as acquisition, installation and commissioning, operation, maintenance and repair and disposal. The focus is mainly on modelling the maintenance and repair costs, which are the major elements of repairable system life cycle cost. To model maintenance and repair costs, the stochastic point process approach is employed. The lifetime of repairable system is modelled using a two parameter Weibull distribution. The expected number of failures are estimated based on the assumption that the number of replacements of the components in an interval (0, t) follow renewal process (RP) in the first case and minimal repair process in the second case. Based on the expected number of failures, the lifetime maintenance and repair costs are estimated for the RP and the minimal repair process. A methodology to decide whether a renewal approach or minimal repair approach should be planned for a particular component is also presented. The proposed technique is then illustrated through its application to a typical repairable system, namely an industrial pump and the results obtained are presented along with a review for future work. The proposed model is believed to be a simple way for system designers to estimate and compare the life cycle cost of their different design alternatives at system design stage using system R & M parameters.

Keywords:

• life cycle cost modelling
• repairable systems
• reliability modelling
• stochastic point process
• renewal process
• minimal repair process

Acknowledgements

The authors thank the product engineering division of Kirloskar Brothers Limited, Kirloskarwadi for providing the necessary data. The authors also thank Dr. S. G. Joshi, Formerly Professor and Head, Department of Mechanical Engineering, Walchand College of Engineering, Sangli for his constructive suggestions during this work.