Availability evaluation of manufacturing systems using Semi-Markov model

Abstract

Availability is a key measure of performance of systems in general and manufacturing systems are no exception. The elements of complex manufacturing systems such as Computer Integrated Manufacturing (CIM) follow variable, i.e., decreasing or increasing failure and repair rates. This creates difficulty in their availability evaluation. Conventional methods, which predict availability based on past experience, are inadequate for such systems. Existing analytical or simulation methods provide inaccurate availability estimate as these assume constant failure and repair rates, which follow exponential distribution. To address this concern, this paper suggests a methodology for availability evaluation of manufacturing systems using Semi-Markov model, which considers variable failure or repair rates. This is carried out by first understanding the system structure by identifying its elements; subsystem, assembly and component at its hierarchical levels and subsequently identifying their states; failed, operating, etc. Based on this, Semi-Markov models are developed for each element at various hierarchical levels of the system. The unique feature of this approach is that it does assume Weibull distribution for variable failure times and lognormal for variable repair times. The developed models are solved using an analytical solution method to obtain steady-state probabilities of their states and hence, the system steady-state availability. The methodology is illustrated by means of a case study conducted on a Vertical Machining Center (VMC) that is used in an automotive production plant.