Reliability assessment of non-Markovian complex production systems using a hierarchical approach

In the actual context of global, intense competitiveness, the performance of the production systems is a key competitiveness factor for manufacturing companies. Factors such as the availability of the manufacturing cells and the frequency of production shortages are very important indexes for system designers and managers, both at the planning and at the operational stages of the production systems life cycle. The reliability, maintainability and redundancy of the equipment are well known performance drivers of the production system, but intermediate work-in-process (WIP) buffers are another fundamental driver. Despite the endless inventory reduction efforts made by product managers, very often, WIP buffers still play a central role in the operation of the production systems. They smooth the unbalance of manufacturing cells and limit the consequences of events such as equipment failures and non-conforming lots, preventing them to propagate to the downstream production units. This paper will present a set of tools and methods for the assessment of performance indexes of production systems. Particular attention will be paid to the assessment of the impact of the dimension and the localization of the WIP buffers on the global performance of the systems. The assessment of availability, frequency and duration related indexes is a complex task for production systems, due to the dimension of the systems under study, and the fact that their behaviour, normally, will not be Markovian. To overcome these difficulties, a hierarchical, non-Markovian approach was developed. Its originality relies on the fact that it allows evaluation of the performance indexes from a global system model that was obtained from the integration of a set of equivalent models derived at the subsystem level. In the final part of the paper, a numerical example concerning a production system made by three cells and two buffers will be presented.