ORIGINAL ARTICLE Performance-based ranking and selection of complex coherent systems Debasis Bhattacharya • Soma Roychowdhury Received: 22 September 2014 / Revised: 10 December 2014 Ó The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2015 Abstract Ranking of competing systems and selecting the best according to some performance measure is an important issue to the reliability engineers. It is quite common to consider the reliability, a function of life- lengths of systems, to be an appropriate performance measure. Here the limitations of direct method and signa- ture based method of comparison have been elaborated. It has been seen that the reliability analysis becomes difficult for complex systems of higher orders. It is not possible for the signature based method to compare the systems with different orders. Moreover, the assumption of indepen- dence of component lifetimes, though works well in some cases, may not necessarily be valid always in real-life sit- uations. The minimal cut set-based method of comparison discussed here is capable of combating with the limitations of the above methods and suggests a simple, useful method enabling comparison of the simple or complex systems of same or different orders, with independent or dependent component lives. Examples have been included to illustrate the method. Keywords Coherent system  Dependent component lives  Minimal cut set  Stochastic ordering  System life Mathematics Subject Classification Primary 90B25  60E15  60K10  Secondary 62N05  62P30 1 Introduction System performance is of great concern to both, manu- facturers and the users. It is usually measured by system reliability, which is a function of system life length. Poor performance of a system affects user’s satisfaction, which has a negative impact on overall business. If a critical component, that is, a component whose failure results in product failure, has low reliability, then a large number of failures will occur, and hence a large number of claims under warranty can result, which may lead to high warranty costs. The adverse impacts can be minimized by properly managing reliability of the system over its life cycle. There are various ways of improving system reliability, for example, using high quality components, reducing the operational load on the components, by implementing better maintenance, by increasing redundancy for critical components etc., and it is very difficult task to select the optimal one. Many models that deal with reliability related decisions during design, manufacture and post-sale service have been developed and their impacts on various objec- tives have been assessed. Bhattacharya and Samaniego (2008), Roychowdhury and Bhattacharya (2009) discussed various ways to improve system reliability for different coherent systems with independent component lives. For definition of coherent system Barlow and Proschan (1981) may be referred to. Reliability practitioners, usually, are interested either in improving system reliability or comparing competing sys- tems for choosing the best. Different systems under com- parison may be of same or of different orders. Kochar et al. (1999) used an example of comparing reliabilities of two or more automobiles of different make before choosing one. Block and Borges (1984) and Bhattacharya and D. Bhattacharya Visva-Bharati University, Santiniketan, India S. Roychowdhury (&) Indian Institute of Social Welfare and Business Management, Calcutta, India e-mail: srcdb@yahoo.com 123 Int J Syst Assur Eng Manag DOI 10.1007/s13198-014-0330-6