ORIGINAL PAPER Availability analysis of a repairable duplex system: a z-dependent Sokhotski–Plemelj problem E. J. Vanderperre • S. S. Makhanov Received: 8 July 2013 / Accepted: 17 November 2013 Ó Sociedad de Estadı ´stica e Investigacio ´n Operativa 2013 Abstract We analyse the point availability of a repairable duplex system char- acterized by cold standby and by a priority rule. The system is attended by two (general) heterogeneous repairmen. To describe the random behaviour of the sys- tem, we introduce a stochastic process endowed with probability measures satis- fying (coupled) partial differential equations. The solution procedure is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. The unique solution of the equations determines the point availability of the system. Computational results for the point availability are derived by a numerical solution of an appropriate integral equation. Keywords Cold standby  Priority rule  Point availability  Functional equation  Cauchy integral  Weibull–Gnedenko distribution Mathematics Subject Classification 60K10 1 Introduction Standby provides a powerful tool to increase the availability, reliability, quality and safety of operational plants, e.g. Birolini (2007), Gnedenko and Ushakov (1995), Ushakov (2012). A frequently employed standby mode is the so-called ‘‘cold’’ standby. The notion of cold standby signifies that a backup system is kept in reserve, with a zero E. J. Vanderperre Reliability Engineering Research Unit, Ruzettelaan 183, Bus 158, 8370 Blankenberge, Belgium e-mail: evanderperre@yahoo.com S. S. Makhanov (&) School of Information and Computer Technology, Sirindhorn International Institute of Technology, Thammasat University, Tiwanont Road, T. Bangkadi, A. Muang, Pathum Thani 12000, Thailand e-mail: makhanov@siit.tu.ac.th 123 TOP DOI 10.1007/s11750-013-0307-7