Iranian Institute of Industrial Engineering Journal of Industrial and Systems Engineering 1735-8272 10 special issue on Quality Control and Reliability 2017 06 20 Cold standby redundancy optimization for nonrepairable series-parallel systems: Erlang time to failure distribution 1 16 39491 EN Meisam Sadeghi Department of Industrial Engineering, K. N. Toosi University of Technology Emad Roghanian Department of Industrial Engineering, K. N. Toosi University of Technology Hamid Shahriari Department of Industrial Engineering, K. N. Toosi University of Technology Journal Article 2016 08 06 In modeling a cold standby redundancy allocation problem (RAP) with imperfect switching mechanism, deriving a closed form version of a system reliability is too difficult. A convenient lower bound on system reliability is proposed and this approximation is widely used as a part of objective function for a system reliability maximization problem in the literature. Considering this lower bound does not necessarily lead to an optimal solution. In this study by assuming that working time of switching mechanism is exponentially distributed, exact value of system reliability is derived analytically through applying Markov process and solving a relevant set of differential-difference equations. The Runge-Kutta numerical scheme is also employed to verify the accuracy of the results. It is assumed that components time to failure follow an Erlang distribution which is appropriate for most engineering design problems by giving the possibility of modeling different increasing hazard functions. A new mathematical model is presented and its performance is evaluated through solving a well-known example in the literature. Results demonstrate that a higher level of system reliability is achievable through implementing the proposed model.   https://www.jise.ir/article_39491_fb628a9f2005fb3e8152ca8a66ca4515.pdf