Int. J. Operational Research, Vol. 21, No. 3, 2014 365 Copyright © 2014 Inderscience Enterprises Ltd. Transient analysis of a machine repair system with standby, two modes of failure, discouragement and switching failure Madhu Jain Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India E-mail: madhufma@iitr.ernet.in Preeti* Faculty of Humanity, Physical and Mathematical Sciences, Shobhit University Meerut-250110, India E-mail: preetypro06@gmail.com *Corresponding author Abstract: The present study is concerned with a machine repair problem with mixed standbys, permanent and additional repairmen. To deal with the realistic situation, the concepts of balking and reneging are also included. The operating units as well as standby units are assumed to fail in two modes. The units have exponential life time and repair time distributions. It is also assumed that there is a probability of a switching failure of the standby units to the operating state. The transient state probabilities are obtained by Runge-Kutta method. Some performance indices such as expected number of failed units, expected number of standby units, machine availability, etc., are obtained. To determine the expected total cost per unit time, a cost function has been facilitated. The numerical experiment is carried out to validate the analytical results of the developed model. The sensitivity analysis is also performed to explore the effect of different parameters on the performance indices. Keywords: mixed standby; balking; reneging; transient state probabilities; switching; failure; additional repairmen; Runge-Kutta method. Reference to this paper should be made as follows: Jain, M. and Preeti (2014) ‘Transient analysis of a machine repair system with standby, two modes of failure, discouragement and switching failure’, Int. J. Operational Research, Vol. 21, No. 3, pp.365–390. Biographical notes: Madhu Jain is an Associate Professor in the Department of Mathematics in Indian Institute of Technology Roorkee, India. She is a recipient of two gold medals of Agra University at MPhil level. There are more than 330 research publications in refereed international/national journals and more than 20 books to her credit. She was a recipient of the Young Scientist Award and a SERC Visiting Fellow in the Department of Science and Technology (DST), India and Career Award of University Grants Commission (UGC), India. She has successfully completed six sponsored major research projects of MHRD, DST, UGC and CSIR. Her current research interest includes the performance modelling, stochastic models, soft computing, bio-informatics, reliability engineering and queueing theory.