234 Int. J. Mechanisms and Robotic Systems, Vol. 4, No. 3, 2018 Copyright © 2018 Inderscience Enterprises Ltd. Cost analysis of systems with mixed standby units Ibrahim Yusuf* Department of Mathematical Sciences, Bayero University, Kano, 700241, Nigeria Email: iyusuf.mth@buk.edu.ng *Corresponding author Ya’u Balarabe Musa Department of Mathematics and Computer Science, Sule Lamido University, Kafin Hausa, Nigeria Email: ybm1968@yahoo.com Abstract: This paper deals with evaluation of cost of four dissimilar configurations with mixed standby units. The standby units exist as warm and cold standby. It is assumed that failure and repair time of all units are assumed to be exponentially distributed. Explicit expressions for busy period of repairmen, steady-state availability and profit function are derived using linear first order differential equations. Several cases are analysed graphically to investigate the effects of various system parameters on profit. The paper also presents graphical comparison for specific values of system parameters and finds that the optimal system configuration is configuration I. Keywords: profit; mixed standby; availability. Reference to this paper should be made as follows: Yusuf, I. and Musa, Y.B. (2018) ‘Cost analysis of systems with mixed standby units’, Int. J. Mechanisms and Robotic Systems, Vol. 4, No. 3, pp.234–251. Biographical notes: Ibrahim Yusuf is a Senior Lecturer at the Department of Mathematical Sciences, Bayero University, Kano. He received his MSc and PhD in Mathematics from Bayero University, Kano. His research interests include operation research, stochastic modelling and reliability analysis of k-out-of-n system. Ya’u Balarabe Musa is a Lecturer at the Department of Mathematics and Computer Science, Sule Lamido University, Kafin Hausa. He is currently pursuing his PhD from Department of Mathematical Sciences, Bayero University, Kano. His research interest includes numerical analysis, non linear optimisation.