The increasing level of operation in high-tech industry is likely to require ever more complex structure in reliability problem. Furthermore, system failures are more significant on society as a whole than ever before. Reliability redundancy optimization problem (RROP) plays a important role in the designing and analyzing the complex system. RROP involves selection of components with multiple choices and redundancy levels for maximizing system reliability with constraints such as cost, weight, etc. Meanwhile, previous works on RROP dealt with system with perfect failure detection, which gave at most a good solution. However, we studied RROP with imperfect failure detection and switching. Using absorbing Markov Chain, we present not a good solution but the optimal one. In this study, the optimal system configuration is designed with warm and cold-standby redundancy for k-out-of-n system in terms of MTTF that is one of the performance measures of reliability.