Maintaining an asset with life-limited parts, e.g., a jet engine or an electric generator, may be costly. Certain costs, e.g., setup cost, can be shared if some parts of the asset are replaced jointly. Reducing the maintenance cost by good joint replacement policies is difficult in view of complicate asset dynamics, large problem sizes and the irregular optimal policy structures. This paper addresses these difficulties by using a rollout optimization framework. Based on a novel application of time-aggregated Markov decision processes, the ldquoOne-Stage Analysisrdquo method is first developed. The policies obtained from the method are investigated and their effectiveness is demonstrated by examples. This method and the existing threshold method are then improved by the ldquorollout algorithmrdquo for the total cost case and the average cost case. Based on ordinal optimization, it is shown that excessive simulations are not necessary for the rollout algorithm. Numerical testing demonstrates that the policies obtained by the rollout algorithms with either the ldquoOne-Stage Analysisrdquo or the threshold method significantly outperform traditional threshold policies.