The Taguchi approach to maintaining stochastically failing production systems became known to us recently. He proposed a periodic inspection policy which is easily calculable and only requires the knowledge of the mean time to failure. However, his policy is approximate in nature, and therefore, it is of interest to evaluate its performance relative to the optimal sequential or optimal periodic policies. For the cost model which Taguchi assumes, this thesis develops procedures for deterring the optimal sequential and periodic policies, and computational experiments are conducted to evaluate the relative efficiencies of the three policies for various combinations of parameter values. Analyses of the computational results show that the loss in efficiency caused by using the Taguchi approximate policy is not sever in most cases considered.