Abstract: Most of mechanical equipments have 3 states: normal, abnormal and failure. When the equipments are checked and diagnosed in abnormal, they will accept predictive maintenance. And if the equipments fail, they will accept failure repair. It is assumed that the predictive maintenance makes equipments “as good as new”, while the failure repair does not makes equipment “as good as new”. Monotone process is introduced to describe the case that failure repair does not makes equipment “as good as new”. Under above assumption and others, reliability and check replacement policy of mechanical equipments are studied by using probability analysis and vector markov process method. The explicit expression of the reliabil-ity index and average profit rate (I.e., the long-run average profit per unit time) are derived and the rule of feasibility for the optimal check replacement policy under the largest average profit rate is obtained. The corresponding optimal check re-placement policy can be determined analytically or numerically. The research on the actual example shows that the result can provide some scientific basis for improving the reliability, safety and economic profit of mechanical equipments.

Key words: Check and diagnosis, Check replacement policy, Monotone process Vector markov process method Reliability index, Quasi-physical Virtual assembly Digital measurement Fat-model