The evolution of maintenance management is briefly introduced in this paper, from corrective maintenance to preventive maintenance. First, a range of condition monitoring and fault diagnosis techniques developed in different industries are surveyed; Second, many methods of condition monitoring are presented; Third, mathematical methods used in condition monitoring are given; Then the merits and shortcomings are discussed.Efficient maintenance policies are of fundamental importance in system engineering because of their fallbacks into the safety and economics of plant operation. Applying condition-based maintenance to a system can reduce the cost and extend the availability of facilities. With the advent of personal computers as fast and cost effective machines for data acquisition and processing of multiple signals some shortcomings mentioned in condition monitoring could be solved or reduced to some extent. These PCs can be a solution as a condition monitoring based maintenance system. The evolution of maintenance management is briefly introduced in this paper, from corrective maintenance to preventive maintenance. First, a range of condition monitoring and fault diagnosis techniques developed in different industries are surveyed; Second, many methods of condition monitoring are presented; Third, mathematical methods used in condition monitoring is given; Then the merits and shortcomings are discussed; Efficient maintenance policies are of fundamental importance in system engineering because of fallbacks into the safety and economics of plant operation. With the advent of personal computers as fast and cost effective machines for data acquisition and processing of multiple signals some shortcomings mentioned in condition monitoring could be solved or reduced to some extent. These PCs can be a solution as a condition monitoring based maintenance system .