The thesis develops the application of delay time analysis to the area ofmathematical modelling of planned maintenance and inspection ofindustrial systems. Chapter 1 gives an introduction to the history andtechniques in use of maintenance modelling and surveys appropriateliterature in the field. A section is devoted to papers published on delaytime analysis. Chapter 2 introduces and develops mathematical models formodelling the reliability, maintenance and inspection of repairablesystems. Chapter 3 gives an account of parameter estimation and modelupdating techniques in the light of subjective and observational data setscollected over a period of system operation. Chapter 4 addresses a biasin the probability distribution function of delay t...