A Quasi-renewal Process and Its Applications

4.5 Concluding Discussions

All imperfect maintenance models in this chapter are based on the quasi-renewal process: successive operating times of a system are independent and decreasing by a fraction (1 − α, and successive maintenance times are independent and increasing by a fraction (β − 1), or alternatively, upon each repair the time to failure will be reduced to a fraction α of the immediately previous one and be independent of all previous ones and the repair time will be increased to a multiple β of the immediately previous one and be independent of all the previous ones. In other words, the successive times to failure form a decreasing quasi-renewal process with parameter α, and the successive maintenance times constitute an increasing quasi-renewal process with parameter β. One can see that most results obtained in this chapter are in closed forms. Based on these results the optimal maintenance policies can be easily obtained by using any nonlinear programming software. Therefore, the quasi-renewal process is effective to treat hardware imperfect maintenance.

For most technical systems, such as cars or refrigerators, when a new one is put into use, it will be in a good operating state and may not need major repairs at the beginning period. After a period of operating, to say, after a certain number of imperfect (usually minor) repairs at failure the system will be in a worse operating condition and then a better or perfect maintenance (preventive or unplanned, especially preventive) is necessary at a higher cost to bring the system to a better operating condition with higher reliability. Therefore, the imperfect maintenance models discussed in this chapter will be practical in reliability and maintenance practice.