Age Dependent Minimal Repair.
Abstract
The failure process studied in this paper models the following maintained system setting. A piece of equipment is put in operation at time t=0. Each time it fails, a maintenance action is taken which, with probability p(t), is a complete repair or, with probability q(t)=1-p(t), is a minimal repair, where t is the age at failure of the equipment under maintenance. Since availability results are not pursued in this paper, only operating time will be recorded. This is equivalent to assuming that maintenance is executed in negligible time. It is also assumed that complete repairs restore failed items to their good as new condition in such a way that the times between successive complete repairs are independent and identically distributed. The formal development of the model is given in an appendix where the basic facts are established. In section 2, we show that some aging properties of the equipment's life distribution are inherited by the distribution of the time between successive complete repairs under suitable monotonicity of the function p. A counterexample is also given to the conjecture of Brown and Proschan (1980) that the NBUE aging property is also inherited when the function p is constant. In Section 3, some inequalities and further properties of the model are developed which, as in Section 2, extend results obtained by Brown and Proschan.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1982
- Accession Number
- ADA116846
Entities
People
- Henry W. Block
- Thomas H. Savits
- Wagner S. Borges
Organizations
- University of Pittsburgh