Failure models indexed by two scales. (English) Zbl 0930.60075
The currently used failure models in reliability are indexed by a single scale, viz., time. There are situations which require that failure be described by several scales. For example, the setting of optimal warranties on automobiles depends on expected time and mileage to failure. The authors propose a strategy for constructing failure models indexed by two scales, time and a time-dependent quantity such as usage. They consider specific processes such as Poisson, the gamma and the Markov additive. Some of these are in closed form and some require numerical techniques. The method is illustrated for optimal warranties involving real data.
Reviewer: P.R.Parthasarathy (Madras)
MSC:
60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |
62A01 | Foundations and philosophical topics in statistics |
62N05 | Reliability and life testing |
90B25 | Reliability, availability, maintenance, inspection in operations research |