Yes / It is shown that the probability generating function of a lifetime random variable T on a finite lattice with polynomial failure rate satisfies a certain differential equation. The interrelationship with Markov chain theory is highlighted. The differential equation gives rise to a system of differential equations which, when inverted, can be used in the limit to express the polynomial coefficients in terms of the factorial moments of T. This then can be used to estimate the polynomial coefficients. Some special cases are worked through symbolically using Computer Algebra. A simulation study is used to validate the approach and to explore its potential in the reliability context.
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/11682 |
| Date | 13 October 2013 |
| Creators | Csenki, Attila |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Article, Accepted Manuscript |
| Rights | © 2015 Springer. Full-text reproduced in accordance with the publisher’s self-archiving policy. |
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