Stochastic Partial Orders, With Applications to Reliability | ||
| The Egyptian Statistical Journal | ||
| Article 10, Volume 44, Issue 1, June 2000, Pages 112-120 PDF (4 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.2000.313828 | ||
| Authors | ||
| A. N. Ahmed* ; S. I. Mira* | ||
| Cairo University | ||
| Abstract | ||
| Suppose each of two devices is subjected to shocks occurring randomly as events in a Poisson process with constant intensity . Let Pkdenote the probability that the first device will survive the first k shocks and Qkdenote such a probability for the second device. Let H1 (t) and H2 (t) denote the survival functions of the first and second device respectively. In this paper, we show that some new partial ordering, namely dual (D), dual stochastic (DST), dual weak likelihood ratio (DWLR), increasing failure rate (IFR), dual mean residual lives (DMRL) and dual convex (DC) ordering between the shock survival probabilities Pk and Qkare preserved by the corresponding survival functions H1 (t) and H2 (t). We also obtain sufficient conditions under which the above-mentioned relations between the discrete distributions are verified in some commutative damage shock models. | ||
| Keywords | ||
| Stochastic Partial Orders - Namely Dual - Dual Stochastic; DWLR; DMRL; IFR; DC | ||
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