6533b831fe1ef96bd1298cfc
RESEARCH PRODUCT
On the Analysis of a Random Interleaving Walk–Jump Process with Applications to Testing
Ole-christopher GranmoB. John OommenAnis Yazidisubject
Statistics and ProbabilityRandom graphDiscrete mathematicsRandom variateRandom fieldModeling and SimulationRandom compact setRandom functionRandom elementRandom permutationRandom walkAlgorithmMathematicsdescription
Abstract Although random walks (RWs) with single-step transitions have been extensively studied for almost a century as seen in Feller (1968), problems involving the analysis of RWs that contain interleaving random steps and random “jumps” are intrinsically hard. In this article, we consider the analysis of one such fascinating RW, where every step is paired with its counterpart random jump. In addition to this RW being conceptually interesting, it has applications in testing of entities (components or personnel), where the entity is never allowed to make more than a prespecified number of consecutive failures. The article contains the analysis of the chain, some fascinating limiting properties, and simulations that justify the analytic steady-state results. Some simulation results for the chain's transient behavior are also included. Finally, a comparative testing against a hidden Markov model shows that within the testing framework, the results of our model are competitive, if not superior. As far as we...
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-10-01 | Sequential Analysis |