Abstract
The life distributionH(t) of a device subject to shocks governed by a Poisson process and pure birth process is considered as a function of probabilitiesP k of not surviving the firstk shocks. It is shown that some properties of a discrete distribution\(\left\{ {\bar P_k } \right\}\) are reflected on properties of the continuous life distributionH(t). In particular, ifP k has the discrete NBUFR properties, thenH(t) has the continuous NBUFR and NBAFR properties. The NBUFR and NBAFR life distributions are obtained under suitable assumptions on birth rate and the probability of surviving a given number of shocks in a pure birth shock model. Some other general forms of shock models are also considered.
Resumen
La distribución de vidaH(t) de un sistema sujeto ashocks regidos por un proceso de Poisson y un proceso de nacimiento puro se considera como una función de las probabilidadesP k de no sobrevivir después dek shocks. Se demuestra que ciertas propiedades de una distribución discreta {P k} se reflejan en propiedades de la distribución de vida continuaH(t). En particular siP k tiene las propiedades NBUFR discretas, entoncesH(t) tiene las propiedades continuas NBUFR y NBAFR. Las distribuciones de vida NBUFR y NBAFR se obtienen bajo condiciones adecuadas en la tasa de nacimiento y la probabilidad de supervivencia a un cierto número deshocks en un modelo deshock de nacimiento puro. También se consideran otras formas de modelos deshocks.
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Abouammoh, A.M., Hindi, M.I. & Ahmed, A.N. Shock models with NBUFR and NBAFR survivals. TDE 3, 97–113 (1988). https://doi.org/10.1007/BF02863509
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DOI: https://doi.org/10.1007/BF02863509