Reliability Measure of a Relay Parallel System under Dependence Conditions

ABSTRACT

In a relay system of dependent components, the failure to close reliability measure is given as a Girsanov transform of the failure to open reliability measure.

Cite this paper

V. Bueno, "Reliability Measure of a Relay Parallel System under Dependence Conditions,"*American Journal of Operations Research*, Vol. 3 No. 1, 2013, pp. 94-100. doi: 10.4236/ajor.2013.31A009.

V. Bueno, "Reliability Measure of a Relay Parallel System under Dependence Conditions,"

References

[1] R. Barlow and F. Proschan, “Statistical Theory of Reliability and Life Testing: Probability Models,” Mc Ardle Press, Inc. Silver Spring, 1981.

[2] P. Bremaud, “Point Processes and Queues: Martingales Dynamics,” Springer Verlag, New York, 1981. doi:10.1007/978-1-4684-9477-8

[3] E. Arjas and A.Yashin, “A Note on Random Intensities and Conditional Survival Functions,” Journal of Applied Probability, Vol. 25, No. 3, 1988, pp. 630-635. doi:10.2307/3213991

[4] V. C. Bueno and I. M. Carmo, “Active Redundancy Allocation for a k-Out-Of-n:F System of Dependent Components,” European Journal of Operational Research, Vol. 176, No. 2, 2007, pp. 1041-1051. doi:10.1016/j.ejor.2005.09.012

[5] V. C. Bueno and J. E. Menezes, “Patterns Reliability Importance under Dependence Condition and Different Information Levels,” European Journal of Operational Research, Vol. 177, No. 1, 2007, pp.354-364. doi:10.1016/j.ejor.2005.10.042

[6] J. D. Esary, F. Proschan and D. W. Walkup, “Association of Random Variables with Applications,” The Annals of Mathematical Statistics, Vol. 38, No. 5, 1967, pp.1466-1474. doi:10.1214/aoms/1177698701

[7] J. D. Esary and F. Proschan, “A Reliability Bound for System of Maintained, Interdependent Components,” Journal of American Statistical Association, Vol. 65, No. 329, 1970, pp.713-717.

[8] R. Harris, “A Multivariate Definition for Increasing Hazard Rate Distribution Functions,” The Annals of Mathematical Statistics, Vol. 41, No. 2, 1970, pp. 713-717. doi:10.1214/aoms/1177697121

[9] A. W. Marshall, “Multivariate Distributions with Monotone Hazard Rate,” In: R. E. Barlow, J. B. Fussel and N. D. Singpurwalla, Eds., Reliability and Fault Tree Analysis, Edited, Society for Industrial and Applied Mathematics, Philadelphia, 1975, pp. 259-284.

[10] E. Arjas “A Stochastic Process Approach to Multivariate Reliability System: Notions Based on Conditional Stochastic Order,” Mathematics of Operations Research, Vol. 6, No. 2, 1981, pp. 263-276. doi:10.1287/moor.6.2.263

[1] R. Barlow and F. Proschan, “Statistical Theory of Reliability and Life Testing: Probability Models,” Mc Ardle Press, Inc. Silver Spring, 1981.

[2] P. Bremaud, “Point Processes and Queues: Martingales Dynamics,” Springer Verlag, New York, 1981. doi:10.1007/978-1-4684-9477-8

[3] E. Arjas and A.Yashin, “A Note on Random Intensities and Conditional Survival Functions,” Journal of Applied Probability, Vol. 25, No. 3, 1988, pp. 630-635. doi:10.2307/3213991

[4] V. C. Bueno and I. M. Carmo, “Active Redundancy Allocation for a k-Out-Of-n:F System of Dependent Components,” European Journal of Operational Research, Vol. 176, No. 2, 2007, pp. 1041-1051. doi:10.1016/j.ejor.2005.09.012

[5] V. C. Bueno and J. E. Menezes, “Patterns Reliability Importance under Dependence Condition and Different Information Levels,” European Journal of Operational Research, Vol. 177, No. 1, 2007, pp.354-364. doi:10.1016/j.ejor.2005.10.042

[6] J. D. Esary, F. Proschan and D. W. Walkup, “Association of Random Variables with Applications,” The Annals of Mathematical Statistics, Vol. 38, No. 5, 1967, pp.1466-1474. doi:10.1214/aoms/1177698701

[7] J. D. Esary and F. Proschan, “A Reliability Bound for System of Maintained, Interdependent Components,” Journal of American Statistical Association, Vol. 65, No. 329, 1970, pp.713-717.

[8] R. Harris, “A Multivariate Definition for Increasing Hazard Rate Distribution Functions,” The Annals of Mathematical Statistics, Vol. 41, No. 2, 1970, pp. 713-717. doi:10.1214/aoms/1177697121

[9] A. W. Marshall, “Multivariate Distributions with Monotone Hazard Rate,” In: R. E. Barlow, J. B. Fussel and N. D. Singpurwalla, Eds., Reliability and Fault Tree Analysis, Edited, Society for Industrial and Applied Mathematics, Philadelphia, 1975, pp. 259-284.

[10] E. Arjas “A Stochastic Process Approach to Multivariate Reliability System: Notions Based on Conditional Stochastic Order,” Mathematics of Operations Research, Vol. 6, No. 2, 1981, pp. 263-276. doi:10.1287/moor.6.2.263