An Optimal Bivariate Replacement Policy for a Multistate Degenerative System with an Extreme Shock
Keywords:
Extreme Shocks, Degenerative System, Replacement Policy
Abstract
In this paper, an optimal bivariate replacement policy for a multistate degenerative system with an extreme shock is derived.
References
M.S.A-Hameed and F.Proschan, Shock Models with underlying Birth Process, Journal of Applied Probability, 12(1975), 18-28.
R.Barlow and F.Proschan, Mathematical Theory of Reliability, (1965).
R.Barlow and F.Proschan, Statistical Theory of Reliability and life testing, John Wiley, New York, (1975).
W.Feller, An introduction to Probability Theory and its Applications, John Wiley, New York, (1965).
P.Govindaraju, U.Rizwan and V.Thagaraj, Optimal Replacement Policy for a Multistate Degenrative System, Int. J. of Computational and Applied Mathematics, 4(3)(2009), 175-186.
P.Govindaraju, U.Rizwan and V.Thagaraj, An extreme shock maintenance model under a Bivariate Reaplacement Policy, Research Methods in Mathematical Sciences, (2011), 1-10.
Y.Lam, Geometric Processes and Replacement Problem, Acta. Math. Sinica, 4(1988), 366-377.
Y.Lam, An Optimal Repairable Replacement Model for Deteriorating System, J. App. Prob., 28(1991), 843-851.
Y.Lam, A Monotone Process Maintenance Model for a Multistate System, J. App. Prob., 42(2005), 1-14.
Y.Lam and Yeekit, Optimal Maintenance Model for a Multistate Deteriorating System, Int. J. Sys. Sci., 34(5)(2003), 303-308.
Y.Lam and Y.L.Zhang, A Geometric Process Maintenance Model and Deteriorating System under a Random Environment, IEEE Transactions on Reliability, 52(2003), 83-89.
Y.Lam and Y.L.Zhang, A Shock Model for the Maintenance Problem of a Repairable System, Computers and Operations Research, 31(2004), 1807-1820.
K.N.F.Leung, A Note on A Bivariate Optimal Replacement Policy for a Repairable System, Engineering Optimization, 38(5)(2006), 621-625.
E.J.Muth, An Optimal Decision Rule for Repair Vs. Replacement, IEEE Trans. Reliability., 3(1977), 179-181.
F.Pellerey, Shock Models with underlying Counting Process, J. Appl. Prob., 31(1994), 156-166.
Philip J.F.Boland and Frank Proschan, Optimum Replacement of a system subject to shocks, FSU Statistics Report, (1981), 81-131.
S.M.Ross, Stochastic Processes, (2nd ed), John Wiley and Sons, New York, (1996).
S.M.Ross, Introduction to Probability Modelling, Academic Press, New York, (1997).
A.Rangan and A.Tansu, A New Shock Model for Systems Subject to Random Threshold Failure, PWASET, 30(2008).
U.Rizwan, On Stochastic Life Time Models, J. Madras University - Section B : Sciences, 52(2000), 121-143.
J.G.Shantikumar and U.Sumita, General Shock Models Associated with Correlated Renewal Sequences, J. Appl. Prob., 20(1983), 600-614.
J.G.Shantikumar and U.Sumita, Distribution Properties of the System Failure Time in a General Shock Model, Advances in Applied Probability, 16(1984), 363-377.
A.D.J.Stanley, On geometric processes and repair replacement problems, Micro elce. Reliab., 33(1993), 489-491.
H.M.Taylor and S.Karlin, An Introduction to Stochastic Modelling, Academic Press, New York, (1994).
V.Thangaraj and U.Rizwan, Optimal Replacement Policies in Burn-in Process for an Alternative Repair Model, International Journal of Information and Management Sciences, 12(3)(2001), 43-56.
Y.L.Zhang, A Bivariate Optimal Replacement Policy for a Repairable System, J. Appl. Prob., 31(1994), 1123-1127.
Y.L.Zhang, R.C.M.Yam and M.J.Zuo, A Bivariate Optimal Replacement Policy for a Multistate Repairable System, Reliability Engineering and System Safety., 92(2007), 535-542.
D.Zuckerman, Replacement Models under Additive Damage, Naval Research Logistics Quarterly, 24(4)(1977), 549-558.
R.Barlow and F.Proschan, Mathematical Theory of Reliability, (1965).
R.Barlow and F.Proschan, Statistical Theory of Reliability and life testing, John Wiley, New York, (1975).
W.Feller, An introduction to Probability Theory and its Applications, John Wiley, New York, (1965).
P.Govindaraju, U.Rizwan and V.Thagaraj, Optimal Replacement Policy for a Multistate Degenrative System, Int. J. of Computational and Applied Mathematics, 4(3)(2009), 175-186.
P.Govindaraju, U.Rizwan and V.Thagaraj, An extreme shock maintenance model under a Bivariate Reaplacement Policy, Research Methods in Mathematical Sciences, (2011), 1-10.
Y.Lam, Geometric Processes and Replacement Problem, Acta. Math. Sinica, 4(1988), 366-377.
Y.Lam, An Optimal Repairable Replacement Model for Deteriorating System, J. App. Prob., 28(1991), 843-851.
Y.Lam, A Monotone Process Maintenance Model for a Multistate System, J. App. Prob., 42(2005), 1-14.
Y.Lam and Yeekit, Optimal Maintenance Model for a Multistate Deteriorating System, Int. J. Sys. Sci., 34(5)(2003), 303-308.
Y.Lam and Y.L.Zhang, A Geometric Process Maintenance Model and Deteriorating System under a Random Environment, IEEE Transactions on Reliability, 52(2003), 83-89.
Y.Lam and Y.L.Zhang, A Shock Model for the Maintenance Problem of a Repairable System, Computers and Operations Research, 31(2004), 1807-1820.
K.N.F.Leung, A Note on A Bivariate Optimal Replacement Policy for a Repairable System, Engineering Optimization, 38(5)(2006), 621-625.
E.J.Muth, An Optimal Decision Rule for Repair Vs. Replacement, IEEE Trans. Reliability., 3(1977), 179-181.
F.Pellerey, Shock Models with underlying Counting Process, J. Appl. Prob., 31(1994), 156-166.
Philip J.F.Boland and Frank Proschan, Optimum Replacement of a system subject to shocks, FSU Statistics Report, (1981), 81-131.
S.M.Ross, Stochastic Processes, (2nd ed), John Wiley and Sons, New York, (1996).
S.M.Ross, Introduction to Probability Modelling, Academic Press, New York, (1997).
A.Rangan and A.Tansu, A New Shock Model for Systems Subject to Random Threshold Failure, PWASET, 30(2008).
U.Rizwan, On Stochastic Life Time Models, J. Madras University - Section B : Sciences, 52(2000), 121-143.
J.G.Shantikumar and U.Sumita, General Shock Models Associated with Correlated Renewal Sequences, J. Appl. Prob., 20(1983), 600-614.
J.G.Shantikumar and U.Sumita, Distribution Properties of the System Failure Time in a General Shock Model, Advances in Applied Probability, 16(1984), 363-377.
A.D.J.Stanley, On geometric processes and repair replacement problems, Micro elce. Reliab., 33(1993), 489-491.
H.M.Taylor and S.Karlin, An Introduction to Stochastic Modelling, Academic Press, New York, (1994).
V.Thangaraj and U.Rizwan, Optimal Replacement Policies in Burn-in Process for an Alternative Repair Model, International Journal of Information and Management Sciences, 12(3)(2001), 43-56.
Y.L.Zhang, A Bivariate Optimal Replacement Policy for a Repairable System, J. Appl. Prob., 31(1994), 1123-1127.
Y.L.Zhang, R.C.M.Yam and M.J.Zuo, A Bivariate Optimal Replacement Policy for a Multistate Repairable System, Reliability Engineering and System Safety., 92(2007), 535-542.
D.Zuckerman, Replacement Models under Additive Damage, Naval Research Logistics Quarterly, 24(4)(1977), 549-558.
How to Cite
U.Rizwan, Syed Tahir Hussainy, & J.Manigandan. (2021). An Optimal Bivariate Replacement Policy for a Multistate Degenerative System with an Extreme Shock. International Journal of Current Research in Science and Technology, 3(6), 1-9. Retrieved from https://crst.gfer.org/index.php/crst/article/view/90
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