A Discretizing Method for Reliability Computation in Complex Stress-strength Models
This paper proposes, implements and evaluates an original discretization method for continuous random variables, in order to estimate the reliability of systems for which stress and strength are defined as complex functions, and whose reliability is not derivable through analytic techniques. This method is compared to other two discretizing approaches appeared in literature, also through a comparative study involving four engineering applications. The results show that the proposal is very efficient in terms of closeness of the estimates to the true (simulated) reliability. In the study we analyzed both a normal and a non-normal distribution for the random variables: this method is theoretically suitable for each parametric family.
[1] T. Aven, U. Jensen, Stochastic models in reliability, Springer-Verlag,
New-York, 1999.
[2] G. R. Dargahi-Noubary, "Estimation of stress-strength reliability based
on tail-modelling", Applied Stochastic Models and Data Analysis, vol.
18(1), pp. 17-24, 1992.
[3] R.L. Disney, N.J. Sheth, and C. Lipson, "The determination of the
probability of failure by stress/strength interference theory", Proc. Ann.
Symp. Reliability, pp. 417-422, 1968.
[4] J. R. English, T. Sargent, and T. L. Landers, "A discretizing approach
for stress/strength analysis", IEEE Trans. Reliability, vol. 45, pp. 84-89,
1996.
[5] J. R. D-Errico and N. A. Zaino Jr., "Statistical tolerancing using a
modification of "Taguchi-s method"", Technometrics, vol. 30, pp. 397-
405, 1988.
[6] K.C. Kapur and L.R. Lamberson, Reliability in Engineering Design,
John Wiley & Sons, 1976.
[7] R. C. Geary, "The Frequency Distribution of the Quotient of Two Normal
Variates", Journal of the Royal Statistical Society, vol. 93 (3), pp. 442-
446, 1930.
[8] H. Krishna and P.S. Pundir, "Discrete Maxwell Distribution", InterStat,
Statistics on the Internet, http://interstat.statjournals.net/YEAR/2007/
articles/0711003.pdf, 2007
[9] D. Roy and T. Dasgupta, "A continuous approximation for evaluating
reliability of complex systems under stress-strength model", Communications
in Statistics - Simulation and Computation, vol. 29(3), pp.
829-844, 2000.
[10] D. Roy and T. Dasgupta, "A discretizing approach for evaluating reliability
of complex systems under stress-strength model", IEEE transactions
on reliability, vol. 50(2), 145-150, 2001.
[11] D. Roy and T. Dasgupta, "Evaluation of reliability of complex systems
by means of a discretizing approach Weibull set-up", International
Journal of Quality & Reliability Management, vol. 19(6), pp. 792-801,
2002.
[12] D. Roy, "Discrete Rayleigh distribution", IEEE Transactions on reliability,
vol. 53(2), pp. 255-260, 2004.
[13] D. Roy and T. Ghosh, "A New Discretization ApproachWith Application
in Reliability Estimation", IEEE Transactions on reliability, vol. 58(3),
pp. 456-461, 2009.
[14] G. Taguchi, "Performance Analysis Design", International journal of
production, vol. 16, pp. 521-530, 1978.
[1] T. Aven, U. Jensen, Stochastic models in reliability, Springer-Verlag,
New-York, 1999.
[2] G. R. Dargahi-Noubary, "Estimation of stress-strength reliability based
on tail-modelling", Applied Stochastic Models and Data Analysis, vol.
18(1), pp. 17-24, 1992.
[3] R.L. Disney, N.J. Sheth, and C. Lipson, "The determination of the
probability of failure by stress/strength interference theory", Proc. Ann.
Symp. Reliability, pp. 417-422, 1968.
[4] J. R. English, T. Sargent, and T. L. Landers, "A discretizing approach
for stress/strength analysis", IEEE Trans. Reliability, vol. 45, pp. 84-89,
1996.
[5] J. R. D-Errico and N. A. Zaino Jr., "Statistical tolerancing using a
modification of "Taguchi-s method"", Technometrics, vol. 30, pp. 397-
405, 1988.
[6] K.C. Kapur and L.R. Lamberson, Reliability in Engineering Design,
John Wiley & Sons, 1976.
[7] R. C. Geary, "The Frequency Distribution of the Quotient of Two Normal
Variates", Journal of the Royal Statistical Society, vol. 93 (3), pp. 442-
446, 1930.
[8] H. Krishna and P.S. Pundir, "Discrete Maxwell Distribution", InterStat,
Statistics on the Internet, http://interstat.statjournals.net/YEAR/2007/
articles/0711003.pdf, 2007
[9] D. Roy and T. Dasgupta, "A continuous approximation for evaluating
reliability of complex systems under stress-strength model", Communications
in Statistics - Simulation and Computation, vol. 29(3), pp.
829-844, 2000.
[10] D. Roy and T. Dasgupta, "A discretizing approach for evaluating reliability
of complex systems under stress-strength model", IEEE transactions
on reliability, vol. 50(2), 145-150, 2001.
[11] D. Roy and T. Dasgupta, "Evaluation of reliability of complex systems
by means of a discretizing approach Weibull set-up", International
Journal of Quality & Reliability Management, vol. 19(6), pp. 792-801,
2002.
[12] D. Roy, "Discrete Rayleigh distribution", IEEE Transactions on reliability,
vol. 53(2), pp. 255-260, 2004.
[13] D. Roy and T. Ghosh, "A New Discretization ApproachWith Application
in Reliability Estimation", IEEE Transactions on reliability, vol. 58(3),
pp. 456-461, 2009.
[14] G. Taguchi, "Performance Analysis Design", International journal of
production, vol. 16, pp. 521-530, 1978.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54225", author = "Alessandro Barbiero", title = "A Discretizing Method for Reliability Computation in Complex Stress-strength Models", abstract = "This paper proposes, implements and evaluates an original discretization method for continuous random variables, in order to estimate the reliability of systems for which stress and strength are defined as complex functions, and whose reliability is not derivable through analytic techniques. This method is compared to other two discretizing approaches appeared in literature, also through a comparative study involving four engineering applications. The results show that the proposal is very efficient in terms of closeness of the estimates to the true (simulated) reliability. In the study we analyzed both a normal and a non-normal distribution for the random variables: this method is theoretically suitable for each parametric family.
", keywords = "Approximation, asymmetry, experimental design, interference theory, Monte Carlo simulations.", volume = "4", number = "11", pages = "1409-7", }
