A Heuristic Statistical Model for Lifetime Distribution Analysis of Complicated Systems in the Reliability Centered Maintenance
A heuristic conceptual model for to develop the
Reliability Centered Maintenance (RCM), especially in preventive
strategy, has been explored during this paper. In most real cases
which complicity of system obligates high degree of reliability, this
model proposes a more appropriate reliability function between life
time distribution based and another which is based on relevant
Extreme Value (EV) distribution. A statistical and mathematical
approach is used to estimate and verify these two distribution
functions. Then best one is chosen just among them, whichever is
more reliable. A numeric Industrial case study will be reviewed to
represent the concepts of this paper, more clearly.
[1] Fisher, R. A., Tippett, L., Limiting forms of the frequency
distribution of the largest and smallest member of a sample, Proc
Cambridge Phil Soc, No.24, 1928, pp.180-190.
[2] Gumbel, E. J., statistical Theory of Extreme values and Some
Practical Applications, Applied Mathematics Series Publication,
No. 33, 1954.
[3] Ang, AH-S, Tang, WH., Probability concepts in engineering
planning and design, Vol. 2, New York, John Wiley and Sons,
1984.
[4] Kotz, S., Nagarajah, S., Extreme Value Distribution: Theory and
Applications, London, Imperial College Press, 2000.
[5] Elkahlout, G. R., Bayes Estimators for the Extreme-Value
Reliability Function, Computers and Mathematics with
Applications, No.51, 2006, pp.673-679.
[6] Lye, L. M., Hapuarachchi, K. P., Ryan, S., Bayes estimation of the
extreme-value reliability function, IEEE Trans. Reliability, Vol.4,
No.42, 1993, pp.641-644.
[7] Crandall, S. H., First-crossing probability of the linear oscillator, J
Sound Vib, No.12, 1970, pp.285-299.
[8] Kawano, K., Venkataramana, K., Dynamic response and reliability
analysis of large offshore structures, Comput Methods Appl Mech
Eng, No.168, 1999, pp.255-272.
[9] Chen, J. J., Duan, B.Y., Zeng, Y.G., Study on dynamic reliability
analysis of the structures with multi-degree-of-freedom, Comput
Struct, Vol.5, No.62, 1997, pp.877-881.
[10] Jian-Bing, Chen, Jie, Li, The extreme value distribution and
dynamic reliability analysis of nonlinear structures with uncertain
parameters, Structural Safety, No.29, 2007, pp.77-93.
[11] Hideo, Hirose, More accurate breakdown voltage estimation for the
new step-up test method in the gumbel distribution model,
European Journal of Operational Research, No.177, 2007, pp. 406-
419.
[12] Jie, Li, Jian-bing, Chen, Wen-liang, Fan, The equivalent extremevalue
event and evaluation of the structural system reliability,
Structural Safety, No.29, 2007, pp.112-131.
[13] Gumbel, E. J., Statistics of extremes, Columbia University Press,
1958.
[14] Karbasian, Mahdi, Mahdavi, Mojtaba, A new method for
computing the reliability of composite systems, Proceeding of
Summer Safety and Reliability Seminars (SSARS), Poland, Spot,
2007, Vol.1, pp.199-206.
[15] Andrzej, S. N., Kevin, R. C, Reliability of Structures, Singapore,
Mc Graw Hill, 2000.
[1] Fisher, R. A., Tippett, L., Limiting forms of the frequency
distribution of the largest and smallest member of a sample, Proc
Cambridge Phil Soc, No.24, 1928, pp.180-190.
[2] Gumbel, E. J., statistical Theory of Extreme values and Some
Practical Applications, Applied Mathematics Series Publication,
No. 33, 1954.
[3] Ang, AH-S, Tang, WH., Probability concepts in engineering
planning and design, Vol. 2, New York, John Wiley and Sons,
1984.
[4] Kotz, S., Nagarajah, S., Extreme Value Distribution: Theory and
Applications, London, Imperial College Press, 2000.
[5] Elkahlout, G. R., Bayes Estimators for the Extreme-Value
Reliability Function, Computers and Mathematics with
Applications, No.51, 2006, pp.673-679.
[6] Lye, L. M., Hapuarachchi, K. P., Ryan, S., Bayes estimation of the
extreme-value reliability function, IEEE Trans. Reliability, Vol.4,
No.42, 1993, pp.641-644.
[7] Crandall, S. H., First-crossing probability of the linear oscillator, J
Sound Vib, No.12, 1970, pp.285-299.
[8] Kawano, K., Venkataramana, K., Dynamic response and reliability
analysis of large offshore structures, Comput Methods Appl Mech
Eng, No.168, 1999, pp.255-272.
[9] Chen, J. J., Duan, B.Y., Zeng, Y.G., Study on dynamic reliability
analysis of the structures with multi-degree-of-freedom, Comput
Struct, Vol.5, No.62, 1997, pp.877-881.
[10] Jian-Bing, Chen, Jie, Li, The extreme value distribution and
dynamic reliability analysis of nonlinear structures with uncertain
parameters, Structural Safety, No.29, 2007, pp.77-93.
[11] Hideo, Hirose, More accurate breakdown voltage estimation for the
new step-up test method in the gumbel distribution model,
European Journal of Operational Research, No.177, 2007, pp. 406-
419.
[12] Jie, Li, Jian-bing, Chen, Wen-liang, Fan, The equivalent extremevalue
event and evaluation of the structural system reliability,
Structural Safety, No.29, 2007, pp.112-131.
[13] Gumbel, E. J., Statistics of extremes, Columbia University Press,
1958.
[14] Karbasian, Mahdi, Mahdavi, Mojtaba, A new method for
computing the reliability of composite systems, Proceeding of
Summer Safety and Reliability Seminars (SSARS), Poland, Spot,
2007, Vol.1, pp.199-206.
[15] Andrzej, S. N., Kevin, R. C, Reliability of Structures, Singapore,
Mc Graw Hill, 2000.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:52593", author = "Mojtaba Mahdavi and Mohamad Mahdavi and Maryam Yazdani", title = "A Heuristic Statistical Model for Lifetime Distribution Analysis of Complicated Systems in the Reliability Centered Maintenance", abstract = "A heuristic conceptual model for to develop the
Reliability Centered Maintenance (RCM), especially in preventive
strategy, has been explored during this paper. In most real cases
which complicity of system obligates high degree of reliability, this
model proposes a more appropriate reliability function between life
time distribution based and another which is based on relevant
Extreme Value (EV) distribution. A statistical and mathematical
approach is used to estimate and verify these two distribution
functions. Then best one is chosen just among them, whichever is
more reliable. A numeric Industrial case study will be reviewed to
represent the concepts of this paper, more clearly.", keywords = "Lifetime distribution, Reliability, Estimation,
Extreme value, Improving model, Series, Parallel.", volume = "4", number = "11", pages = "1189-5", }