A Heuristic Statistical Model for Lifetime Distribution Analysis of Complicated Systems in the Reliability Centered Maintenance

Authors: Mojtaba Mahdavi, Mohamad Mahdavi, Maryam Yazdani

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330395

References:

[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.