Abstract
A k-out-of-n:F system with both of soft and hard failures is considered such that its components degrade through internal and external factors. A linear model is considered for degradation path of each component. Reliability function of the system is derived and the effect of varying the parameters are studied on reliability function for some systems. Moreover, the effect of calibration on reliability and maximum working time of such a system is investigated. The optimal number of calibrations is also determined for some special cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asadi, M., Bayramoglu, I. (2006). The mean residual life function of a \(k\)-out-of-\(n\) structure at the system level. IEEE Transactions on Reliability, 55(2), 314–318.
Bairamov, I., Arnold, B. C. (2008). On the residual life lengths of the remaining components in an \((n-k+1)\)-out-of-\(n\) system. Statistics & Probability Letters, 78(8), 945–952.
Coit, D. W., Evans, J. L., Vogt, N. T., Thompson, J. R. (2005). A method for correlating field life degradation with reliability prediction for electronic modules. Quality and Reliability Engineering International, 21(7), 715–726.
Cui, L., Haung, J., Li, Y. (2016). Degradation models with Wiener diffusion processes under calibrations. IEEE Transactions on Reliability, 65(2), 613–623.
David, H. A., Nagaraja, H. N. (2003). Order statistics (3rd ed.). New York: Wiley.
Haghighi, F., Bae, S. J. (2015). Reliability estimation from linear degradation and failure time data with competing risks under a step-stress accelerated degradation Test. IEEE Transactions on Reliability, 64(3), 960–971.
Haghighi, F., Nikulin, M. (2010). On the linear degradation model with multiple failure modes. Journal of Applied Statistics, 37(9), 1499–1507.
Kong, D., Cui, L. (2015). Bayesian inference of multi-stage reliability for degradation systems with calibrations. Journal of Risk and Reliability, 230(1), 1–16.
Lawless, J. F. (2003). Statistical models and methods for lifetime data (2nd ed.). New York: Wiley.
Li, J., Coit, D. W., Elsayed, E. A. (2011). Reliability modeling of a series system with correlated or dependent component degradation processes. In 2011 International conference on quality, reliability, risk, maintenance, and safety engineering (ICQR2MSE) (pp. 388–393).
Liu, Z., Ma, X., Zhao, Y. (2013). Field reliability prediction based on degradation data and environmental data. Reliability and maintainability symposium (RAMS), 2013 proceedings-annual (pp. 1–6).
Lu, C. J., Meeker, W. O. (1993). Using degradation measures to estimate a time-to-failure distribution. Technometrics, 35(2), 161–174.
Nikulin, M., Wu, H. D. I. (2016). Cox model for degradation and failure time data. The Cox model and its applications (1st ed., pp. 109–114). New York: Springer.
Noortwijk, J. M. V. (2009). A survey of the application of gamma processes in maintenance. Reliability Engineering and System Safety, 94(1), 2–21.
Rodrguez-Narciso, S., Christen, J. A. (2016). Optimal sequential bayesian analysis for degradation tests. Lifetime Data Analysis, 22(3), 405–428.
Song, S., Chatwattanasiri, N., Coit, D. W., Feng, Q., Wattanapongsakorn, N. (2012). Reliability analysis for k-out-of-n systems subject to multiple dependent competing failure processes. In 2012 International conference on quality, reliability, risk, maintenance, and safety engineering (ICQR2MSE) (pp. 36–42).
Tavangar, M., Bairamov, I. (2015). On conditional residual lifetime and conditional inactivity time of \(k\)-out-of-\(n\) systems. Reliability Engineering and System Safety, 144, 225–233.
Xu, Z., Hong, Y., Jin, R. (2016). Nonlinear general path models for degradation data with dynamic covariates. Applied Stochastic Models in Business and Industry, 32(2), 153–167.
Zhao, M., Xie, M. (1994). A model of storage reliability with possible initial failures. Reliability Engineering and System Safety, 43(3), 262–273.
Zhao, M., Xie, M., Zhang, Y. (1995). A study of a storage reliability estimation problem. Quality and Reliability Engineering International, 11(2), 123–127.
Acknowledgements
The authors express their sincere thanks to anonymous referees for their useful comments and constructive criticisms on the original version of this manuscript, which led to this considerably improved version.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Nezakati, E., Razmkhah, M. & Haghighi, F. Reliability analysis of a k-out-of-n:F system under a linear degradation model with calibrations. Ann Inst Stat Math 71, 537–552 (2019). https://doi.org/10.1007/s10463-018-0650-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10463-018-0650-4