Prediction for the future system failures based on Type-II censored coherent systems data under a proportional hazard model

Document Type : Original Scientific Paper

Author

Department of Statistics‎, ‎University of Payame Noor‎, ‎Tehran‎, ‎Iran

Abstract

In this paper‎, ‎we consider a k-component coherent system while the system lifetimes are observed‎, ‎the system structure is known and the component lifetime follows the proportional hazard rate model‎. ‎We discuss the prediction problem based on Type-II censored coherent system lifetime data‎. ‎For predicting the future system failures‎, ‎we obtain the maximum likelihood predictor‎, ‎the best unbiased predictor‎, ‎the conditional median predictor and the Bayesian predictors‎. ‎As it seems that the integrals of the Bayes prediction do not possess closed forms‎, ‎the Metropolis-Hastings method is applied to approximating these integrals‎. ‎Different interval predictors based on classical and Bayesian approaches are derived‎. ‎A numerical example is presented to illustrate the prediction methods used in this paper‎. ‎A Monte Carlo simulation study is performed to evaluate and compare the performances of different prediction methods.

Keywords

Main Subjects

References

Balakrishnan, N., Ng, H.K.T. and Navarro, J. (2011a). Linear inference for Type-II censored lifetime data of reliability systems with known signatures. IEEE Transactions on Reliability, 60(2):426–440.
Balakrishnan, N., Ng, H.K.T. and Navarro, J. (2011b). Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures. Journal of Nonparametric Statistics, 23(3):741–752.
Bhattacharya, D. and Samaniego, F.J. (2010). Estimating component characteristics from system failure time data. Naval Research Logistics (NRL), 57:380–389.
Chahkandi, M., Ahmadi, J. and Baratpour, S. (2014). Non-parametric prediction intervals for the lifetime of coherent systems. Statistical Papers, 55(4):1019–1034.
Chivers, C. (2012). MHadaptive: General Markov Chain Monte Carlo for Bayesian Inference Using Adaptive Metropolis-Hastings Sampling. URL: cran.r-project.org/web/packages/MHadaptive/MHadaptive.pdf.
Fallah, A., Asgharzadeh, A. and Ng, H.K.T. (2021a). Statistical inference for component lifetime distribution from coherent system lifetimes under a proportional reversed hazard model. Communications in Statistics-Theory and Methods, 50(16):3809–3833.
Fallah, A., Asgharzadeh, A. and Ng, H.K.T. (2021b). Prediction based on Type-II censored coherent system lifetime data under a proportional reversed hazard rate model. Journal of The Iranian Statistical Society, 20(1):153–181.
Kaminsky, K.S. and Rhodin, L.S. (1985). Maximum likelihood prediction. Annals of the Institute of Statistical Mathematics, 3(Part A):507–517.
Kochar, S., Mukerjee, H. and Samaniego, F.J. (1999). The "signature" of a coherent system and its application to comparisons among systems. Naval Research Logistics (NRL), 46(5):507–523.
MirMostafaee, S.M.T.K., Amini, M. and Asgharzadeh, A. (2016). Bayesian prediction of minimal repair times of a series system based on hybrid censored sample of components' lifetimes under Rayleigh distribution. Communications in Statistics-Theory and Methods, 46(4):1788–1806.
Navarro, J., Ruiz, J.M. and Sandoval, C.J. (2007). Properties of coherent systems with dependent components. Communications in Statistics-Theory and Methods, 36(1):175–191.
Ng, H.K.T., Navarro, J. and Balakrishnan, N. (2012). Parametric inference from system lifetime data under a proportional hazard rate model. Metrika, 75:367–388.
R Core Team (2019). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.
Raqab, M.Z. and Nagaraja, H.N. (1995). On some predictors of future order statistics. Metron, 53(12):185–204.
Robert, C. and Casella, G. (2004). Monte Carlo Statistical Methods. 2nd edition, New York: Springer.
Samaniego, F.J. (1985). On closure of the IFR class under formation of coherent systems. IEEE Transactions on Reliability Theory, 34(1):69–72.
Samaniego, F.J. (2007). System Signatures and their Applications in Engineering Reliability. Vol. 110, Springer Science & Business Media.
Tavangar, M. and Asadi, M. (2020). Component reliability estimation based on system failure-time data. Journal of Statistical Computation and Simulation, 90(17):3232–3249.
Varian, H.R. (1975). A Bayesian approach to real estate assessment. Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage, Amsterdam, 195–208.
Yang, Y., Ng, H.K.T. and Balakrishnan, N. (2016). A stochastic expectation-maximization algorithm for the analysis of system lifetime data with known signature. Computational Statistics, 31:609–641.
Yang, Y., Ng, H.K.T. and Balakrishnan, N. (2019). Expectation maximization algorithm for system based lifetime data with unknown system structure. AStA Advances in Statistical Analysis, 103:69–98.
Zellner, A. (1986). Bayesian estimation and prediction using asymmetric loss function. Journal of the American Statistical Association, 81(394):446–451.
Zhang, J., Ng, H.K.T. and Balakrishnan, N. (2015a). Statistical inference of component lifetimes with location-scale distributions from censored system failure data with known signature. IEEE Transactions on Reliability, 64(2):613–626.
Zhang, J., Ng, H.K.T. and Balakrishnan, N. (2015b). Tests for homogeneity of distributions of component lifetimes from system lifetime data with known system signatures. Naval Research Logistics (NRL), 62(7):550–563.
Journal of Statistical Modelling: Theory and Applications
Volume 3, Issue 2
July 2022
Pages 119-143

Files

History

  • Receive Date: 19 January 2023
  • Revise Date: 29 June 2023
  • Accept Date: 27 October 2023

Share

How to cite

Statistics