Reliability Assessment for 2-Out-Of-3 System Using Freund Model

Authors

  • Saraswati V Katagi Department of studies in Statistics, Karnatak University, Dharwad-580003, Karnataka, India Author
  • S. B. Munoli Department of studies in Statistics, Karnatak University, Dharwad-580003, Karnataka, India Author

DOI:

https://doi.org/10.32628/IJSRST251274

Keywords:

2-out-of-3 system, Freund bivariate model, Reliability function, Lifetime performance study, MLE, Bayes estimator

Abstract

The study aims to model and estimate the reliability function for 2-out-of-3 system using Freund bivariate model. Reliability estimators are obtained using MLE and Bayes approaches using data of lifetime performance study. The limiting distribution of maximum likelihood estimators is obtained. The computation and comparison of two estimators is carried out through simulation studies. The results showed that MLEs perform better than Bayes estimator in terms of mean absolute bias.

Downloads

Download data is not yet available.

References

Freund, J. E. (1961). A bivariate extension of the exponential distribution. Journal of the American Statistical Association, 56(296), 971-977. DOI: https://doi.org/10.1080/01621459.1961.10482138

Basu, A. P. (1964). Estimates of reliability for some distributions useful in life testing. Technometrics, 6(2), 215-219. DOI: https://doi.org/10.1080/00401706.1964.10490165

Bhattacharya, S. K. (1967). Bayesian approach to life testing and reliability estimation. Journal of the American Statistical Association, 62(317), 48-62. DOI: https://doi.org/10.1080/01621459.1967.10482887

Downton, F. (1970). Bivariate exponential distributions in reliability theory. Journal of the Royal Statistical Society: Series B (Methodological), 32(3), 408-417. DOI: https://doi.org/10.1111/j.2517-6161.1970.tb00852.x

Hawkes, A. G. (1972). A bivariate exponential distribution with applications to reliability. Journal of the Royal Statistical Society. Series B (Methodological), 129-131. DOI: https://doi.org/10.1111/j.2517-6161.1972.tb00895.x

Downton, F. (1973). The estimation of Pr (Y DOI: https://doi.org/10.1080/00401706.1973.10489081

Block, H. W., and Basu, A. P. (1974). A continuous, bivariate exponential extension. Journal of the American Statistical Association, 69(348), 1031-1037. DOI: https://doi.org/10.1080/01621459.1974.10480249

Weier, D. R. (1981). Bayes estimation for a bivariate survival model based on exponential distributions. Communications in Statistics-Theory and Methods, 10(14), 1415-1427. DOI: https://doi.org/10.1080/03610928108828123

Klein, J. P., and Basu, A. P. (1985). Estimating reliability for bivariate exponential distributions. Sankhyā: The Indian Journal of Statistics, Series B, 346-353.

Kunchur, S. H., and Munoli, S. B. (1994). Estimation of reliability in freund model for two component system. Communications in Statistics-Theory and Methods, 23(11), 3273-3283. DOI: https://doi.org/10.1080/03610929408831446

Jain, P., Pawar, D., Malik, S. C., and Garg, V. (2022). Analysis of reliability measures of 1-out-of-2 unit system subject to conditional use of standby. International Journal of Agricultural & Statistical Sciences, 18.

Narwal, A., and Malik, S. C. (2024). Mathematical techniques for computing the reliability of a parallel-series system of order (2, 3, 1) under Rayleigh failure laws. International Journal of Agricultural & Statistical Sciences, 20(1). DOI: https://doi.org/10.59467/IJASS.2024.20.217

Mann, N. R., Schafer, R. E., and Singpurwalla, N. D. (1974). Methods for statistical analysis of reliability and life data (Book). Research supported by the U. S. Air Force and Rockwell International Crop. New York, John Wiley and Sons, Inc.

Blischke, W. R., and Prabhakar Murthy, D. N. (2000). Reliability: Modelling, Prediction and Optimization. John Willey & Sons. DOI: https://doi.org/10.1002/9781118150481

Downloads

Published

07-07-2025

Issue

Section

Research Articles