On the reliability characteristics of the standard two-sided power distribution
Year 2021,
Volume: 70 Issue: 2, 796 - 826, 31.12.2021
Çağatay Çetinkaya
,
Ali Genc
Abstract
In this study, the standard two-sided power (STSP) distribution is considered with regard to statistical reliability analysis in detail. For this purpose, along with the reliability and hazard functions of the distribution, particular reliability indices that are useful in maintenance and replacement policies are obtained and they are evaluated with their plots. The STSP distribution is classified based on aging according to various cases of its parameters. Then, we studied the classical and Bayesian estimations of the reliability and hazard functions. In Bayesian estimation, symmetric and different asymmetric loss functions are considered. For obtaining the Bayes estimates, Monte Carlo Markov Chain simulation using the Gibbs algorithm is performed. Various simulation schemes are performed for comparing the performances of the estimators. Further, the Bayesian predictions of the future observations based on the observed samples are obtained. A real data example is used to illustrate the theoretical outcomes.
References
- Barlow, R.E., Proschan, F., Statistical Theory of Reliability & Life Testing, Holt, Rinehart and Winston, Inc., New York, 1975.
- Basu, A.P., Ebrahimi, N., Bayesian approach to life testing and reliability estimation using asymmetric loss function, J. Statist. Plann. Infer., 29 (1991), 21-31.
https://doi.org/10.1016/0378-3758(92)90118-C
- Brick, M.J., Michael, J.R., Morganstein, D., Using statistical thinking to solve maintanance problems, Quality Progress, 22(5) (1989), 55-60.
- Birnbaum, Z.W., Esary, J.D., Marshall, A.W., A stochastic characterization of wear-out for component and systems, The Annals of Mathematical Statistics, 37(4) (1966), 816-825.
- Calabria, R., Pulcini, G., Point estimation under asymmetric loss functions for lefttruncated exponential samples, Commun. Statist. Theory Meth., 25 (1996), 585-600.
https://doi.org/10.1080/03610929608831715
- Plummer, M., Best, N., Cowles, K., Vines, K., CODA: Convergence diagnosis and output analysis for MCMC, R News 6 (2006), 7-11.
- Crowder, M.J., Tests for a family of survival models based on extremes, n Recent Advances in Reliability Theory, N. Limnios and M. Nikulin, Eds., Birkhauser, Boston, (2000), 307-321.
- Cetinkaya, C., Genc, A.İ., Moments of order statistics of the standard two-sided power distribution, Comm. in Statistics-Theory and Methods, 47(17) (2018), 4311-4328.https://doi.org/10.1080/03610926.2017.1373818
- Cetinkaya, C., Genc, A.İ., Stress-strength reliability estimation under the standard two-sided power distribution, Applied Mathematical Modelling, 65 (2019), 72-88.https://doi.org/10.1016/j.apm.2018.08.008
- Gupta, P.L., Gupta, R.C., The monotonicity of the reliability measures of the beta distribution, Applied Mathematics Letters, 13 (2000), 5-9. https://doi.org/10.1016/S0893-9659(00)00025-2
- Ho, C., Damien, P., Walker, S., Bayesian mode regression using mixture of triangular densities, J. Econometrics, 197 (2017), 273-283. https://doi.org/10.1016/j.jeconom.2016.11.006
- Kotz, S., van Dorp, J.R., Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications, Singapure, World Scienti
fic, 2004.
- Mance, C.M., Barker, K., Chimka, J.R., Modeling reliability with a two-sided power distribution, Quality Engineering, 29:4 (2017), 643-655. https://doi.org/10.1080/08982112.2016.1213395
- Mukherjee, S.P., Islam, A., A finite-range distribution of failure times, Naval Research Logistics Quarterly, John Wiley & Sons, Inc., 30 (1983), 487-491. https://doi.org/10.1002/nav.3800300313
- Newby, M., Applications of concepts of ageing in reliability data analysis, Reliability Engineering, 14 (4) (1986), 291-308. https://doi.org/10.1016/0143-8174(86)90063-6
- Singh, S. K., Singh U., Sharma V.K., Bayesian estimation and prediction for the generalized Lindley distribution under asymmetric loss function, Hacettepe Journal of Mathematics and
Statistics, 43(4) (2014), 661-678.
- Singh, S. K., Singh U., Kumar D., Estimation of parameters and reliability function of exponentiated exponential distribution: Bayesian approach under general entropy loss function, Pak. J. Stat. Oper. Res., 7(2) (2011), 199-216. https://doi.org/10.18187/pjsor.v7i2.239
- Smith, P.J., Analysis of failure and survival data, Texts in Statistical Sciences, Chapman & Hall/CRC, 2002.
- Srivastava, R., Li, P., Sengupta, D., Testing for Membership to the IFRA and the NBU Classes of Distributions. 15 th International Conference on Arti
ficial Intelligence ans Statistics(AISTATS), La Palma, Canary Islands, Volume XX of JMLR: W & CP XX, 2012.
- Varian, H.R., A Bayesian Approach to Real Estate Assessment, Studies in Bayesian econometrics and statistics in honor of Leonard J. Savage, (1975), 195-208.
ficial Intelligence ans Statistics(AISTATS), La Palma, Canary Islands, Volume XX of JMLR: W & CP XX, 2012.
- Team, R.C., R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/, (2013).
- Van Dorp, J.R., Kotz, S., The standard two-sided power distribution and its properties: with applications in fi
nancial engineering, Amer, Stat., 56 (2002), 90-99.https://doi.org/10.1198/000313002317572745
- Van Dorp, J.R., Kotz, S., The standard two-sided power distribution and its properties: with applications in fi
nancial engineering, Amer, Stat., 56 (2002), 90-99.https://doi.org/10.1198/000313002317572745
- Varian, H.R., A Bayesian Approach to Real Estate Assessment, Studies in Bayesian econometrics and statistics in honor of Leonard J. Savage, (1975), 195-208.
Year 2021,
Volume: 70 Issue: 2, 796 - 826, 31.12.2021
Çağatay Çetinkaya
,
Ali Genc
References
- Barlow, R.E., Proschan, F., Statistical Theory of Reliability & Life Testing, Holt, Rinehart and Winston, Inc., New York, 1975.
- Basu, A.P., Ebrahimi, N., Bayesian approach to life testing and reliability estimation using asymmetric loss function, J. Statist. Plann. Infer., 29 (1991), 21-31.
https://doi.org/10.1016/0378-3758(92)90118-C
- Brick, M.J., Michael, J.R., Morganstein, D., Using statistical thinking to solve maintanance problems, Quality Progress, 22(5) (1989), 55-60.
- Birnbaum, Z.W., Esary, J.D., Marshall, A.W., A stochastic characterization of wear-out for component and systems, The Annals of Mathematical Statistics, 37(4) (1966), 816-825.
- Calabria, R., Pulcini, G., Point estimation under asymmetric loss functions for lefttruncated exponential samples, Commun. Statist. Theory Meth., 25 (1996), 585-600.
https://doi.org/10.1080/03610929608831715
- Plummer, M., Best, N., Cowles, K., Vines, K., CODA: Convergence diagnosis and output analysis for MCMC, R News 6 (2006), 7-11.
- Crowder, M.J., Tests for a family of survival models based on extremes, n Recent Advances in Reliability Theory, N. Limnios and M. Nikulin, Eds., Birkhauser, Boston, (2000), 307-321.
- Cetinkaya, C., Genc, A.İ., Moments of order statistics of the standard two-sided power distribution, Comm. in Statistics-Theory and Methods, 47(17) (2018), 4311-4328.https://doi.org/10.1080/03610926.2017.1373818
- Cetinkaya, C., Genc, A.İ., Stress-strength reliability estimation under the standard two-sided power distribution, Applied Mathematical Modelling, 65 (2019), 72-88.https://doi.org/10.1016/j.apm.2018.08.008
- Gupta, P.L., Gupta, R.C., The monotonicity of the reliability measures of the beta distribution, Applied Mathematics Letters, 13 (2000), 5-9. https://doi.org/10.1016/S0893-9659(00)00025-2
- Ho, C., Damien, P., Walker, S., Bayesian mode regression using mixture of triangular densities, J. Econometrics, 197 (2017), 273-283. https://doi.org/10.1016/j.jeconom.2016.11.006
- Kotz, S., van Dorp, J.R., Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications, Singapure, World Scienti
fic, 2004.
- Mance, C.M., Barker, K., Chimka, J.R., Modeling reliability with a two-sided power distribution, Quality Engineering, 29:4 (2017), 643-655. https://doi.org/10.1080/08982112.2016.1213395
- Mukherjee, S.P., Islam, A., A finite-range distribution of failure times, Naval Research Logistics Quarterly, John Wiley & Sons, Inc., 30 (1983), 487-491. https://doi.org/10.1002/nav.3800300313
- Newby, M., Applications of concepts of ageing in reliability data analysis, Reliability Engineering, 14 (4) (1986), 291-308. https://doi.org/10.1016/0143-8174(86)90063-6
- Singh, S. K., Singh U., Sharma V.K., Bayesian estimation and prediction for the generalized Lindley distribution under asymmetric loss function, Hacettepe Journal of Mathematics and
Statistics, 43(4) (2014), 661-678.
- Singh, S. K., Singh U., Kumar D., Estimation of parameters and reliability function of exponentiated exponential distribution: Bayesian approach under general entropy loss function, Pak. J. Stat. Oper. Res., 7(2) (2011), 199-216. https://doi.org/10.18187/pjsor.v7i2.239
- Smith, P.J., Analysis of failure and survival data, Texts in Statistical Sciences, Chapman & Hall/CRC, 2002.
- Srivastava, R., Li, P., Sengupta, D., Testing for Membership to the IFRA and the NBU Classes of Distributions. 15 th International Conference on Arti
ficial Intelligence ans Statistics(AISTATS), La Palma, Canary Islands, Volume XX of JMLR: W & CP XX, 2012.
- Varian, H.R., A Bayesian Approach to Real Estate Assessment, Studies in Bayesian econometrics and statistics in honor of Leonard J. Savage, (1975), 195-208.
ficial Intelligence ans Statistics(AISTATS), La Palma, Canary Islands, Volume XX of JMLR: W & CP XX, 2012.
- Team, R.C., R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/, (2013).
- Van Dorp, J.R., Kotz, S., The standard two-sided power distribution and its properties: with applications in fi
nancial engineering, Amer, Stat., 56 (2002), 90-99.https://doi.org/10.1198/000313002317572745
- Van Dorp, J.R., Kotz, S., The standard two-sided power distribution and its properties: with applications in fi
nancial engineering, Amer, Stat., 56 (2002), 90-99.https://doi.org/10.1198/000313002317572745
- Varian, H.R., A Bayesian Approach to Real Estate Assessment, Studies in Bayesian econometrics and statistics in honor of Leonard J. Savage, (1975), 195-208.