Research Article
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On the reliability characteristics of the standard two-sided power distribution

Year 2021, Volume: 70 Issue: 2, 796 - 826, 31.12.2021
https://doi.org/10.31801/cfsuasmas.810424

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
https://doi.org/10.31801/cfsuasmas.810424

Abstract

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.
There are 24 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Çağatay Çetinkaya 0000-0001-8010-4261

Ali Genc 0000-0001-7880-5587

Publication Date December 31, 2021
Submission Date October 14, 2020
Acceptance Date April 15, 2021
Published in Issue Year 2021 Volume: 70 Issue: 2

Cite

APA Çetinkaya, Ç., & Genc, A. (2021). On the reliability characteristics of the standard two-sided power distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 796-826. https://doi.org/10.31801/cfsuasmas.810424
AMA Çetinkaya Ç, Genc A. On the reliability characteristics of the standard two-sided power distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2021;70(2):796-826. doi:10.31801/cfsuasmas.810424
Chicago Çetinkaya, Çağatay, and Ali Genc. “On the Reliability Characteristics of the Standard Two-Sided Power Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 2 (December 2021): 796-826. https://doi.org/10.31801/cfsuasmas.810424.
EndNote Çetinkaya Ç, Genc A (December 1, 2021) On the reliability characteristics of the standard two-sided power distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 796–826.
IEEE Ç. Çetinkaya and A. Genc, “On the reliability characteristics of the standard two-sided power distribution”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 2, pp. 796–826, 2021, doi: 10.31801/cfsuasmas.810424.
ISNAD Çetinkaya, Çağatay - Genc, Ali. “On the Reliability Characteristics of the Standard Two-Sided Power Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (December 2021), 796-826. https://doi.org/10.31801/cfsuasmas.810424.
JAMA Çetinkaya Ç, Genc A. On the reliability characteristics of the standard two-sided power distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:796–826.
MLA Çetinkaya, Çağatay and Ali Genc. “On the Reliability Characteristics of the Standard Two-Sided Power Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 2, 2021, pp. 796-2, doi:10.31801/cfsuasmas.810424.
Vancouver Çetinkaya Ç, Genc A. On the reliability characteristics of the standard two-sided power distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):796-82.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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