966
Views
10
CrossRef citations to date
0
Altmetric
Research Articles

Bayesian and non-Bayesian reliability estimation of multicomponent stress–strength model for unit Weibull distribution

ORCID Icon, , ORCID Icon & ORCID Icon
Pages 1164-1181 | Received 08 Apr 2020, Accepted 03 Aug 2020, Published online: 16 Aug 2020

References

  • Mudholkar GS, Srivastava DK. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans Reliab. 1993;42:299–302.
  • Mudholkar GS, Srivastava DK, Freimer M. The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics. 1995;37:436–445.
  • Singh U, Gupta PK, Upadhyay SK. Estimation of parameters for exponentiated-Weibull family under type-II censoring scheme. Comput Statist Data Anal. 2005;48:509–523.
  • Marshall AW, Olkin I. A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika. 1997;84:641–652.
  • Zhang T, Xie M. Failure data analysis with extended Weibull distribution. Comm Statist Simul Comput. 2007;36:579–592.
  • Jiang H, Xie M, Tang LC. Markov chain Monte Carlo methods for parameter estimation of the modified Weibull distribution. J Appl Stat. 2008;35:647–658.
  • Lai CD, Xie M, Murthy DNP. A modified Weibull distribution. IEEE Trans Reliab. 2003;52:33–37.
  • Ng HKT. Parameter estimation for a modified Weibull distribution, for progressively type-II censored samples. IEEE Trans Reliab. 2005;54:374–380.
  • Cooray K. Generalization of the Weibull distribution: the odd Weibull family. Stat Model. 2006;6:265–277.
  • Alzaatreh A, Famoye F, Lee C. A new method for generating families of continuous distributions. METRON. 2013;71(1):63–79.
  • Bourguignon M, Silva RB, Cordeiro GM. The Weibull-G family of probability distributions. J Data Sci. 2014;11:1–27.
  • Korkmaz MC. A new family of the continuous distributions: the extended Weibull-G family. Commun Fac Sci Univ Ank Ser A1 Math Stat. 2019;68(1):248–270.
  • Kumaraswamy P. A generalized probability density function for double-bounded random processes. J Hydrol (Amst). 1980;46(1–2):79–88.
  • Mazucheli J, Menezes AFB, Dey S. Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution. Commun Statist Theory Methods. 2018a;47(15):3767–3778.
  • Mazucheli J, Menezes AFB, Dey S. The unit-Birnbaum–Saunders distribution with applications. Chil J Stat. 2018b;9(1):47–57.
  • Mazucheli J, Menezes AFB, Dey S. Unit-Gompertz distribution with applications. Statistica. 2019;79(1):25–43.
  • Mazucheli J, Menezes AFB, Ghitany ME. The unit-Weibull distribution and associated inference. J Appl Probab Stat. 2018;13(2):1–22.
  • Bhattacharyya G, Johnson RA. Estimation of reliability in a multicomponent stress–strength model. J Am Stat Assoc. 1974;69(348):966–970.
  • Rao GS, Aslam M, Kundu D. Burr-XII distribution parametric estimation and estimation of reliability of multicomponent stress–strength. Commun Statist Theory Methods. 2015;44:4953–4961.
  • Dey S, Mazucheli J, Anis M. Estimation of reliability of multicomponent stress–strength for a Kumaraswamy distribution. Commun Statist Theory Methods. 2017;46:1560–1572.
  • Kayal T, Tripathi YM, Dey S, et al. On estimating the reliability in a multicomponent stress–strength model based on Chen distribution. Commun Statist Theory Methods. 2020;49(10):2429–2447.
  • Kizilaslan F, Nadar M. Classical and Bayesian estimation of reliability in multicomponent stress–strength model based on Weibull distribution. Rev Colomb Estadstica. 2015;38(2):67–484.
  • Pak A, Gupta AK, Khoolenjani NB. On reliability in a multicomponent stress–strength model with power Lindley distribution. Rev Colomb Estadstica. 2018;41(2):251–267.
  • Dey S, Moala FA. Estimation of reliability of multicomponent stress–strength of a bathtub shape or increasing failure rate function. Int J Qual Reliab Manag. 2019;36(2):122–136.
  • Seadawy AR, Luc D, Yue C. Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability. J Taibah Univ Sci. 2017;11:623–633.
  • Seadawy AR, Iqbal M, Luc D. Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid–gas bubbles under the consideration of heat transfer and viscosity. J Taibah Univ Sci. 2019;13:1060–1072.
  • Ahmad H, Seadawy AR, Khan TA, et al. Analytic approximate solutions for some nonlinear parabolic dynamical wave equations. J Taibah Univ Sci. 2020;14:346–358.
  • Khaliq Q, Riaz M, Ahmad S. On designing a new Tukey-EWMA control chart for process monitoring. Int J Adv Manufacturing Technol. 2016;82(1–4):1–23.
  • Abbasi SA, Khaliq QUA, Omar MH, et al. On designing a sequential based EWMA structure for efficient process monitoring. J Taibah Univ Sci. 2020;14(1):177–191.
  • Efron B. The jackknife, the bootstrap, and other resampling plans. Philadelphia (PA): SIAM; 1982.
  • Hall P. On some simple estimates of an exponent of regular variation. J R Statist Soc Ser B (Method). 1982;44(1):37–42.
  • Swain JJ, Venkatraman S, Wilson JR. Least-squares estimation of distribution functions in Johnson's translation system. J Stat Comput Simul. 1988;29(4):271–297.
  • Cheng R, Amin N. Estimating parameters in continuous univariate distributions with a shifted origin. J R Statist Soc Ser B (Method). 1983;45(3):394–403.
  • Lindley DV. Approximate bayesian methods. Trabajos Estadst Invest Oper. 1980;31(1):223–245.
  • Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika. 1970;57(1):97–109.
  • Metropolis N, Rosenbluth AW, Rosenbluth MN, et al. Equation of state calculations by fast computing machines. J Chem Phys. 1953;21(6):1087–1092.
  • Chen M-H, Shao Q-M. Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat. 1999;8(1):69–92.
  • Basirat M, Baratpour S, Ahmadi J. Statistical inferences for stress–strength in the proportional hazard models based on progressive type-II censored samples. J Stat Comput Simul. 2015;85(3):431–449.
  • Xia Z, Yu J, Cheng L, et al. Study on the breaking strength of jute fibres using modified Weibull distribution. Comp Part A Appl Sci Manufac. 2009;40(1):54–59.
  • Team RC. R: a language and environment for statistical computing. 2013.
  • Al-Mutairi DK, Ghitany ME, Kundu D. Inferences on stress–strength reliability from Lindley distributions. Commun Statist Theory Methods. 2013;42(8):1443–1463.