Estimation of stress–strength reliability for generalized Maxwell failure distribution under progressive first failure censoring

References

• Johnson LG. Theory and technique of variation research. Amsterdam: Elsevier; 1964.
   Google Scholar
• Balasooriya U. Failure-censored reliability sampling plans for the exponential distribution. J Stat Comput Simulat. 1995;52:337–349.
   Web of Science ®Google Scholar
• Balakrishnan N, Sandhu RA. A simple simulational algorithm for generating progressively type-II censored samples. Am Stat. 1995;49(2):229–230.
   Web of Science ®Google Scholar
• Balakrishnan N, Aggarwala R. Progressive censoring: theory, methods and applications. Boston: Birkhäuser; 2000.
   Google Scholar
• Balakrishnan N, Cramer E. Theart of progressive censoring. statistics for Industry and technology. New York: Birkhäuser; 2014.
   Google Scholar
• Chaturvedi A, Kumar N, Kumar K. Statistical inference for the reliability functions of a family of lifetime distributions based on progressive type II right censoring. Statistica. 2018;78(1):81–101.
   Web of Science ®Google Scholar
• Wu SJ, Kus C. On the estimation based on progressive first failure-censored sample. Comput Stat Data Anal. 2009;53(10):3659–3670.
   Web of Science ®Google Scholar
• Soliman AA, Abd Ellah AH, Abou-Elheggag NA, et al. A simulation-based approach to the study of coefficient of variation of Gompertz distribution under progressive first-failure censoring. Indian J Pure Appl Math. 2011;42(5):335–356.
   Web of Science ®Google Scholar
• Soliman AA, Abd-Ellah AH, Abou-Elheggag NA, et al. Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data. Comput Stat Data Anal. 2012;56:2471–2485.
   Web of Science ®Google Scholar
• Soliman AA, Abd-Ellah AH, Abou-Elheggag NA, et al. Estimation from Burr type XII distribution using progressive first-failure censored data. J Stat Comput Simul. 2013;83(12):2270–2290.
   Web of Science ®Google Scholar
• Dube M, Garg R, Krishna H. On progressively first failure censored Lindley distribution. Comput Stat. 2016;31(1):139–163.
   Web of Science ®Google Scholar
• Maurya RK, Tripathi YM, Rastogi MK. Estimation and prediction for a progressively first-failure censored inverted exponentiated Rayleigh distribution. J Stat Theory Practice. 2019;13:39. Available from https://doi.org/10.1007/s42519-019-0038-7.
   Web of Science ®Google Scholar
• Johnstone MA. Bayesian estimation of reliability in the stress–strength context. J Washington Acad Sci. 1983;73(4):140–150.
   Google Scholar
• Johnson RA. Stress-Strength models for reliability. Handbook Stat. 1988;7:27–54.
   Google Scholar
• Kotz S, Lumelskii Y, Pensky M. The stress-Strength model and its generalizations: theory and applications. Singapore: World Scientific Publishing; 2003.
   Google Scholar
• Lio YL, Tsai TR. Estimation of δ=P(X<Y) for Burr XII distribution based on the progressively first failure-censored samples. J Appl Stat. 2012;39(2):309–322.
   Web of Science ®Google Scholar
• Kumar K, Krishna H, Garg R. Estimation of P(Y<X) in Lindley distribution using progressively first failure censoring. Int J Syst Assurance Engin Manage. 2015;6(3):330–341.
   Web of Science ®Google Scholar
• Krishna H, Dube M, Garg R. Estimation of P(Y<X) for progressively first-failure censored generalized inverted exponential distribution. J Stat Comput Simul. 2017;87(11):2274–2289.
   Web of Science ®Google Scholar
• Rowlinson JS. The Maxwell–Boltzmann distribution. Mol Phys. 2005;103(21–23):2821–2828.
   Web of Science ®Google Scholar
• Tyagi R, Bhattacharya S. Bayes estimation of the Maxwell's velocity distribution function. Statistica. 1989;49(4):563–567.
   Google Scholar
• Tyagi R, Bhattacharya S. A note on the MVU estimation of reliability for the Maxwell failure distribution. Estadistica. 1989;41(137):73–79.
   Google Scholar
• Bekker A, Roux J. Reliability characteristics of the Maxwell distribution: a Bayes estimation study. Commun Stat-Theory Methods. 2005;34(11):2169–2178.
   Web of Science ®Google Scholar
• Krishna H, Malik M. Reliability estimation in Maxwell distribution with progressively type-II censored data. J Stat Comput Simulat. 2012;82(4):623–641.
   Web of Science ®Google Scholar
• Tomer SK, Panwar MS. Estimation procedures for Maxwell distribution under type-I progressive hybrid censoring scheme. J Stat Comput Simul. 2015;85(2):339–356.
   Web of Science ®Google Scholar
• Krishna H, Vivekanand , Kumar K. Estimation in Maxwell distribution with randomly censored data. J Stat Comput Simul. 2015;85(17):3560–3578.
   Web of Science ®Google Scholar
• Chaturvedi A, Rani U. Classical and Bayesian reliability estimation of the generalized Maxwell failure distribution. J Stat Res. 1998;32:113–120.
   Google Scholar
• Gradshteyn I, Ryzhik IM. Tables of integrals, series and products. New York: Academic Press; 1965.
   Google Scholar
• Rao C. Linear statistical inference and its applications. New York: John Wiley and Sons; 1973.
   Google Scholar
• Efron BT. An introduction to the bootstrap. New York: Chapman and Hall; 1993.
   Google Scholar
• Metropolis N, Rosenbluth AW, Rosenbluth MN, et al. Equation of state calculations by fast computing machines. J Chem Phys. 1953;21:1087–1092.
   Web of Science ®Google Scholar
• Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika. 1970;57(1):97–109.
   Web of Science ®Google Scholar
• Ntzoufras I. Bayesian modeling using winBugs. New York: Wiley; 2009.
   Google Scholar
• Chen MH, Shao QM. Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat. 1999;8(1):69–92.
   Web of Science ®Google Scholar
• Nadar M, Papadopoulos A, Kızılaslan F. Statistical analysis for Kumaraswamy's distribution based on record data. Statistical Papers. 2013;54(2):355–369.
   Web of Science ®Google Scholar
• Kohansal A. On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample. Stat Papers. 2019;60(6):2185–2224.
   Web of Science ®Google Scholar