Determination of warranty length for one-shot devices with Rayleigh lifetime distribution

References

• Abdel-Hamid, A. H., and E. K. Al-Hussaini. 2014. Bayesian prediction for type-II progressive-censored data from the Rayleigh distribution under progressive-stress model. Journal of Statistical Computation and Simulation 84 (6):1297–312. doi: 10.1080/00949655.2012.741132.
   Web of Science ®Google Scholar
• Agrawal, J., P. S. Richardson, and P. E. Grimm. 1996. The relationship between warranty and product reliability. The Journal of Consumer Affairs 30 (2):421–43. doi: 10.1111/j.1745-6606.1996.tb00065.x.
   Web of Science ®Google Scholar
• Almarashi, A. M., A. Algarni, G. A. Abd-Elmougod, and S. Abdel-Khalek. 2019. Statistical analysis of Rayleigh competing risks model based on partially step stress type-II censoring samples. Journal of Nonlinear Sciences and Applications 12 (04):230–38. doi: 10.22436/jnsa.012.04.04.
   Google Scholar
• Arnold, B. C., and S. J. Press. 1983. Bayesian inference for Pareto populations. Journal of Econometrics 21 (3):287–306. doi: 10.1016/0304-4076(83)90047-7.
   Web of Science ®Google Scholar
• Balakrishnan, N., E. Castilla, N. Martín, and L. Pardo. 2019. Robust estimators for one-shot device testing data under gamma lifetime model with an application to a tumor toxicological data. Metrika 82 (8):991–1019. doi: 10.1007/s00184-019-00718-5.
   Web of Science ®Google Scholar
• Balakrishnan, N., and E. Chimitova. 2017. Goodness-of-fit tests for one-shot device accelerated life testing data. Communications in Statistics - Simulation and Computation 46:3723–34.
   Web of Science ®Google Scholar
• Balakrishnan, N., and M. H. Ling. 2014a. Gamma lifetimes and one-shot device testing analysis. Reliability Engineering & System Safety 126:54–64. doi: 10.1016/j.ress.2014.01.009.
   Web of Science ®Google Scholar
• Balakrishnan, N., and M. H. Ling. 2014b. Best constant-stress accelerated life-test plans with multiple stress factors for one-shot device testing under a Weibull distribution. IEEE Transactions on Reliability 63:944–52. doi: 10.1109/TR.2014.2336391.
   Web of Science ®Google Scholar
• Bernardo, J. M., and A. F. M. Smith. 1994. Bayesian theory. New York: Wiley.
   Google Scholar
• Blischke, W. R., and D. N. P. Murthy. 1993. Warranty cost analysis. New York: Marcel Dekker.
   Google Scholar
• Blischke, W. R., and D. N. P. Murthy. 1996. Product warranty handbook. New York: Marcel Dekker.
   Google Scholar
• Cheng, Y., and E. A. Elsayed. 2017. Optimal sequential ALT plans for systems with mixture of one-shot units. IEEE Transactions on Reliability 66 (4):997–1011. doi: 10.1109/TR.2017.2728625.
   Web of Science ®Google Scholar
• Chien, Y.-H. 2008. Optimal age-replacement policy under an imperfect renewing free-replacement warranty. IEEE Transactions on Reliability 57:125–33.
   Web of Science ®Google Scholar
• Dey, T., S. Dey, and D. Kundu. 2016. On progressively type-II censored two-parameter Rayleigh distribution. Communications in Statistics - Simulation and Computation 45 (2):438–55. doi: 10.1080/03610918.2013.856921.
   Web of Science ®Google Scholar
• Fan, T.-H., N. Balakrishnan, and C.-C. Chang. 2009. The Bayesian approach for highly reliable electro-explosive devices using one-shot device testing. Journal of Statistical Computation and Simulation 79 (9):1143–54. doi: 10.1080/00949650802142592.
   Web of Science ®Google Scholar
• Fernández, A. J. 2000. Bayesian inference from type II doubly censored Rayleigh data. Statistics & Probability Letters 48 (4):393–9. doi: 10.1016/S0167-7152(00)00021-3.
   Web of Science ®Google Scholar
• Fernández, A. J. 2010. Bayesian estimation and prediction based on Rayleigh sample quantiles. Quality & Quantity 44 (6):1239–48. doi: 10.1007/s11135-009-9270-7.
   Google Scholar
• Gutiérrez-Pulido, H., V. Aguirre-Torres, and J. A. Christen. 2006. A Bayesian approach for the determination of warranty length. Journal of Quality Technology 38 (2):180–9. doi: 10.1080/00224065.2006.11918604.
   Web of Science ®Google Scholar
• Huang, H.-Z., Z.-J. Liu, and D. N. P. Murthy. 2007. Optimal reliability, warranty and price for new products. IIE Transactions 39 (8):819–27. doi: 10.1080/07408170601091907.
   Web of Science ®Google Scholar
• Huang, Y.-S., C.-H. Hsieh, and J.-W. Ho. 2008. Decisions on an optimal life test sampling plan with warranty considerations. IEEE Transactions on Reliability 57:643–9.
   Web of Science ®Google Scholar
• Kaushik, A. 2019. A progressive interval type-I censored life test plan for Rayleigh distribution. Austrian Journal of Statistics 48 (3):76–86. doi: 10.17713/ajs.v48i3.781.
   Web of Science ®Google Scholar
• Kelley, C. A. 1996. Warranty and consumer behavior: Product choice. In Product warranty handbook, ed. W. R. Blischke and D. N. P. Murthy, 409–19. New York: Marcel Dekker.
   Google Scholar
• Lejeune, M., and G. D. Faulkenberry. 1982. A simple predictive density function. Journal of the American Statistical Association 77 (379):654–7. doi: 10.1080/01621459.1982.10477866.
   Web of Science ®Google Scholar
• Ling, M. H., and N. Balakrishnan. 2017. Model mis-specification analyses of Weibull and gamma models based on one-shot device test data. IEEE Transactions on Reliability 66 (3):641–50. doi: 10.1109/TR.2017.2703111.
   Web of Science ®Google Scholar
• Ling, M. H., and X. W. Hu. 2020. Optimal design of simple step-stress accelerated life tests for oneshot devices under Weibull distributions. Reliability Engineering & System Safety 193:106630. doi: 10.1016/j.ress.2019.106630.
   Web of Science ®Google Scholar
• Menezes, M. A. J., and I. S. Currim. 1992. An approach for determination of warranty length. International Journal of Research in Marketing 9 (2):177–95. doi: 10.1016/0167-8116(92)90037-L.
   Google Scholar
• Morris, M. D. 1987. A sequential experimental design for estimating a scale parameter from quantal life testing data. Technometrics 29 (2):173–81. doi: 10.1080/00401706.1987.10488208.
   Web of Science ®Google Scholar
• Nassar, M., and S. Dey. 2018. Different estimation methods for exponentiated Rayleigh distribution under constant-stress accelerated life test. Quality and Reliability Engineering International 34 (8):1633–45. doi: 10.1002/qre.2349.
   Web of Science ®Google Scholar
• Nelder, J. A., and R. Mead. 1965. A simplex algorithm for function minimization. The Computer Journal 7 (4):308–13. doi: 10.1093/comjnl/7.4.308.
   Web of Science ®Google Scholar
• Newby, M. 2008. Monitoring and maintenance of spares and one shot devices. Reliability Engineering & System Safety 93 (4):588–94. doi: 10.1016/j.ress.2007.02.008.
   Web of Science ®Google Scholar
• Patankar, J. G., and A. Mitra. 1996. Warranty and consumer behavior: Warranty execution. In Product warranty handbook, ed. W. R. Blischke and D. N. P. Murthy, 421–38. New York: Marcel Dekker.
   Google Scholar
• Polovko, A. M. 1968. Fundamentals of reliability theory. New York: Academic Press.
   Google Scholar
• Sharma, R., and K. Upadhyay. 2018. A hierarchical Bayes analysis for one-shot device testing experiment under the assumption of exponentiality. Communications in Statistics - Simulation and Computation 47 (5):1297–314. doi: 10.1080/03610918.2017.1310233.
   Web of Science ®Google Scholar
• Sherwin, E. R. 2000. Analysis of “One-Shot” Devices, START (Selected topics in assurance related technologies). A Publication of DoD Reliability Analysis Center 7 (4):1–4.
   Google Scholar
• Singpurwalla, N. D., and S. P. Wilson. 1998. Failure models indexed by two scales. Advances in Applied Probability 30 (4):1058–72. doi: 10.1239/aap/1035228207.
   Web of Science ®Google Scholar
• Thomas, M. U. 2005. Engineering economic decisions and warranties. The Engineering Economist 50 (4):307–26. doi: 10.1080/00137910500348327.
   Google Scholar
• Wu, S.-J., D.-H. Chen, and S.-T. Chen. 2006. Bayesian inference for Rayleigh distribution under progressive censored sample. Applied Stochastic Models in Business and Industry 22 (3):269–79. doi: 10.1002/asmb.615.
   Web of Science ®Google Scholar
• Wu, S.-J., and S.-R. Huang. 2010. Optimal warranty length for a Rayleigh distributed product with progressive censoring. IEEE Transactions on Reliability 59 (4):661–6. doi: 10.1109/TR.2010.2055950.
   Web of Science ®Google Scholar
• Yates, S. W., and A. Mosleh. 2006. A Bayesian approach to reliability demonstration for aerospace systerms. Reliability and Maintainability Symposium, 611–7.
   Google Scholar