A model for k-out-of-m load-sharing systems

References

• Akaike, H. (1974). A new look at the statistical model identification. I.E.E.E. Trans. Autom. Control 19:716–723.
   Web of Science ®Google Scholar
• Balakrishnan, N., Kateri, M. (2008). On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data. Stat. Probab. Lett. 78:2971–2975.
   Web of Science ®Google Scholar
• Birnbaum, Z.W., Saunders, S.C. (1958). A statistical model for life-length of materials. J. Am. Stat. Assoc. 53:151–160.
   Web of Science ®Google Scholar
• Coleman, B.D. (1958). Statistics and time dependence of mathematical breakdowns in fibers. J. Appl. Phys. 29:968–983.
   Web of Science ®Google Scholar
• Cramer, E., Kamps, U. (1996). Sequential order statistics and k-out-of-n-system with sequentially adjusted failure rates. Ann. Inst. Stat. Math. 48:535–549.
   Web of Science ®Google Scholar
• Cramer, E., Kamps, U. (2001). Sequential k-out-of-n Systems. In: Balakrishnan, N., Rao, C. R., eds. Handbook of Statistics, vol. 20, North Holland: Elsevier (pp. 301–372).
   Google Scholar
• Daniels, H.E. (1945). The statistical theory of the strength of bundles of threads. I. Proc. Royal Soc. London A. 183:404–435.
   Google Scholar
• Davis, D.J. (1952). An analysis of some failure data. J. Am. Stat. Assoc. 47:113–150.
   Web of Science ®Google Scholar
• Deshpande, J.V., Dewan, I., Naik-Nimbalkar, U.V. (2010). A family of distributions to model load sharing systems. J. Stat. Plann. Infer. 140:1441–1451.
   Web of Science ®Google Scholar
• Dewan, I., Naik-Nimbalkar, U.V. (2010). Load-sharing systems. In: Wiley Encyclopedia of Operations Research and Management Science DOI: 10.1002/9780470400531.eorms0476.
   Google Scholar
• Drummond, H., Vazquez, E., Sanchez-Colon, S., Martinez-Gomez, M., Hudson, R. (2000). Competition for milk in the domestic rabbit: survivors benefit from littermate deaths. Ethology 106:511–526.
   Web of Science ®Google Scholar
• Durham, S.D., Lynch, J.D. (2000). A threshold representation for the strength distribution of a complex load sharing system. J. Stat. Plann. Inference. 83:25–46.
   Web of Science ®Google Scholar
• Efron, B. (1988). Logistic regression, survival analysis, and the Kaplan–Meier curve. J. Am. Stat. Assoc. 83:414–425.
   Web of Science ®Google Scholar
• Ghosh, J.K., Delampady, M., Samanta, T. (2006). An Introduction to Bayesian Analysis: Theory and Methods.New York: Springer-Verlag.
   Google Scholar
• Gross, A.J., Clark, V.A., Liu, V. (1971). Estimation of survival parameters when one of two organs must function for survival. Biometrics 27:69–377.
   Web of Science ®Google Scholar
• Gupta, R.C., Gupta, P.L., Gupta, R.D. (1998). Modeling failure time data with Lehman alternative. Commun. Stat. Theor. Meth. 27:887–904.
   Web of Science ®Google Scholar
• Gupta, R.D., Kundu, D. (2001). Exponentiated exponential family: An alternative to Gamma and Weibull distributions. Biomet. J. 43:117–130.
   Web of Science ®Google Scholar
• Hollander, M., Pena, E.A. (1995). Dynamic reliability models with conditional proportional hazards. Life Time Data Anal. 1:377–401.
   PubMedGoogle Scholar
• Joe, H. (1997). Multivariate Models and Dependence Concepts. London: Chapman and Hall.
   Google Scholar
• Kamps, U. (1995). A concept of generalized order statistics. J. Stat. Plann. Inference. 48:1–23.
   Web of Science ®Google Scholar
• Kim, H., Kvam, P.H. (2004). Reliability estimation based on system data with an unknown load share rule. Lifetime Data Anal. 10:83–94.
   PubMed Web of Science ®Google Scholar
• Kvam, P.H., Pena, E.A. (2005). Estimating load sharing properties in a dynamic reliability system. J. Am. Stat. Assoc. 100:263–272.
   Web of Science ®Google Scholar
• Lehmann, E.L. (1953). The power of rank tests. Ann. Math. Stat. 24:28–43.
   Google Scholar
• Lynch, J.D. (1999). On the joint distribution of component failures for monotone load-sharing systems. J. Stat. Plann. Inference 78:13–21.
   Web of Science ®Google Scholar
• Mudholkar, G.S., Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans. Reliab. Theory 42:299–302.
   Web of Science ®Google Scholar
• Mudholkar, G.S., Srivastava, D.K., Freimer, M. (1995). The exponentiated Weibull family: A reanalysis of the bus-motor failure for data. Technometrics. 37:36–445.
   Google Scholar
• Mudholkar, G.S., Hutson, A.D. (1996). The exponentiated Weibull family: some properties and a flood data application. Commun. Stat. Theory Methods 25:3059–3083.
   Web of Science ®Google Scholar
• McCool, J.I. (2006). Testing for dependency of failure times in life testing. Technometrics 48:41–48.
   Web of Science ®Google Scholar
• Pena, E.A. (2006). Dynamic modelling and statistical analysis of event times. Stat. Sci. 21:487–500.
   Web of Science ®Google Scholar
• Phoenix, S.L. (1978). The asymptotic time to failure of a mechanical system of parallel members. SIAM J. Appl. Math. 34:227–246.
   Web of Science ®Google Scholar
• Rosen, B.W. (1964). Tensile failure of fibrous composites. AIAA J. 2:1985–1991.
   Google Scholar
• Reliability Edge Home., (2003). Quarter 2, 3. Available at: http://www.reliasoftindia.com/newsletter/ 4q2002/qalt.htm
   Google Scholar
• Singpurwalla, N.D. (1995). Survival in dynamic environments. Stat. Sci. 10:86–103.
   Web of Science ®Google Scholar
• Sen, A., Bhattacharyya, G.K. (1995). Inference procedures for the linear failure rate model. J. Stat. Plann. Inference 46:57–76.
   Web of Science ®Google Scholar
• Srivastava, H.M., Hussain, M.A. (1995). Fractional integration of the H-Function of several variables. Comput. Math. Appl. 9:73–85.
   Web of Science ®Google Scholar