Optimal Number of Failures in Type II Censoring for Rayleigh Distribution

Document Type: Research Paper

Author

Department of Statistics, Kosar University of Bojnord, Bojnord, Iran.

Abstract

Recently, Rayleigh distribution has received considerable attention in the statistical literature. This paper describes the Bayesian prediction of the ‎one parameter Rayleigh ‎‎distribution when the data are Type II censored data. Suppose we are planning to collect a Type II censored sample from the ‎one parameter Rayleigh distribution in order to find a point predictor for a future order statistic with smallest mean squared prediction error (MSPE) among other point predictors. Although, considering large values for failure numbers yields a point predictor with smaller MSPE, the average cost may increase considerably. One question arises here that “How many failure is enough?”. The aim of this paper is finding the optimal value for number of failures in Type II censoring by considering two criteria, total cost of experiment and mean squared prediction error. Towards this end, we find the Bayesian point predictor for the parameter of distribution. Then, the optimal value for number of failures is obtained when the mean squared prediction error and the total cost of experiment are bounded. To show the usefulness of the obtained results, a simulation study is presented.

Keywords

Main Subjects


[1] Gerasimidis, S. (2014). Analytical assessment of steel frames progressive collapse vulnerability to corner column loss. Journal of Constructional Steel Research, 95(2014), 1-9.

[2] Rong, H.C.; and Li, B. (2007). Probabilistic response evaluation for RC flexural members subjected to blast loadings. Journal of Structural Safety, 29(2), 146-163.

[3] Shi, Y.; Li Z.X.; and Hao, H. (2010). A new method for progressive collapse analysis of RC frames under blast loading. Journal of Engineering Structures, 32(6), 1691-1703.

[4] Stewart, M.G.; and Netherton, M.D. (2008). Security risks and probabilistic risk assessment of glazing subject to explosive blast loading. Journal of Reliability Engineering and System Safety, 93(4), 627-638.

[5] Parisi, F.; and Augenti, N. (2012). Influence of seismic design criteria on blast resistance of RC framed buildings: A case study. Journal of Engineering Structures, 44, 78-93.

[6] Cizelj, L.; Leskovar, M.; Čepin, M.; and Mavko, B. (2009). A method for rapid vulnerability assessment of structures loaded by outside blasts. Journal of Nuclear Engineering and Design, 239(9), 1641-1646.

[7] 12. Mander, J.B.; Priestley, J.N.; and Park, R. (1988). Theoretical stress-strain model for confined concrete. Journal of Structural Engineering, 114(8), 1804-1826.

[8] 13. Lu, Y.; and Xu, K. (2004). Modelling of dynamic behaviour of concrete materials under blast loading. International Journal of Solids and Structures, 41(1), 131-143.

[9] Baker, W.E. (1973). Explosions in the air. Austin and London: University of Texas Press.

[10] Baker, W.W.; Cox, P.A.; Westine, P.S.; Kulesz, J.J.; and Strehlow, R.A. (1983). Explosion hazards and evaluation. Amsterdam: Elsevier.

[11] Henrych, J. (1979). The dynamics of explosion and its use. Amsterdam and New York: Elsevier Scientific Publishing Company.

[12] Sadovsky, M.A. (1952). Mechanical effects of air shock waves from explosion according to experiments. In: Physics of explosions: symposium - no. 4, AN SSR, Moscow.

[13] Council, B. S. S. (2000). Prestandard and commentary for the seismic rehabilitation of buildings. Report FEMA-356, Washington, DC.

[14] International Conference of Building Officials. (2007). Unified Building Code.

[15] Mander, J. B., Priestley, M. J., & Park, R. (1988). Theoretical stress-strain model for confined concrete. Journal of structural engineering, 114(8), 1804-1826.

[16] Fragiadakis, M., & Papadrakakis, M. (2008). Modeling, analysis and reliability of seismically excited structures: computational issues. International journal of computational methods, 5(04), 483-511.

[17] Asgarian, B. and Hashemi Rezvani, F. (2010). Determination of Progressive collapse-impact factor of concentric braced frames, Proceedings of the fourteenth European conference on earthquake engineering. Ohrid, Republic of Macedonia.

[18] Black, R. G. and Wenger, W.A.B and Popov, E.P. (1980). Inelastic buckling of steel struts under cyclic load reversals. Report No: UCB/EERC-80/40.

[19] Vamvatsikos, D., & Cornell, C. A. (2002). Incremental dynamic analysis. Earthquake Engineering & Structural Dynamics, 31(3), 491-514.