Statistical Inference on the Basis of Sequential Order Statistics under a Linear Trend for Conditional Proportional Hazard Rates
AbstractThis paper deals with systems consisting of independent and heterogeneous exponential components. Since failures of components may change lifetimes of surviving components because of load sharing, a linear trend for conditionally proportional hazard rates is considered. Estimates of parameters, both point and interval estimates, are derived on the basis of observed component failures for s(≥ 2) systems. Fisher information matrix of the available data is also obtained which can be used for studying asymptotic behaviour of estimates. The generalized likelihood ratio test is implemented for testing homogeneity of s systems. Illustrative examples are also given.
N. Balakrishnan, U. Kamps and M. Kateri (2012). A Sequential Order Statistics Approach to Step-Stress Testing. Annals of the Institute of Statistical Mathematics, 64(2), pp. 302–318.
N. Balakrishnan and V. B Nevzorov. (2003). A Primer on Statistical Distributions. John Wiley & Sons, Inc., Hoboken, New Jersey.
R. E. Barlow and F. Proschan. (1981). Statistical theory of reliability and life testing: probability models, Springer, Second Edition.
D. R. Cox. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B (Methodological), 34(2), pp. 187–202.
S. Bedbur. (2010). UMPU Tests based on Sequential order statistics. Journal of Statistical Planning and Inference, 140, pp. 2520C- 2530.
E. Beutner and U. Kamps. (2009). Order restricted statistical inference for scale parameters based on sequential order statistics. Journal of Statistical Planning and Inference, 139, pp. 2963–2969.
E. Cramer and U. Kamps. (1996). Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates. Annals of the Institute of Statistical Mathematics. 48(3), pp. 535–549.
E. Cramer and U. Kamps. (2001a). Estimation with Sequential Order Statistics from exponential distributions. Annals of the Institute of Statistical Mathematics, 53(2), pp. 307–324.
E. Cramer and U. Kamps. (2001b). Sequential k-out-of-n systems. In N. Balakrishnan and E. Rao, editors, Handbook of Statistics, Advances in Reliability, volume 20, Chapter 12 , pp. 301–372.
E. Cramer and U. Kamps. (2003). Marginal distributions of sequential and generalized order statistics. Metrika, 58, pp. 293–310.
H. A. David and Nagaraja. (2003). Order Statistics. John Wiley & Sons, Inc.
M. Esmailian and M. Doostparast. (2014). Estimation based on sequential order statistics with random removals. Probability and Mathematical Statistics, 34(1) , pp. 81–95.
M. Hashempour and M. Doostparast. (2016). Bayesian inference on multiple sequential order statistics from heterogeneous exponential populations with GLR test for homogeneity. Communications in Statistics-Theory and Methods, 46(16) , pp. 8086– 8100.
M. Hashempour. (2017). Classical, Bayesian and evidential inferences based on sequential order statistics, PhD thesis in Mathematical Statistics, Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran.
U. Kamps. (1995a). A Concept of Generalized Order Statistics. Teubner.
U. Kamps. (1995b). A concept of generalized order statistics. Journal of Statistical Planning and Inference, 48, pp. 1–23.
A. I. Khuri. (2003). Advanced Calculus With Applications in Statistics. 2-th Edition, John Wiley & Sons, Inc., Hoboken, New Jersey.
E. L. Lehmann, and J. Romano. (2005). Testing Statistical Hypothesis. 3-th Edition, Springer, New York.
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