• Journal of Applied Reliability
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• v.18 no.3
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• pp.220-228
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• 2018

Purpose: The purpose of this study is to investigate the tail behavior of the life distribution which exhibits an increasing failure rate or other positive aging effects after a certain time point. Methods: We characterize the tail behavior of the life distribution with regard to certain reliability measures such as failure rate, mean residual life and reliability function and derive several stochastic properties regarding such life distributions. Also, utilizing an L-statistic and its asymptotic normality, we propose new nonparametric testing procedures which verify if the life distribution has an increasing tail failure rate. Results: We propose the IFR-Tail (Increasing Failure Rate in Tail), DMRL-Tail (Decreasing Mean Residual Life in Tail) and NBU-Tail (New Better than Used in Tail) classes, all of which represent the tail behavior of the life distribution. And we discuss some stochastic properties of these proposed classes. Also, we develop a new nonparametric test procedure for detecting the IFR-Tail class and discuss its relative efficiency to explore the power of the test. Conclusion: The results of our research could be utilized in the study of wide range of applications including the maintenance and warranty policy of the second-hand system.