Some Reliability Properties of the Inactivity Time

In this article, it is shown that, apart from the expected inactivity time, the second-order moment of inactivity time determines the distribution uniquely. We also show that any one partial moment, fractional or integral, of inactivity time uniquely determines a distribution. Different properties of the inactivity time of the components of a parallel system, at the system level, have been studied. Stochastic comparisons between two parallel systems based on this is also studied here.

[1]  Ming J. Zuo,et al.  Stochastic Comparison of Residual Life and Inactivity Time at a Random Time , 2004 .

[2]  Chanchal Kundu,et al.  Some distributional results through past entropy , 2010 .

[3]  Majid Asadi,et al.  On the mean past lifetime of the components of a parallel system , 2006 .

[4]  Pushpa L. Gupta,et al.  On the moments of residual life in reliability and some characterization results , 1983 .

[5]  N. L. Lawrie,et al.  Comparison Methods for Queues and Other Stochastic Models , 1984 .

[6]  Cao Jinhua,et al.  Some results on the residual life at random time , 2000 .

[7]  Xiaohu Li,et al.  STOCHASTIC COMPARISONS ON RESIDUAL LIFE AND INACTIVITY TIME OF SERIES AND PARALLEL SYSTEMS , 2003, Probability in the Engineering and Informational Sciences.

[8]  Ramesh C. Gupta.  On the monotonic properties of the residual variance and their applications in reliability , 1987 .

[9]  John Cawley,et al.  The determination of , 1993 .

[10]  A. K. Nanda,et al.  On Generalized Stochastic Orders of Dispersion-Type , 2009 .

[11]  Dilip Roy,et al.  SOME RESULTS ON REVERSED HAZARD RATE , 2001, Probability in the Engineering and Informational Sciences.

[12]  New Stochastic Orders Based on Double Truncation , 1997 .

[13]  Jorge Navarro,et al.  CHARACTERIZATION THROUGH MOMENTS OF THE RESIDUAL LIFE AND CONDITIONAL SPACINGS , 1998 .

[14]  Majid Asadi,et al.  On the discrete mean past lifetime , 2008 .

[15]  Jorge Navarro,et al.  Characterizations based on conditional expectations of the doubled truncated distribution , 1996 .

[16]  J. Galambos,et al.  The characterization of a distribution function by the second moment of the residual life , 1992 .

[17]  Stochastic Orders , 2008 .

[18]  Ward Whitt,et al.  Comparison methods for queues and other stochastic models , 1986 .

[19]  K. T. Marshall.  Bounds for Some Generalizations of the GI/G/1 Queue , 1968, Oper. Res..

[20]  I. Ahmad,et al.  ON THE MEAN INACTIVITY TIME ORDERING WITH RELIABILITY APPLICATIONS , 2004, Probability in the Engineering and Informational Sciences.

[21]  Stephen M. Stigler,et al.  Fractional Order Statistics, with Applications , 1977 .

[22]  Taizhong Hu,et al.  DISPERSION-TYPE VARIABILITY ORDERS , 2003, Probability in the Engineering and Informational Sciences.

[23]  Gary M. Roodman,et al.  The Determination of Partial Moments , 1972 .

[24]  Harshinder Singh,et al.  Reliability Properties of Reversed Residual Lifetime , 2003 .