On some comparisons of lifetimes for reliability analysis

Ordering of non-negative random variables (lifetimes) has been intensively studied in the literature. When comparing lifetimes in different applications such as reliability and risk analysis, it is often of interest to analyze also the distances between these lifetimes. In this paper, we define and discuss the stress–strength ordering and distance on the basis of the well-known stress–strength model that describes, e.g., the probability that the strength of a structure is larger than the external stress. We also compare this probability with the distance based on the difference between the means of random variables of interest and discuss several examples. The results can be useful, e.g., for analyzing reliability and safety requirements at the design stage for various engineering objects.

[1]  Maxim Finkelstein,et al.  Failure Rate Modelling for Reliability and Risk , 2008 .

[2]  K. Krishnamoorthy,et al.  CONFIDENCE LIMITS FOR STRESS STRENGTH RELIABILITY INVOLVING WEIBULL MODELS , 2010 .

[3]  S. Kotz,et al.  The stress-strength model and its generalizations : theory and applications , 2003 .

[4]  Jan M. van Noortwijk,et al.  A survey of the application of gamma processes in maintenance , 2009, Reliab. Eng. Syst. Saf..

[5]  D. Freedman,et al.  Some Asymptotic Theory for the Bootstrap , 1981 .

[6]  On some measures and distances for positive random variables , 2003 .

[7]  Maxim Finkelstein,et al.  Stochastic Modeling for Reliability , 2013 .

[8]  Samuel Kotz,et al.  The stress-strength model and its generalizations , 2013 .

[9]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[10]  Samuel Kotz,et al.  Formulas for risk of failure , 2007 .

[11]  Maxim Finkelstein,et al.  Shocks in homogeneous and heterogeneous populations , 2005, Reliab. Eng. Syst. Saf..

[12]  Frank Beichelt,et al.  A unifying treatment of replacement policies with minimal repair , 1993 .

[13]  Richard A. Johnson,et al.  Testing reliability in a stress-strength model when X and Y are normally distributed , 1992 .

[14]  Maxim Finkelstein,et al.  Stochastic Modeling for Reliability: Shocks, Burn-in and Heterogeneous populations , 2013 .

[15]  Richard E. Barlow,et al.  Stochastic Ageing and Dependence for Reliability , 2006 .