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Using an arrangement monotonicity property of the parametrized family of hazard rate ordered random variables, and a bivariate characterization of the hazard rate ordering, we obtain some new stochastic arrangement inequalities for the random variables that are hazard rate ordered. Some applications of optimal allocation and assembly are also discussed.

In this note, the early research in reliability is reviewed. The focus is on the theoretical development of aging and reliability bounds. Some conceptual issues with the interpretation of subjective reliability are also discussed.

A system of two components is analyzed as a two-period game. After period 1 the system can be fully operational, in two states of intermediate degradation, or fail. Analogously to changing failure rates in dependent systems analyzed with Markov analysis, unit costs of defense and attack, and contest intensities, change in period 2. As the values of the two intermediate states increase from zero which gives the series system, towards their maxima which gives the parallel system, the defender becomes more advantaged, and the attacker more disadvantaged. Simulations illustrate the players' efforts in the two time periods and utilities dependent on parametric changes. The defender withdraws from defending the system when the values of both degraded states are very low. The attacker withdraws from attacking the system when the values of both degraded states are very high. In the benchmark case the defender prefers the one-period game and the attacker prefers the two-period game, but if the attacker's unit cost of attack is large for one component, and the value of the degraded system with this component operational is above a low value, the defender prefers the two-period game to obtain high utility in period 2 against a weak attacker. When the values of the degraded states are above certain low values, the players exert higher efforts in period 1 of a two-period game than in a one-period game, as investments into the future to ensure high versus low reliability in period 2.

The aim of this paper is to investigate the effects of the load range on the spatial variation of fatigue crack growth resistance in three different zones, WM, HAZ and BM for flux cored arc welded API 2W Gr. 50 steel using the stochastic model based on reliability theory. Experimental fatigue crack growth tests were performed on ASTM standard CT specimens. The results indicates that the load range has strong dependency on probabilistic fatigue crack growth for the three different zones WM, HAZ and BM, and also the spatial variation of fatigue crack growth resistance.

In this article we review recent work on generalizations of the total time on test transform, and on stochastic orders that are based on these generalizations. Applications in economics, statistics, and reliability theory, are described as well.

In shield tunnel, segments and bolts are important components of lining structure, which is to assure tunnel safety in the period of construction and operation. All risk factors and related hazards in the lining construction of large-diameter shield tunnel were systematically analyzed, and then Fault Tree Analysis (FTA) model on risk analysis of lining structure construction was proposed. It is known that the stress and strain of lining structure are key indexes which can reflect its safety condition. The lining structure may be damaged once its stress or strain is beyond its design limit value. Therefore by using structural reliability theory and stochastic FEM, the authors analyzed and calculated risk-occurring probability of those basic events in the FTA model in view of the variability of lining structure and soil parameters. In the end, the FTA model was applied in Shanghai Yangtze River Tunnel, and risk assessment was finished for the lining structure in large-diameter shield tunnel project during its construction period. Simultaneity, the key degree of each risk-induced factor was also discussed.

The load limitation standard of trucks has an immediate influence on the actual vehicle load level and its probability distribution characteristics. Further, the standard may affect the serviceability of constructed infrastructures, for example bridges. To investigate the truck load limitation issue of small-medium span bridges, a probabilistic model of load limitation analysis was firstly established. In the second part, the truck load characteristics were discussed based on long-term WIM data and the truck types were extracted. Subsequently, the higher limit of truck mass was obtained through inverse iteration based on the established flexural functions and selected multi-level target reliability index. The effect of target reliability index and differences in regional load characteristics on the limited truck mass were discussed based on the analysis results. Further, the applicability of current standard was analyzed through a comparison. The following conclusion were obtained based on the former analysis: the limited truck mass decreases linearly with the increasing of target reliability index. Besides, the influence of differences in regional load characteristics on the results is non-ignorable. The current standard of overload control is suitable for small-medium span bridges. Nonetheless, it is ideal for different regions to refine regional standards based on actual conditions.