ABSTRACT
The meaningful interpretation of other algebraic inequalities yielded a highly counter-intuitive result related to purchasing components from suppliers with unknown proportions of high-reliability components. Despite the complete lack of knowledge related to the proportions of high-reliability components characterising the separate suppliers and despite existing dependencies among the proportions of high-reliability components, purchasing all components from the same supplier is characterised by the highest probability that all purchased components will be of high reliability. A similar result holds also in the case of assigning devices of different types to missions involving identical tasks. If the probabilities of successful accomplishment of a task characterising the devices are unknown, the best strategy for successful accomplishment of the mission consists of selecting randomly an arrangement including devices of the same type. This strategy is always correct, irrespective of existing interdependencies between the probabilities of successful accomplishment of the tasks, characterising the devices.
Finally, a new algebraic inequality has been interpreted as the probability of simultaneous presence of more than a specified number of risk-critical random events (e.g. random demands placed by users). The compact inequality has wide applications because it describes the behaviour of a complex system with a number of features: (i) an arbitrary number of users initiating demands, (ii) each demand is randomly placed along a specified time interval and (iii) different number of available sources for servicing the random demands.
