Generalised probabilistic ranking competition model with quality inspection technique

The world of competition is not only constrained to the discrete cases but also envisages finite and infinite continuous cases of ranks of competitors in a generalised competition. The more applicable and general modelling is possible only through including single ranked competitors as well as the frequency of different ranks or positions. In this article, we propose a mathematical model which deals competition with ranks or positions with various frequency distributions applicable to quality inspection systems. The current article includes the equilibrium positions and failure gates in competitions for a single factor ranking system and discusses the multi-level competition which is more relevant in practical environment. The outcome probability of best, least and intermediate positions are analysed for discrete frequency model with finite ranks and also for continues frequency model with infinite ranks. The article likewise facilitates the feasibility of the model for implementation as a probabilistic inspection technique. The same technique is helpful to ascertain the quality of inspection units in a long term production cycle.