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Received: 12 June 2019 Accepted: 10 January 2020 The world of competition is not always deterministic. Probabilistic approach is more relevant and practical in any competitive environments. The effect of random failure gate which usually comes in the way of anything that promotes the low quality and at the same time denies high quality to come up in a competition and having a probability distribution for an instant of time is discussed in the present article. For this purpose the article introduces a novel methodology using the outcome probability of each rank along with the newly added concept of position ratios with a view to study the possibility of making proper predictions in the competitive environment discussed. The study also extends to infinite rank model cases as well. Moreover, a case study has been conducted to predict the risk of appropriate forecasting of different quality level using the model developed. The article emphasized the impact of number of failure gate and their respective influence in the area of ascertaining production quality making use of the concept of position ratio along with the outcome probabilities, which in turn improves the decision making to foresee the possible product quality variations in any manufacturing system, after a specific tenure of production. The methodology developed here will definitely find its application in the area of designing some powerful Decision Support Systems (DSS), where competition is fundamentally concerned with.

mathematical modelling and engineering problems/mathematical modelling of engineering problems

Effect-Cause Analysis and Prediction Convergence of Random Failure Gate in a Probabilistic Competitive Environment with Case Study on Quality Control Process