Most of the competitive environments are highly dynamic in nature and also fragile. The active and inactive participation of competitors may prompt an improper decision making. The article focuses on the behaviour and impact of dummy (inactive) competitors in the system. The study is to generate a maxima or minima in a time-probability distribution of all competitors in terms of inactive competitors. The inefficiency of the discrete ranking model without frequency to generate a maxima or minima in the corresponding position-probability distribution and also the capability of continuous infinite model with frequency for the same purpose conferred. The necessary conditions on behalf of with and without dummy variable to create a peak or dip in the position-probability distribution through one tail and two tail addition in the competitor frequency distribution curve is additionally contemplated. The cutting edge e-SCM scenario comprising of fake rating and reviewing is regularly critical in e-Marketing. The summed up model examined here along these lines causes us to anticipate the probabilities for selling and the related risk factor required by thinking about the number of fake rating as a spurious variable in the framework. A case study has been incorporated to study the impact of dummy variable in the system. The model will definitely find application in decision making and strategic formation process in the various fields of quality and inspection engineering, economics and social sciences etc.

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Purpose In any machining process, the surface profile of the workpiece is continuously changing with respect to time and input parameters. In a conventional machining process, input parameters are feed and depth of cut whilst other parameters are considered to be constant throughout the process. Design/methodology/approach The direct and indirect participation of this instantaneous curvature can be used to optimize the strategy of cutting operation in terms of different parameters like heat generation-induced stresses, etc. The concepts of the metric tensor and Riemannian curvature tensor are made use in this study as a representation of curvature itself. The objective of this study is to create a mathematical methodology that can be implemented on a highly flexible machining process to find an optimum cutting strategy for a particular output parameter. Findings The study also includes different case studies for the validation of this newly introduced mathematical methodology. Originality/value The study will also find its position in other mechanical processes like forging and casting where instantaneous curvature affects various mechanical properties.