In reliability analysis, the residual life of a component or system plays a key role in explaining a component's present condition as well as how long it will continue to function as intended under specific circumstances, thereby preventing premature failure and saving money. Based on this, Nair and Rajesh [Geometric vitality function and its applications to reliability. IAPQR Trans. 2000;25(1):1–8] proposed a new measure called the geometric vitality function that explains the system's failure pattern. In the present study, we have introduced the geometric vitality function in the context of order statistics by means of the relevation transform and also analysed the monotone and ordering properties of the proposed measure. The application of the proposed measure in the stock markets are explored in the present study. Finally, to estimate the proposed measure using a real life data set, a simple estimator has been introduced as well.
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