Quantile Based Geometric Vitality Function of Order Statistics

In [ 1 ], the authors introduced the geometric vitality function that explains the failure pattern of components or systems based on the geometric mean of the remaining lifetime. Recently, studies based on quantile function played an essential role in the research domain because of its unique properties than the distribution function method. Based on this, we define geometric vitality function in terms of quantile function and established monotone, ordering properties for the proposed measure. In addition to this, we also introduce the proposed measure in the context of order statistics. Some important properties were discussed for the proposed measure. Finally, we provide an application of the new measure for some distributions useful in lifetime data analysis.