Some reliability aspects of record values using quantile functions

Abstract

In some experiments such as stress testing and industrial quality control experiments, only values which are larger or smaller than all previous ones are observed. Study of such extremes are of great importance. An extensive research on record values using distribution function are available in literature; however, a quantile-based study on the same have not been considered so far. Motivated with these, in this article, we introduce a quantile function approach of record values, which is an equivalent and alternative to the traditional distribution function approach. We study various properties of quantile-based measures of record values. We also obtain some stochastic comparison and ageing properties of quantile-based record values. The L-moment estimation method of hazard quantile function of record values is explained using a real-data example.

KEYWORDS:

• Record values
• quantile function
• quantile density function
• Hazard quantile function

Acknowledgements

We thank the editor and the reviewers for their constructive comments on the original draft.

Additional information

Funding

The authors are thankful to Kerala State Council for Science, Technology and Environment (KSCSTE) for the financial support.