Title On partial orderings and testing of new better than renewal used classes

Partial orderings are used to compare ageing behaviour of components or systems. In this paper a new partial ordering, namely the renewal super-additivity, is introduced. This concept is used to characterise the new better than renewal used criterion of ageing. The dual criterion the new worse than renewal used is characterised by the renewal sub-additivity concept. The relation of these ageing properties with existing criteria of ageing is shown via the partial orderings. Test statistic of exponentiality versus the new better (worse) than renewal used as alternatives is established. The percentiles of this test statistic are tabulated for small samples. These tables can be used by reliability engineers to check whether a set of life data has the new renewal better than used property or its dual. The power estimates of the test are simulated for some commonly used distributions in reliability. Two sets of real data are used as examples to elucidate the use of the proposed test statistics for practical reliability analysis