Testing Hypothesis for New Class of Life Distribution NBUFR-t0

A new concept of ageing distribution, namely new better (worse) than used in failure rate at specific time 0t (NBUFR- 0t (NWUFR- 0t)) are introduced. The problem is investigated how to prove that after a specified time 0t of operation the failure rate of an item is greater than the corresponding failure rate of a new item. This problem occurs in various areas like for instance in industry, when designing a maintenance policy. A test statistics that based on the goodness of fit method are derived for testing exponentially versus the NBUFR- 0t alternatives. The percentiles and powers of this test statistic are tabulated. The asymptotic efficiencies for some alternatives are derived. A medical data is taken as a practical application