On Some Finite Range Life Distributions

Abstract

Various reliability properties, including some characterization results, have been investigated for two finite range life distributions. One of these, namely, the exponentiated rectangular distribution, exhibits a bath-tub failure rate when the shape parameter has a value less than unity and, as expected, does not conform to certain results relating to ageing properties, which hold in the case of distributions with monotone failure rates. Moments as well as best percentile estimates of the shape parameter for this distribution have been worked out. Stress–strength reliability when stress and strength follow the same distribution of this type over the same range, but with different shape parameter values, has been derived and shown to be related to the Bhattacharyya distance between the two probability distributions. Distributions of parallel and standby system lives for two independent components, with this distribution having varying shape parameters, have been derived.