S. M. Umar

We consider a replacement problem of n units parallel system, where a component failure is rectified by minimal repairs. We exchanged the system preventively before failure if the number of minimal repairs reaches m r m m − − − ,..., 2, 1 and is preventively replace if the sum of minimal repair reaches threshold value m . Keywords: minimal repairs, parallel system, failure,

A new way of introducing a parameter to expand a family of exponential and Weibull distributions is introduced and studied. It is applied to yield a new two-parameter extension of the bivariate exponential distribution which may serve as a competitor to such commonly used two-parameter family of the life distribution as the Weibull, gamma and lognormal distributions. The general method is applied to give a new three-parameter Weibull distribution.