FAILURE RATE OF THE WEIBULL-WEIBULL LENGTH-BIASED MIXTURE MODEL

In this paper the failure rate of the Weibull-Weibull length-biased mixture distribution which is characterized by five parameters is studied. Depending on the parameter values, it is shown that this failure rate can have one of six shapes, which are increasing failure rate (IFR), decreasing failure rate (DFR), upside down bathtub (UBT), modified upside down bathtub (MUBT), bathtub (BT), and modified bathtub (MBT) failure rates, by consequence it has zero, one or two turning points