Continuous Mixtures of Exponentials and IFR Gammas Having Bathtub-Shaped Failure Rates

• Activity Number: 649
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Jie Wang*+ and Henry W. Block and Naftali A. Langberg and Thomas H. Savits
• Companies: and University of Pittsburgh and University of Haifa and University of Pittsburgh
• Keywords: Reliability ; Failure rate function ; bathtub failure rate

Abstract

It can be seen that a mixture of an exponential distribution and a gamma distribution with increasing failure rate for the right choice of parameters can yield a distribution with a bathtub-shaped failure rate. In the paper which will be presented, we consider a continuous mixture of exponentials and a continuous mixture of gammas with increasing failure rates and show that the resulting mixture has a bathtub-shaped failure rate.