DETERMINATION OF CHANGE POINTS OF NON-MONOTONIC FAILURE RATES

Abstract

This paper was motivated by the problem of the determination of the change points of the failure rate of a mixture of two gamma distributions. For certain values of the parameters the existing methods are not applicable since, in this case, there are two turning points of the failure rate. Thus, we extend the results to models having two or more turning points of the failure rates. The extended procedure helps us to identify failure rates of more complex forms. Finally, the mixture gamma case is completely resolved employing theoretical, graphical and numerical techniques wherever necessary.

Keywords:

• Monotonicity
• Mixed gamma
• Bathtub failure rate
• Upside bathtub failure rate

ACKNOWLEDGMENTS

The authors are thankful to the referee for some useful comments which enhanced the presentation.