Hazard Rate Function of the Discrete Distributions

• Activity Number: 125
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Pushpa Gupta*+
• Companies: University of Maine
• Keywords: Monotonicity ; Discrete Hazard Rate ; Logconcavity ; Series Systems ; Parallel System

Abstract

PUSHPA L.GUPTA: Discrete failure rates arise in various common situations. For example: (1) a device can be monitored only per time period and the observation is taken as the number of time periods successfully completed prior to the failure of the device (2) a piece of equipment may operate in cycles and the data consist of the number of cycles completed prior to failure. Discrete failure rates also arise in several common situations in reliability theory where clock time is not the best scale on which to describe the life time. For example, in weapons reliability, the number of rounds fixed until failure is more important than the age in failure. In this presentation, we shall discuss techniques for the determination of the IFR and DFR property for a wide class of discrete distributions. This will include: (1) Extended Katz family (2) Inverse linear failure rate distributions (3) a class of Hurwitz-Lerch-Zeta distributions and (4) in the case of Poisson distribution,the distribution of series and parallel systems.