Properties of residual mixing distributions resulting from arbitrary mixtures of exponential life distributions
Campbell, David Russell
Esary, James D.
MetadataShow full item record
A mixture of failure rates can be present in an apparently homogeneous population of "devices" due to variability either in their manufacture or in the severity of their service environments. An initial mixing distribution is the probability distribution for different failure rates in such a population. This distribution may be updated to yield its related residual mixing distribution, which is the probability distribution for different failures rates in the population of survivors after a specified period of service or "burn-in". Residual mixing distributions resulting from arbitrary mixtures of constant failure rates are shown to be stochastically ordered (decreasingly) as the period of service or burn-in is increased, and to approach in the limit a distribution degenerate at the smallest failure rate "present" in the population. Properties of expected value ordering, stochastic ordering, failure rate ordering and likelihood ration ordering are investigated to show that, of these, only likelihood ratio ordering between the initial mixing distributions is sufficient to guarantee an ordering between the expected values of their respective residual mixing distributions over time.
Approved for public release; distribution is unlimited
Showing items related by title, author, creator and subject.
Campbell, David Russell (Monterey, California. Naval Postgraduate School, 1974-07); NPS-64Cm74071A mixture of failure rates can be present in an apparently homogeneous population of "devices" because of variability either in their manufacture or in the severity of their service environments. A mixing distribution is ...
Kamin, Deborah Y.; Sutherland, Paula K. (Monterey, California. Naval Postgraduate School, 1981-12);Declining pools of service-eligible men and increasing demands upon military manpower nave forced the armed services to consider expanding the role of military women. The success or failure of increased utilization can ...
Hicks, David M. (Monterey, California. Naval Postgraduate School, 2005-12);The Armed Forces of the United States are becoming more expeditionary in nature, in that more forces will be home-ported or home-stationed in the Continental U.S. One of the major characteristics associated with future ...