Gamma prior distribution selection for Bayesian analysis of failure rate and reliability

Conference · Sat Jan 01 04:00:00 EST 1977

OSTI ID:7211728

Waler, R A; Johnson, M M; Waterman, M S; Martz, Jr, H F

It is assumed that the phenomenon under study is such that the time-to-failure may be modeled by an exponential distribution with failure-rate parameter, lambda. For Bayesian analyses of the assumed model, the family of gamma distributions provides conjugate prior models for lambda. Thus, an experimenter needs to select a particular gamma model to conduct a Bayesian reliability analysis. The purpose of this paper is to present a methodology which can be used to translate engineering information, experience, and judgment into a choice of a gamma prior distribution. The proposed methodology assumes that the practicing engineer can provide percentile data relating to either the failure rate or the reliability of the phenomenon being investigated. For example, the methodology will select the gamma prior distribution which conveys an engineer's belief that the failure rate, lambda, simultaneously satisfies the probability statements, P(lambda less than 1.0 x 10/sup -3/) = 0.50 and P(lambda less than 1.0 x 10/sup -5/) = 0.05. That is, two percentiles provided by an engineer are used to determine a gamma prior model which agrees with the specified percentiles. For those engineers who prefer to specify reliability percentiles rather than the failure-rate percentiles illustrated above, one can use the induced negative-log gamma prior distribution which satisfies the probability statements, P(R(t/sub 0/) less than 0.99) = 0.50 and P(R(t/sub 0/) less than 0.99999) = 0.95 for some operating time t/sub 0/. Also, the paper includes graphs for selected percentiles which assist an engineer in applying the methodology.

• Research Organization: Los Alamos Scientific Lab., NM (USA)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 7211728
• Report Number(s): LA-UR-77-155; CONF-770625-2
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
220900* -- Nuclear Reactor Technology-- Reactor Safety
DISTRIBUTION FUNCTIONS
FAILURES
NUCLEAR FACILITIES
NUCLEAR POWER PLANTS
POWER PLANTS
REACTOR COMPONENTS
RELIABILITY
SYSTEM FAILURE ANALYSIS
SYSTEMS ANALYSIS
THERMAL POWER PLANTS