A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, December 2014. / Industrial units cannot operate without failure forever. When the operation of a unit deviates
from industrial standards, it is considered to have failed. The time from the moment a unit enters
service until it fails is its lifetime. Within reliability and often in life data analysis in general,
lifetime is the event of interest. For highly reliable units, accelerated life testing is required to
obtain lifetime data quickly. Accelerated tests where failure is not instantaneous, but the end
point of an underlying degradation process are considered. Failure during testing occurs when
the performance of the unit falls to some specified threshold value such that the unit fails to meet
industrial specifications though it has some residual functionality (degraded failure) or decreases
to a critical failure level so that the unit cannot perform its function to any degree (critical failure).
This problem formulation satisfies the random signs property, a notable competing risks
formulation originally developed in maintenance studies but extended to accelerated testing here.
Since degraded and critical failures are linked through the degradation process, the open problem
of modelling dependent competing risks is discussed. A copula model is assumed and expert
opinion is used to estimate the copula. Observed occurrences of degraded and critical failure
times are interpreted as times when the degradation process first crosses failure thresholds and
are therefore postulated to be distributed as inverse Gaussian. Based on the estimated copula,
a use-level unit lifetime distribution is extrapolated from test data. Reliability metrics from the
extrapolated use-level unit lifetime distribution are found to differ slightly with respect to different
degrees of stochastic dependence between the risks. Consequently, a degree of dependence
between the risks that is believed to be realistic to admit is considered an important factor when
estimating the use-level unit lifetime distribution from test data.
Keywords: Lifetime; Accelerated testing; Competing risks; Copula; First passage time.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/17630 |
| Date | 06 May 2015 |
| Creators | Hove, Herbert |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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