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ACCELERATED LIFE
TESTING
Accelerated
life testing describes the process of testing items at stress levels above
those usually encountered. This effectively accelerates the time scale, so
that failures can be witnessed earlier than would be expected in the field.
The technique is much-used and therefore important.
BAYESIAN
STATISTICS
The
Bayesian approach to statistical inference and decision making revolves
around the paradigm that probability and its calculus is the only coherent approach
for the treatment of uncertainty. Very often, the interpretation of
probability is "personal" or "subjective." Bayesian
methods have proven to be very useful in engineering applications because
they allow for the formal incorporation of scientific knowledge, expertise,
and informed judgement into a statistical analysis. The application of such
methods to problems in reliability is rapidly growing, and many of the
papers given below pertain to these.
DEGRADATION
MODELING
To engineers degradation is the irreversible accumulation of
damage throughout life that leads to failure. The term “damage”
is not defined; however it is claimed that damage manifests itself via
surrogates such as cracks, corrosion, measured wear, etc. Similarly, in the
biosciences, the notion of “ageing” pertains to a unit's
position in a state space wherein the probabilities of failure are greater
than in a former position. Ageing manifests itself in terms of biomedical
and physical difficulties experienced by individuals and other such
biomarkers. We conceptualize ageing and degradation as unobservable
constructs (or latent variables) that serve to describe a process that
results in failure. These constructs can be seen as the cause of observable
surrogates like cracks, corrosion, and biomarkers such as CD4 cell counts.
The prevailing view is that degradation is an observable phenomenon that
reveals itself in the guise of crack length and CD4 cell counts. The item
fails when the observable phenomenon hits some threshold whose nature is
not specified. Whereas this may be meaningful in some cases, a more general
view is to separate the observable and the unobservable and to attribute
failure as a consequence of the behavior of the unobservable.
EXPERT JUDGEMENT
For the
Bayesian statistician, it is quite natural to work with subjective
opinions. A subject of much interest is how to elicit opinions from
experts, how to combine these opinions and how to represent them as prior
information in models.
FORECASTING AND
TIME SERIES ANALYSIS
Time
series analysis deals with data that is collected over time, and
demonstrates changes overtime. For the Bayesian statistician, the main tool
is the dynamic linear model, which can be adapted to many situations to
make forecasts about future observations, and to smooth past observations.
The Institute has extensive publications in this area.
FOUNDATIONAL
ISSUES
Foundational
issues in reliability pertain to topics that are general and do not pertain
to a specific application. As such, these topics are relevant to those
interested in reliability, biometry, economics, and finance, subjects
wherein the occurence times to certain events are of interest. The papers
described below pertain to issues such as the source of failure models, the
interpretation of a failure rate, the meaning of a bath-tub curve,
paradoxes in reliability, and the validity of the exponentiation formula.
PREDICTION
INTERVALS
Coverage probabilities for prediction intervals are germane to filtering,
previsions, regression, and time series analysis. It is a common practice
to choose the coverage probabilities for such intervals by convention, or
astute judgment. We argue that coverage probabilities can be chosen by
decision theoretic considerations. But to do so, we need to specify
meaningful utility functions.
QUALITY CONTROL
Quality
Control is the theory behind controlling product quality. It is used
extensively on the factory floor, and is possibly the most used of all
statistical methods. Control charts are typically used to plot how product
quality changes over time, and to warn of changes in quality. Utility based
approaches were suggested by Taguchi.
RELIABILITY MODELS
One of
the most important aspects of reliability theory is the selection of
appropriate statistical models for the modelling of failures. The Institute
has a number of papers in this area, concerned with the reliability of
multiple items, when these items act dependently, either due to a common
environment or common shocks.
RELIABILITY THEORY
Reliability
theory is the theory of failure; when do items fail, how do items fail,
what causes items to fail?
RISK ANALYSIS
Risk
analysis is concerned with estimating risks, and determining courses of
action based upon these risks. It is used extensively in decision problems.
SOFTWARE
RELIABILITY
Software
reliability is concerned with the failure of software. A great deal of
research has been done in this area, since it is both a very important area
and an interesting research area. Most papers concern the modelling of
failures during the software testing cycle, where, after a failure is
discovered, the code is modified to remove the error
UTILITY
ELICITATION
Utility theory provides a way to make decisions when faced with
uncertain outcomes by maximizing expected utility. Thus in order to apply
this approach it is necessary to elicit the utilities that a decision maker
ascribes to the possible outcomes.
WARRANTY ANALYSIS
AND DESIGN
The
warranty problem is an important problem. There are many statistical
problems associated with the offering of warranties. The calculation of
optimal warranty periods is of primary importance, along with the
forecasting of warranty claims, and the estimation of warranty reserves.
To see a list of publications, see
members’ websites and resumes.
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