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 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.
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.
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.
TIME SERIES ANALYSIS
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.
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
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.
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.
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.
theory is the theory of failure; when do items fail, how do items fail,
what causes items to fail?
analysis is concerned with estimating risks, and determining courses of
action based upon these risks. It is used extensively in decision problems.
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
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 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.