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A new incomplete data model, the trunsored model,
in lifetime analysis is introduced. This model can be regarded
as a unified model of the censored and truncated models. Using
the model, we can not only estimate the ratio of the fragile population
to the mixed fragile and durable populations, but also test a hypothesis
that the ratio is equal to a prescribed value. A central point
of the paper is that such a test can easily be realized through
the newly introduced trunsored model, because it has been difficult
to do such a hypothesis test under only the framework of censored
and truncated models. Therefore, the relationship of the trunsored
model to the censored and truncated models is clarified because
the trunsored model unifies the censored and truncated models.
The paper also shows how to obtain the estimates of the parameters
in lifetime estimation, and corresponding confidence intervals
for the fragile population. Typical examples applied to electronic
board failures, and to breast cancer data, for lifetime estimation
are demonstrated, and successfully worked using the trunsored model.
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Bootstrap, censored data, durable population,
exponential distribution, fragile population, grouped data,
likelihood ratio test, limited failure population, mixture
model, truncated data, Weibull distribution. FAILURE-RATE
FUNCTIONS; EXPONENTIAL-DISTRIBUTIONS; RANDOM-VARIABLES;
PARAMETERS;
TESTS; RELIABILITY; SAMPLE; SIZE
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