Abstract: In this paper, we propose a method to model the
relationship between failure time and degradation for a simple step
stress test where underlying degradation path is linear and different
causes of failure are possible. It is assumed that the intensity function
depends only on the degradation value. No assumptions are made
about the distribution of the failure times. A simple step-stress test
is used to shorten failure time of products and a tampered failure
rate (TFR) model is proposed to describe the effect of the changing
stress on the intensities. We assume that some of the products that
fail during the test have a cause of failure that is only known to
belong to a certain subset of all possible failures. This case is known
as masking. In the presence of masking, the maximum likelihood
estimates (MLEs) of the model parameters are obtained through an
expectation-maximization (EM) algorithm by treating the causes of
failure as missing values. The effect of incomplete information on the
estimation of parameters is studied through a Monte-Carlo simulation.
Finally, a real example is analyzed to illustrate the application of the
proposed methods.
Abstract: In this paper, we present a new maintenance model
for a partially observable system subject to two failure modes,
namely a catastrophic failure and a failure due to the system
degradation. The system is subject to condition monitoring and the
degradation process is described by a hidden Markov model. A
cost-optimal Bayesian control policy is developed for maintaining
the system. The control problem is formulated in the semi-Markov
decision process framework. An effective computational algorithm is
developed, illustrated by a numerical example.
Abstract: In this paper, we investigate the residual life prediction
problem for a partially observable system subject to two failure
modes, namely a catastrophic failure and a failure due to the system
degradation. The system is subject to condition monitoring and the
degradation process is described by a hidden Markov model with
unknown parameters. The parameter estimation procedure based on
an EM algorithm is developed and the formulas for the conditional
reliability function and the mean residual life are derived, illustrated
by a numerical example.
Abstract: Competing risks survival data that comprises of more
than one type of event has been used in many applications, and one
of these is in clinical study (e.g. in breast cancer study). The
decision tree method can be extended to competing risks survival
data by modifying the split function so as to accommodate two or
more risks which might be dependent on each other. Recently,
researchers have constructed some decision trees for recurrent
survival time data using frailty and marginal modelling. We further
extended the method for the case of competing risks. In this paper,
we developed the decision tree method for competing risks survival
time data based on proportional hazards for subdistribution of
competing risks. In particular, we grow a tree by using deviance
statistic. The application of breast cancer data is presented. Finally,
to investigate the performance of the proposed method, simulation
studies on identification of true group of observations were executed.
Abstract: The objective of the present research manuscript is to
perform parametric, nonparametric, and decision tree analysis to
evaluate two treatments that are being used for breast cancer patients.
Our study is based on utilizing real data which was initially used in
“Tamoxifen with or without breast irradiation in women of 50 years
of age or older with early breast cancer" [1], and the data is supplied
to us by N.A. Ibrahim “Decision tree for competing risks survival
probability in breast cancer study" [2]. We agree upon certain aspects
of our findings with the published results. However, in this
manuscript, we focus on relapse time of breast cancer patients instead
of survival time and parametric analysis instead of semi-parametric
decision tree analysis is applied to provide more precise
recommendations of effectiveness of the two treatments with respect
to reoccurrence of breast cancer.