Competing Risk Models in Reliability Systems, a Weibull Distribution Model with Bayesian Analysis Approach
In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failur...
| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English English |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://umpir.ump.edu.my/id/eprint/11562/ http://umpir.ump.edu.my/id/eprint/11562/1/Competing%20risk%20models%20in%20reliability%20systems%2C%20a%20weibull.pdf http://umpir.ump.edu.my/id/eprint/11562/7/Competing%20risk%20models%20in%20reliability%20systems%2C%20a%20weibull-abstract.pdf |
| Summary: | In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models.
The estimation may be based on data collected over censored or uncensored life tests. In many reliability
problems, the failure data are simply quantitatively inadequate, especially in engineering design
and maintenance system. The Bayesian analyses are more beneficial than the classical one in
such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in
the form of an apriori distribution with life test data to make inferences of the parameter of interest .
In this paper, we have investigated the application of the Bayesian estimation analyses to competing
risk systems. The cases are limited to the models with independent causes of failure by using the
Weibull distribution as our model. A simulation is conducted for this distribution with the objectives
of verifying the models and the estimators and investigating the performance of the estimators for
varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood
analyses.
The simulation results show that the change of the true of parameter relatively to another will change
the value of standard deviation in an opposite direction. For a perfect information on the prior distribution,
the estimation methods of the Bayesian analyses are better than those of the maximum likelihood.
The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations.
They also show the robustness of the Bayesian analysis within the range between the true value and
the maximum likelihood estimated value lines. |
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