Abstract
Non-Homogeneous Gamma Process (NHGP) is characterized by an arbitrary trend function and a gamma renewal distribution. In this paper, we estimate the confidence intervals of model parameters of NHGP via two parametric bootstrap methods: simulation-based approach and re-sampling-based approach. For each bootstrap method, we apply three methods to construct the confidence intervals. Through simulation experiments, we investigate each parametric bootstrapping and each construction method of confidence intervals in terms of the estimation accuracy. Finally, we find the best combination to estimate the model parameters in trend function and gamma renewal distribution in NHGP.
Highlights
The former estimates model parameters or reliability measures as numeric values. Since these model parameters have to be estimated based on the limited information such as failure data observed in a specific period, the estimators of model parameters always include the estimation errors
The interval estimation is more suitable, and the confidence intervals of model parameters will give the statistically significant information because the resulting estimates of model parameters or reliability measures are given by confidence regions
Concluding Remarks and Future Work In this paper, we have proposed two bootstrap methods and three construction methods of confidence intervals for the model parameters of Non-Homogeneous Gamma Process (NHGP)
Summary
In various fields of reliability engineering, stochastic point processes are used to describe probabilistic behavior of the cumulative number of events occurred as time goes by (see Meeker and Escobar, 1998). By applying stochastic point processes to various situations, we can derive some important measures quantitatively, such as mean time between failures for repairable systems or software reliability for software products. The most important issue for applying them is to statistically estimate the model parameters which characterize the stochastic point process in order to evaluate the quantitative measures. Statistical estimation can be classified into point estimation and interval estimation The former estimates model parameters or reliability measures as numeric values. Different failure time data may often result different model parameters, and these may not guarantee any confidence of the model parameters estimated by means of the point estimation. A lot of existing works on interval estimation of model parameters for representative stochastic point processes have
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