Parametric and nonparametric statistical modeling: Reliability analysis
Abstract (summary)
The aim of the present study is to investigate several important problems in probability distribution, reliability analysis and nonparametric probability density estimation.
Extensive investigation of the basic properties of the Weibull process/nonhomogeneous Poisson process that characterizes the reliability growth behaviors of various components and systems was performed. In addition, linearly derived best efficient estimates of the parameters of the subject process were developed. Using real world data, we have illustrated the effectiveness of the results of this study.
Computerized simple iterative procedures have been developed for estimating the two and three parameters of the Weibull probability distributions. Our procedure will always converge and converge very rapidly.
An effective method has been developed to estimate the nonparametric probability density functions of data that possesses bimodal characteristics.
Finally, a procedure has been developed to perform reliability analysis when the failure model is characterized nonparametrically.