Abstract
In this paper, a Nonhomogeneous Poisson Process (NHPP) reliability model based on the two-parameter Log-Logistic (LL) distribution is considered. The essential model’s characteristics are derived and represented graphically. The parameters of the model are estimated by the Maximum Likelihood (ML) and Non-linear Least Square (NLS) estimation methods for the case of time domain data. An application to show the flexibility of the considered model are conducted based on five real data sets and using three evaluation criteria. We hope this model will help as an alternative model to other useful reliability models for describing real data in reliability engineering area.
Highlights
The Log-Logistic (LL) distribution that results from a simple transformation of the familiar logistic distribution has been found useful in many areas such as engineering, reliability data analysis, economics and hydrology
The parameter estimation and evaluation criteria results of the Nonhomogeneous Poisson Process (NHPP) LL model for the five considered data sets using the Maximum Likelihood (ML) and Non-linear Least Square (NLS) estimation methods are respectively shown in Table [7] and Table [8]
By comparing the results in these two tables, it is clear that the Nonhomogeneous Poisson Process Log-Logistic (NHPP LL) model provides better values of the Mean Square Error (MSE), R, and Theil Statistic (TS) criteria when using the NLS estimation method for all cases
Summary
The Log-Logistic (LL) distribution that results from a simple transformation of the familiar logistic distribution has been found useful in many areas such as engineering, reliability data analysis, economics and hydrology. The Maximum Likelihood (ML) estimation method of several existing finite-failure NHPP models, as well as the log-logistic model was conducted based on inter-failure times data They presented analysis using two real data sets which encouraged the development of the log-logistic model. (Harishchandra, 2016) considered a software reliability model in which time between two successive failures is assumed to follow the log-logistic distribution The parameters of their model were estimated using the ML method in the cases of interval domain data and time domain data. Nonhomogeneous Poisson Process Log-Logistic (NHPP LL) model is considered Reliability characteristics of this model including: intensity function, number of remaining errors function, error detection rate function, instantaneous and cumulative mean time between failure function, and conditional reliability function are provided and represented graphically.
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