Estimation Based on Sequential Order Statistics Coming from the Weibull Distribution
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Mahdy Esmailian, Department of Statistics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
In engineering systems, it is usually assumed that the lifetime of the componentsare independent and identically distributed. But with the failure of any component, the pressure comes more to the remaining components. Thus, the distribution of the survivingcomponents would be changed. For modeling this kind of systems, the theoryof sequential order statistics (SOS) may be used. In this paper, SOS with the conditional proportional hazard rates (CPHR) model, coming from the two-parameter Weibull distribution, are used for modeling lifetimes of sequential r-out-of-n: F systems. The Newton-Raphson method to determine the maximum likelihood estimates of parameters is implemented. For illustration purposes, an example is analyzed.
Sequential Order Statistics, Weibull Distribution, Point Estimation, Newton-Raphson Method
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