Parameter Estimation for the Power Generalized Weibull Distribution Based on One- and Two-Stage Ranked Set Sampling Designs

2019 ◽  
Vol 8 (2) ◽  
pp. 113-128 ◽  
Author(s):  
Sabry M., Muhammed H., Nabih, Shaaban A., Z., A., M.
Keyword(s):  
Parameter Estimation ◽  
Weibull Distribution ◽  
Ranked Set Sampling ◽  
Two Stage

scholarly journals Parameter Estimation Based on Double Ranked Set Samples with Applications to Weibull Distribution

2022 ◽  
Vol 19 (1) ◽  
pp. 2-24
Author(s):  
Mohamed Abd Elhamed Sabry ◽  
Hiba Zeyada Muhammed ◽  
Mostafa Shaaban ◽  
Abd El Hady Nabih
Keyword(s):  
Parameter Estimation ◽  
Weibull Distribution ◽  
Random Sampling ◽  
Likelihood Function ◽  
Maximum Likelihood Estimators ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Distribution Parameters ◽  
Two Parameters ◽  
Mean Square Errors

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating the two parameters of the Weibull distribution (WD).

scholarly journals Reliability-Centered Maintenance: Analyzing Failure in Harvest Sugarcane Machine Using Some Generalizations of the Weibull Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Pedro L. Ramos ◽  
Diego C. Nascimento ◽  
Camila Cocolo ◽  
Márcio J. Nicola ◽  
Carlos Alonso ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Cost Savings ◽  
Maintenance Scheduling ◽  
Predictive Analysis ◽  
Main Interest ◽  
Mathematical Background ◽  
Reliability Centered Maintenance ◽  
Best Fit

We considered five generalizations of the standard Weibull distribution to describe the lifetime of two important components of sugarcane harvesting machines. The harvesters considered in the analysis harvest an average of 20 tons of sugarcane per hour and their malfunction may lead to major losses; therefore, an effective maintenance approach is of main interest for cost savings. For the considered distributions, mathematical background is presented. Maximum likelihood is used for parameter estimation. Further, different discrimination procedures were used to obtain the best fit for each component. At the end, we propose a maintenance scheduling for the components of the harvesters using predictive analysis.

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