### Comparing Three Different Estimators of Reliability Function of Lognormal Distribution

*AL-MANSOUR JOURNAL*

2018, Volume , Issue 30, Pages 101-114

2018, Volume , Issue 30, Pages 101-114

#### Abstract

The estimation of reliability function is important to indicate the ability of machine and system to work without failure work for long time, this lead to increase productivity, the research include estimating reliability function of some probability distribution (which is the lognormal) with two parameters (μ,σ^2), where this distribution is necessary when the time failure is measured in hours, so it may be of large values, so transformation is taken on it and change values of (t_i) into (log〖t_i 〗). It is found that (log〖t_i 〗) follow normal distribution (μ,σ^2), then estimating these parameters by maximum likelihood and moments estimator, also introduce simple linear regression in estimating (μ,σ^2) then [R ̂(t)]. The comparison has been done through simulation using different sets of initial values for (μ,σ^2) and different sets of (n=20,40,80), the results are compared using statistical measure mean square error (MSE), and each experiment repeated (L=1000 times)

#### Keywords

Reliability Function, normal distribution, maximum likelihood, regression method estimation.#### Metrics