Equipment reliability analysis based on the Mean-rank method of two-parameter Weibull distribution

Weibull distribution is a continuous probability distribution model and it has been widely used in reliability engineering. When we use Least-squares method to estimate the parameters of Weibull distribution, the empirical distribution function of life model is a key factor in accuracy. Typically to some complex mechanical products in the life test of reliability, the test sample is incomplete because of the test time, conditions, cost and other factors. If we directly use the approximate Median-rank formula to calculate the equation, it will cause large errors. In this paper, we use the Mean-rank method to calculate the equation. According to the Mean-rank method increment formula by statisticians, we can insert it into approximate Median-rank formula to get the sample empirical distribution. This method can improve the precision of parameter estimation.