A Study of Overall Least Squares Estimation Based on The Weibull Distribution

Aiming at the problem that only the error of the measured value x is taken into account while the error of the observed value y is ignored when the classical least squares is used for the estimation of the parameters of the reliability model, the estimation method of total least squares is introduced. In this paper, the model is determined by comparing the goodness-of-fit using the data collected from one series of numerical control lathe (CNC) lathes with timed truncated faults; Based on the selected Weibull distribution model using two methods of least squares and total least squares for parameter estimation, the Mean Time Between Failures (MTBF) value and the D-test value are used as indicators for effect evaluation and empirical studies are carried out in conjunction with relevant literature data. In this paper, we use the data collected from one series of CNC lathes with timed ending faults to calculate the linear correlation coefficient, compare the degree of linear correlation to complete the initial selection of the model, and select the Weibull distribution as the life model of a series of CNC lathes. It is shown that the introduced total least squares parameter estimation method gives more accurate estimates than the least squares method and ultimately results in a more realistic reliability function.