A New Approach to Testing the Distribution Type of Life Data

In order to calculate reliability indices of some important equipment, the life data type of equipment or product needs to be ascertained firstly. Aiming to this question, the linear regression and correlation coefficient method is suggested. The linearization of common distribution like as exponential distribution is complied with the principle of linear regression. But for three-parameter Weibull distribution, the location parameter usually cannot be ascertained. A binary search algorithm is programmed to locate the location parameter firstly. Then through the comparison of correlation coefficient, the most fitted distribution type can be found out quickly. The result also shows that the inferred distribution type is in accord with the facts. Example illustrates the effectiveness and validness of linear regression and correlation coefficient for the inference of distribution type of life data. KeywordsLinear Regression, Correlation Coefficient, Life Data, Three-Parameter Weibull Distribution, Reliability

[1]  John C. Fothergill,et al.  Estimating the cumulative probability of failure data points to be plotted on Weibull and other probability paper , 1990 .

[2]  G. C. Montanari,et al.  Comparison of maximum likelihood unbiasing methods for the estimation of the Weibull parameters , 1996 .

[3]  E. Reschenhofer.  Generalization of the Kolmogorov-Smirnov test , 1997 .

[4]  Takenori Takahashi.  Statistical inference by normal probability paper , 1999 .

[5]  T. Hauschild,et al.  Comparison of maximum likelihood estimation and chi-square statistics applied to counting experiments , 2001 .

[6]  Ibrahim Esat,et al.  A NEW APPROACH TO TIME-DOMAIN VIBRATION CONDITION MONITORING: GEAR TOOTH FATIGUE CRACK DETECTION AND IDENTIFICATION BY THE KOLMOGOROV–SMIRNOV TEST , 2001 .

[7]  Jen-Tzung Chien.  Quasi-Bayes linear regression for sequential learning of hidden Markov models , 2002, IEEE Trans. Speech Audio Process..

[8]  Jen-Tzung Chien.  Linear regression based Bayesian predictive classification for speech recognition , 2003, IEEE Trans. Speech Audio Process..

[9]  Loon Ching Tang,et al.  Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data , 2006, Reliab. Eng. Syst. Saf..

[10]  S. Kotz,et al.  Maximum likelihood estimation in the 3-parameter weibull distribution: a look through the generalized extreme-value distribution , 1996, IEEE Transactions on Dielectrics and Electrical Insulation.

[11]  Zvi Drezner,et al.  A Modified Kolmogorov–Smirnov Test for Normality , 2010, Commun. Stat. Simul. Comput..

[12]  Meng Chang Chen,et al.  Using chi-square statistics to measure similarities for text categorization , 2011, Expert Syst. Appl..