Variation Coefficient and Some Distribution Laws in the Context of Cutting Tools and Other Technical Objects Reliability Modeling

In the paper some practice of the usage of three distribution laws: Gauss, Gamma, and Weibull for reliability modeling of technical objects in general and metal cutting tools in particular are analyzed and arranged. Selection of distribution law and estimation of its parameters based on empirical data are the main tasks in reliability simulation. It is stressed that selection of the above-mentioned laws should be made taking into account the process mechanism; otherwise, it leads to some false conclusions such as equivalence of Gamma and Weibull distribution. Mentioned distribution laws and their usage are analyzed from the position of physical interpretation. The conditions are shown when the above-mentioned distribution laws are similar. The simplified dependence that connects the shape parameter of Weibull distribution and variation coefficient is obtained and confirmed statistically. The variation coefficient defines the shape parameters for both Gamma and Weibull distributions uniquely and reflects the mechanism of the process. The variation coefficient and failure rate in addition to formal criteria are shown to be the main indicators for the distribution law selection.