On statistical stability of the Weibull distribution parameters in practical description of the metal-cutting tool resistance

Durability of the metal-cutting tools used in a product manufacture largely determines technological cost of their production and characterizes technical and economic efficiency thereof as a whole. The tool durability has variable nature due to differences in characteristics of the technological system elements and instability in the parameters of processes occurring in a technological system during the product machining. In practice, variability in the metal-cutting tool durability value is often described using the three-parameter Weibull distribution. The corresponding distribution parameters are traditionally determined after completing collection of the statistical data. The paper proposes to make decisions on the parameter values ??of the sought-after distribution law in collecting the statistical data. It means significant reduction in sample volumes, time spent waiting for statistics collection and time before a researcher makes any decision without losing its quality. This solution is based on the sample function statistical stability inherent in many physical processes. The paper provides a practical example of describing durability of the metal-cutting tools using the three-parameter Weibull distribution based on cumulative approach to processing the incoming statistical data.
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