Measurement Data Distribution Selection for Full-Range Fit
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Solution Overview
Problem
Existing statistical modeling methods often fail to accurately describe measurement data over the entire value interval, leading to modeling errors when data points fall outside the distribution range, as they assign zero frequency to values outside the interval, making it difficult to predict such occurrences.
Innovation Solution
A method is proposed to evaluate a random sample of measurement data by checking if the initial statistical distribution is suitable for the entire value interval, determining the moments of skewness and kurtosis, and selecting a suitable statistical distribution from a defined set that can describe the frequency of measurement data values within the entire value interval.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a statistical distribution is created exclusively from existing measurement data, then the distribution fits the data well over a large part of the value interval, but values outside the distribution range cannot be predicted and modeling errors occur
Solution Approach 1:
The patent applies preliminary action by performing a suitability test before finalizing the statistical distribution model. The method checks whether the distribution can describe measurement data over the entire value interval, including extreme values, before accepting it for predictive purposes. This preliminary validation prevents selecting distributions that would fail to predict out-of-range values later.
Solution Approach 2:
The patent implements feedback by using the suitability test results to iteratively refine the statistical distribution selection. The test provides feedback on whether the distribution adequately covers the entire value interval, allowing the selection process to adjust and improve the model until it meets the required predictive capability for the full range of possible measurements.
2Ease of manufacture
If a statistical distribution assigns zero frequency to values outside its interval, then the distribution is mathematically well-defined, but it cannot predict or describe occurrences outside this interval
Solution Approach 1:
The patent performs a preliminary suitability test to verify that the distribution's value interval adequately covers the entire range of possible measurement data before finalizing the model. This advance check ensures the distribution is both mathematically sound and sufficiently versatile for the application.
Solution Approach 2:
The patent introduces dynamics by making the distribution selection adaptive rather than static. The suitability test allows the method to evaluate and select distributions based on their actual performance in covering the measurement data range, rather than relying solely on theoretical mathematical properties. This dynamic approach balances mathematical definition with practical adaptability.
3Ease of operation
If a normal distribution is used to model measurement data, then the modeling process is simple and well-established, but it cannot accurately describe data with limited value intervals or asymmetric distributions
Solution Approach 1:
The patent applies parameter changes by moving beyond the fixed parameters of normal distribution to evaluate multiple distribution types with different parameters. The suitability test framework allows changing the distribution family (e.g., from normal to asymmetric or bounded distributions) based on the actual characteristics of the measurement data, thereby improving accuracy while maintaining systematic evaluation.
Solution Approach 2:
The patent uses feedback from the suitability test to guide the selection of appropriate distribution parameters and types. The test results provide information about which distributions accurately represent the measurement data, allowing the method to select the most appropriate model rather than defaulting to normal distribution, thus improving precision while maintaining operational clarity.
Data Source
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AI summary
The invention relates to a method and an arrangement for evaluating a sample of measurement data from a measurement of a plurality of workpieces, wherein a system of statistical distributions exists or is established which is capable of describing a frequency of measurement data values as a function of the measurement data values, wherein instances of the system of statistical distributions are distinguishable from one another by a moment value of two moments, namely a skewness and a kurtosis, of the respective statistical distribution, and wherein - for a value interval of the measurement data, which is a predetermined value interval or a value interval of the measurement data actually occurring in the sample, a set of all those statistical distributions is defined from the system of statistical distributions (step 5) which are capable of describing a frequency of measurement data values in the entire value interval.- from the sample of measurement data, a moment value for skewness and kurtosis is determined according to a first statistical distribution (step 7), - based on the determined moment values, it is checked whether a statistical distribution exists in the defined quantity that exhibits the determined moment values for skewness and kurtosis, and a corresponding test result is generated (step 9). The invention also relates to a method and an arrangement for preparing an evaluation of a sample of measurement data.