Coordinate Measuring Data Modeling Across the Full Value Interval
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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 measurement values lie outside the described interval, as they assign zero frequency to values outside the interval, rendering them unsuitable for predicting such occurrences.
Innovation Solution
A method is proposed to check and identify unsuitable statistical distributions by evaluating measurement data from coordinate measuring machines, and ascertain suitable distributions that can describe the frequency of measurement data values across the entire value interval by determining the moments of skewness and kurtosis, allowing for the selection of appropriate statistical distributions from a defined set.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a statistical distribution is created based on measurement data within a limited value interval, then the distribution fits the data well within that interval, but measurement values outside the interval cannot be described or predicted by the distribution
Solution Approach 1:
The patent applies preliminary action by determining the support (value interval) of the statistical distribution before fitting the distribution to the measurement data. By pre-defining the interval based on process knowledge or specification limits, the distribution is constrained to cover all relevant measurement values, preventing the problem of values falling outside the describable range. This upfront planning ensures both good fit within the interval and applicability to all possible measurement values.
2Ease of manufacture
If a normal distribution is used to model measurement data, then the modeling is simple and follows known process characteristics, but it cannot describe measurement data that are limited to a specific value interval
Solution Approach 1:
The patent applies parameter changes by transitioning from a normal distribution (unbounded) to a statistical distribution with bounded support. By changing the fundamental parameter of the distribution's support from infinite to finite, the model becomes suitable for measurement data that are naturally constrained to specific intervals, such as dimensions that cannot be negative or exceed certain specification limits.
3Measurement precision
If a statistical distribution is fitted to maximize likelihood based on available data, then the distribution accurately describes the frequency of measurement values within the observed range, but it assigns zero probability to values outside this range
Solution Approach 1:
The patent applies preliminary action by determining the support of the statistical distribution before fitting it to the data. By pre-establishing the value interval based on process knowledge, specification limits, or engineering judgment, the distribution is configured to cover all potentially relevant measurement values. This ensures that the distribution can describe frequencies within the observed range while also assigning non-zero probability to values outside the current sample range, preserving prediction capability.
Data Source
AI summary
A method evaluates a sample of measurement data from measuring multiple workpieces by at least one coordinate measuring machine. A system of statistical distributions describes a frequency of measurement data values. The distributions are distinguishable based on skewness and kurtosis. The method includes defining a set of statistical distributions that are able to describe a frequency of measurement data values in the entire value interval from the system of statistical distributions for a value interval of the measurement data, which is a specified value interval or a value interval of the measurement data actually arising in the sample. The method includes ascertaining the skewness and the kurtosis from the sample of measurement data corresponding to a first statistical distribution. The method includes checking, using the ascertained moment values, whether the defined set contains a statistical distribution that has the ascertained skewness and kurtosis, and producing a corresponding test result.