Coordinate Measurement Control Limits Using Synthetic Sample Values
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Solution Overview
Problem
Current methods for determining control limits in quality control processes using coordinate measuring machines often result in inaccurate interventions due to insufficient statistical basis, especially with small sample sizes, leading to either unnecessary interventions or missed process changes.
Innovation Solution
The method involves generating synthetic values based on a first adjusted continuous statistical distribution to increase the statistical basis, forming subgroups, and determining control limits using a second adjusted distribution to ensure accurate intervention based on a predetermined statistical probability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If control limits are determined using only measured values from small sample sizes, then the evaluation process is simple and quick, but the statistical basis is insufficient leading to inaccurate interventions
Solution Approach 1:
The method performs preliminary actions by generating synthetic measured values based on the fitted distribution before final control limit determination. This preliminary generation of additional data points (synthetic values) enriches the statistical basis without requiring additional physical measurements, thereby resolving the contradiction between small sample size and accurate control limit determination
Solution Approach 2:
The invention creates copies of measured values by generating synthetic data points that follow the same statistical distribution as the original measurements. These synthetic copies augment the limited sample data, providing a more robust statistical foundation for control limit calculation without requiring more physical workpieces
2Reliability
If more measured values are collected to improve statistical basis, then control limit accuracy improves, but measurement time and resources increase
Solution Approach 1:
The method replaces the mechanical measurement process (physically measuring more workpieces) with a computational process (generating synthetic values through computer algorithms). This substitution allows the system to obtain additional statistical data without the time and resource costs of actual measurements, resolving the contradiction between statistical basis and measurement time
Solution Approach 2:
The invention changes the parameter state by transforming limited measured values into a larger dataset through synthetic value generation. By altering the quantity parameter of available data through computational means rather than physical measurement, the method achieves better statistical basis without proportional increase in measurement time
3Measurement precision
If control limits are set to be highly sensitive to detect process changes, then detection accuracy improves, but unnecessary interventions increase
Solution Approach 1:
The method implements feedback by using the fitted distribution and synthetic values to establish more reliable control limits that accurately reflect the true process variation. This feedback mechanism prevents both Type I errors (false positives causing unnecessary interventions) and Type II errors (false negatives missing real changes), thereby resolving the contradiction between detection sensitivity and intervention accuracy
Data Source
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AI summary
In particular, a computer-implemented procedure is carried out by an evaluation device (21) for preparing an evaluation of samples of measured values of a measurand from a measurement of a plurality of workpieces by one or more coordinate measuring machines (1), comprising the following steps: a) fitting (23) a distribution type of a continuous statistical distribution to measured values of a sample of measured values and obtaining a first fitted continuous statistical distribution, b) generating (24) a plurality of synthetic values of the measurand which obey the first fitted continuous statistical distribution with respect to the probability of their occurrence, c) forming (25) a plurality of subgroups from the totality of measured values and the synthetic values of the measurand, wherein each of the plurality of subgroups comprises a plurality of the measured values and/or the synthetic values of the measurand.d) for each of the subgroups, calculation (26) of a calculated value of a derived quantity, namely a location quantity that describes a location of the measured values and/or the synthetic values of the measured quantity of the subgroup, or a dispersion quantity that describes the dispersion of the measured values and/or the synthetic values of the measured quantity of the subgroup; e) fitting (27) a distribution type of a continuous statistical distribution to the calculated values of the derived quantity and obtaining a second fitted continuous statistical distribution; f) determining (28) an upper limit and a lower limit of a range of values of the derived quantity such that, according to the second fitted continuous statistical distribution, values of the derived quantity lie within the range of values bounded by the upper and lower limits with a proportion equal to a given statistical probability.