Extreme-Value Tolerance Band Calculation for Production Sampling
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Solution Overview
Problem
Existing methods for determining tolerance band limit values in sampling plans are inadequate for variables with distributions other than the normal distribution, particularly in extreme value distributions, which are common in medical devices like autoinjectors and multi-dose injection pens, leading to challenges in establishing pre-defined k factors and sample sizes.
Innovation Solution
A method using simulation and conditional probability distribution functions to determine tolerance band limit values for extreme value distributed variables, allowing for the establishment of sampling plans that consider producer and consumer risks, with adjustments for sample size based on precision requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If standardized methods are used for normal distribution variables, then manufacturing precision is improved, but adaptability deteriorates because they cannot be applied to extreme value distributions
Solution Approach 1:
The patent transforms the problem by changing the parameter space - it uses simulation to generate synthetic datasets with known extreme value distribution parameters, then applies statistical methods to estimate tolerance band limit values. This allows the methodology to adapt to extreme value distributions while maintaining systematic precision through controlled simulation parameters and statistical estimation techniques.
2Adaptability or versatility
If simulation is used to generate synthetic datasets, then adaptability is improved, but productivity deteriorates due to computational intensity
Solution Approach 1:
The patent performs preliminary actions by pre-generating synthetic datasets with known parameters before actual tolerance band determination is needed. These pre-computed simulation results and estimated parameters serve as a foundation that reduces the computational burden during actual quality control applications, making the process more efficient when deployed.
3Measurement precision
If sample size is increased to improve precision, then measurement precision is improved, but productivity deteriorates due to larger inspection requirements
Solution Approach 1:
The patent creates synthetic copies of the actual production data through simulation. These synthetic datasets replicate the statistical properties and distribution characteristics of real data but can be generated and processed computationally without physical inspection requirements. This allows precise parameter estimation without the need to physically inspect large numbers of actual products.
Data Source
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AI summary
Disclosed is a method of determining at least one tolerance band limit value (k, kp, kc) for a technical variable (x) under test, comprising: - obtaining (S10, S10p, S10c, S20) the at least one tolerance band limit value (k, kp, kc) from sample tolerance band limit values of different samples, wherein the samples comprise values (z) of the technical variable (x) under test of the associated sample, wherein obtaining the at least one tolerance band limit value (k, kp, kc) comprises using a location measure (mean k, mean kp, mean kc) of a distribution according to which the sample tolerance band limit values (k, kp, kc) are distributed, wherein the technical variable (x) under test is distributed according to an underlying extreme value distribution function (F0, F9, F10), wherein each of the sample tolerance band limit values (k, kp, kc) is calculable or is calculated (S6, S6p, S6c) using a sample-specific conditional probability distribution function (F4, F11) which is a function of sample values (z) of the sample, and wherein the technical variable (x) relates to a physical characteristic of a product that is producible in an industrial mass production process.