Parametric B vs W Confirmation Test for Low-Sample Alpha Risk
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Solution Overview
Problem
Existing confirmation tests, such as the B vs W six pack confirmation test, face challenges in providing less than or equal to 5% alpha risk with a sample size less than five, and they do not utilize information about the population of interest.
Innovation Solution
A parametric B vs W two pack confirmation test is structured and performed using a graphical user interface (GUI), which involves receiving an indication of a desired alpha risk and output sample data, processing the data to generate an estimated distribution, determining bins of equal probability to define best-of-best (BOB) and worst-of-worst (WOW) regions, and analyzing samples within these regions to determine if the test parameter is a cause of the observable problem.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a B vs W six pack confirmation test is used to achieve less than or equal to 5% alpha risk, then the reliability of the test increases, but the sample size required increases to five or more
Solution Approach 1:
The patent changes the fundamental parameter of the confirmation test from non-parametric (six pack) to parametric by incorporating population distribution information. This allows the test to achieve the same or better alpha risk control (less than or equal to 5%) with a reduced sample size of two samples, by using statistical parameters from the estimated population distribution rather than relying solely on sample-based comparisons.
Solution Approach 2:
The patent performs preliminary action by estimating the population distribution from historical output sample data before conducting the confirmation test. This pre-analysis of population characteristics (mean, standard deviation, or Weibull parameters) enables the test to use this prior information to reduce the sample size required while maintaining statistical rigor and alpha risk control.
2Adaptability or versatility
If a non-parametric B vs W six pack confirmation test is used, then the test can be performed without population information, but the sample size required increases and alpha risk control worsens
Solution Approach 1:
The patent transitions from a non-parametric approach to a parametric approach by incorporating population distribution parameters. This allows the test to achieve better alpha risk control (less than or equal to 5%) by using the estimated population distribution (normal or Weibull) to define acceptance regions, rather than relying on the less efficient non-parametric six pack methodology.
3Ease of operation
If existing confirmation tests are used, then the test procedure is straightforward, but the sample size required is large and costly in time or resources
Solution Approach 1:
The patent performs preliminary action by estimating the population distribution from historical data before the confirmation test. This pre-computed population information (mean, standard deviation, or Weibull parameters) is then used during the test to evaluate whether test samples fall within acceptable regions, reducing the number of samples needed from five or more down to just two samples while maintaining test rigor.
Data Source
AI summary
Disclosed is a parametric B vs W two pack confirmation test. The test entails receiving a desired alpha risk and output sample data, processing the output sample data to generate an estimated distribution of the output variable for the population of workpieces, determining bins of equal probability in the estimated distribution to define best-of-best (BOB) and worst-of-worst (WOW) regions based on the desired alpha risk, receiving B and W samples predicted to be within, respectfully, the BOB and WOW regions, and determining whether the B sample falls in the BOB region and the W sample falls within the WOW region.