Defect Significance Analysis Using Agresti-Coull P-Values
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Solution Overview
Problem
Existing methods for statistical analysis, particularly in manufacturing and quality control, face inconsistencies between confidence intervals and p-values when using the Agresti-Coull confidence interval, leading to conflicting results and inefficient decision-making.
Innovation Solution
A method and system that utilize a sensor array to inspect items for defects, compute the statistical significance level of the proportion of defects compared to a predefined threshold by calculating the p-value associated with the Agresti-Coull confidence interval, thereby addressing the inconsistencies and enhancing decision-making accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional statistical methods are used to compute p-values and confidence intervals separately, then each can be calculated independently, but inconsistent results and conflicting conclusions occur between the two methods
Solution Approach 1:
The patent combines the previously separate calculations of confidence intervals and p-values into a single unified statistical framework. By integrating these two distinct statistical computations into one coherent method, the system eliminates the inconsistency and conflicting conclusions that arose when they were performed independently, while maintaining computational efficiency.
2Measurement precision
If Agresti-Coull confidence interval is used, then the confidence interval estimation is improved, but the associated p-value calculation becomes inconsistent with traditional hypothesis testing
Solution Approach 1:
The patent modifies the statistical parameters and calculation methods to ensure that the p-value computation is consistently aligned with the Agresti-Coull confidence interval approach. By changing the parameter estimation technique and ensuring methodological consistency between the confidence interval and hypothesis testing frameworks, the system maintains both the improved confidence interval accuracy and the reliability of hypothesis testing conclusions.
3Measurement precision
If separate statistical tests are performed for confidence intervals and hypothesis testing, then each test can be optimized independently, but the overall decision-making process becomes inefficient and prone to errors
Solution Approach 1:
The patent merges the separate statistical test procedures into a unified computational framework that simultaneously produces both confidence interval estimates and hypothesis test results. This integration eliminates the need for separate, independent calculations, thereby improving decision-making efficiency and reducing the risk of errors while preserving the statistical optimization benefits of both methods.
Data Source
AI summary
An aspect includes inspecting, using a sensor array, a batch of items in a stage of a process for defects that meet a predefined defect criteria, obtaining from the sensor array, a number of items in the batch with the defects, the batch of items is a sample from a population of items. The aspect includes computing a statistical significance level of a difference between a proportion of defects in the stage of the process and a predefined proportion threshold by calculating a p-value of a statistical test about the proportion of the defects through computing a solution to an equation derived from inverting an Agresti-Coull confidence interval for the proportion of defects.