Campus Units

Industrial and Manufacturing Systems Engineering

Document Type


Publication Version

Accepted Manuscript

Publication Date


Journal or Book Title

Journal of Manufacturing Systems




Part A

First Page


Last Page


Research Focus Area(s)

Advanced Manufacturing Research




Current methods for visual inspection of cast metal surfaces are variable in both terms of repeatability and reproducibility. Because of this variation in the inspection methods, extra finishing operations are often prescribed; much of this is over processing in attempt to avoid rework or customer rejection. Additionally, defective castings may pass inspection and be delivered to the customer. Given the importance of ensuring that customers receive high-quality castings, this article analyzes and quantifies the probability of Type I and II errors, where a Type I error is a false alarm, and a Type II error misses a present defect. A probabilistic model frequently used in risk analysis, called an influence diagram, is developed to incorporate different factors impacting the chances of Type I and II errors. These factors include: training for inspectors, the type of judgment used during the inspection process, the percentage of defective castings, environmental conditions, and the inspectors’ capabilities. The model is populated with inputs based on prior experimentation and the authors’ expertise. The influence diagram calculates the probability of a Type I error at 0.35 and the probability of a Type II error at 0.40. These results are compared to a naïve Bayes model. A manufacturer can use this analysis to identify factors in its foundry that could reduce the probability of errors. Even under the best-case scenario, the probability of Type I error is 0.18 and the probability of Type II error is 0.30 for visual inspection. This indicates improvements to the inspection process for cast metal surfaces is required.


This article is published as Michelle M.Stallard (Voelker)Cameron A.MacKenzieFrank E.Peters. A probabilistic model to estimate visual inspection error for metalcastings given different training and judgment types, environmental and human factors, and percent of defects Author links open overlay panel. Journal of Manufacturing Systems, 2018 48(Part A); 97-106. DOI: 10.1016/j.jmsy.2018.07.002. Posted with permission.

Copyright Owner

The Society of Manufacturing Engineers



File Format


Published Version