Bayesian Quality Economics

In both the manufacturing process and testing of software entities, the issue of quality control is essentially an issue of information. The problem is to decide whether to accept or reject a unit (or a test result), given imperfect signals regarding quality. Traditional human inspections will break down because humans have limits (low precision accounted for, fatigue, and the capacity to create false positives (accept a defective unit) and false negatives (reject a good unit)). Organizations can reframe quality control using Bayesian decision theory and use AI systems capable of tracking millions of signals in a way that allows organizations to optimize thresholds and greatly improve yield.

This is the essence of Bayesian Quality Economics: viewing inspection as probabilistic inference to deliver optimal utility, as opposed to a simple human selection.

Bayesian Decision Theory and Threshold Selection

Bayesian decision theory is about a systematic way to update beliefs about the quality of a product using a flow of new incoming signals. The model produces a posterior probability that the unit is defective (given some observed evidence) and then makes the decision about specification levels; accept or reject if the posterior probability is beyond this level of criticality, otherwise the assumed specification is accept. Selecting that same level of inspection threshold is dependent upon the economic consequences of false positives - rejecting salvageable units - and/or false negatives, where salvageable units are shipped which lead to warranty claims, recalls, and possible reputational significance.

The thresholding process can be dynamic through fitted AI based solutions in quality systems. In the case of auto electronics for instance, where the consequence of failure in the field can be excessively high, the threshold levels for acceptance would be more conservative. In the consumables space, thresholds could be assigned with a bias to throughput.

ROC Curves and Economic Trade-offs

A Receiver Operating Characteristic (ROC) curve is a commonly used statistical visualization to show the trade-offs of sensitivity and specificity. Economic decisions can be made at each point along the ROC because the rationale is precisely the trade-offs of false rejects vs. false accepts when each were rejected and accepts were made. If AI can be used to move the operational point closer to the Pareto frontier of inspection accuracy, then firms will maximize expected profit by reducing losses to waste.

Real-world evidence is telling. McKinsey reported that AI-enabled visual inspection in the electronics industry can reduce defects that escape by 90 percent (compared to human inspectors), and also reduce their false rejects by over 50 percent. The benefits are simplicity itself when you consider that yields go up while re-work costs go down.

Sequential Test and Active Learning

Sequential testing is another advantage Bayesian testing brings to the table; inspection does not need to be a single-shot event. If a model from an AI model is uncertain, the system can automatically escalate to use higher resolution imaging, other sensors, or human review. Over time, models will learn from these borderline cases, hence improving predictive accuracy.

In software testing, this is relevant because tools like testRigor use machine learning to identify the code that is most likely to have defects. By dynamically allocating inspection resources, companies can have better coverage and at less cost.

Realtime Feedback and Closed Loop Control

AI-based quality inspection does not simply classify; it also supplies real-time feedback loops to upstream processes. For example, when defect probabilities increase, the system can signal when to make changes (i.e., when to recalibrate a machine, to change a temperature setpoint, or stop with a supplier batch). Quality control becomes prospective process optimization rather than just reactive appraisal and appraisal.

Ultimately, this reduces the variance of quality outputs from an economic perspective, which is beneficial further downstream. In particular, companies can reduce buffer inventories, reduce the cash conversion cycle, and open avenues for "kanban" or just-in-time methodologies with less apprehension of breakdowns in quality.

Economic drivers of adoption

There are several economic forces at play that help explain the rise of Bayesian quality economics:

• Cheap sensors and compute — Amazon and high-resolution cameras combined with cheap GPUs have unlocked a host of affordable AI inspection options.
• Labor market dimensions — Quality control is a low skilled, high-turnover, labor replacement job — it wholly exists due the labor shortage.
• Global competition — Many companies are trying to improve yield as efficiency in manufacturing is increasingly important due to thin margins for products. The global market for AI in manufacturing quality control was $1.1 billion in 2023 and is growing at over 40% CAGR to 2030 according to PwC.

Consequences

The shift to Bayesian AI inspection has a few consequences:

• Displacement of human quality control labor, but creation of high-skill jobs in data science and process engineering
• An altered global value chain, as high-labor cost countries gain a comparative advantage by incorporating automation technology
• Data based competitive differentiation, as firms with a larger defect data set have more opportunities to build better models and capture competitive rents.

Conclusion

Bayesian Quality Economics changes the framing of inspection from a bottleneck inspection process to an information optimization problem, which illustrates how AI is converting inspection into an enhancing value process. Using better thresholds, real-time feedback, and sequential learning, the defective product will decrease along with the overall process productivity increasing.

For undergraduate students learning economics, this illustrates how decision theory, probability, and industrial organization converge in practice. For the firm that uses a platform such as testRigor or AI-vision inspection, this not only represents cost decreases but a whole new potential for competitive advantage.