Credible interval estimation for fraction nonconforming: Analytical and numerical solutions

This paper proposes a Bayesian statistics-based analytical solution and a Markov Chain Monte Carlo (MCMC) method-based numerical solution to estimate the credible interval for fraction nonconforming. Both solutions provide a more accurate, reliable, and interpretable estimation of sampling uncertainty and can be used to improve the functionality of automated, nonconforming quality management systems. To reveal how the inherent mathematical mechanism functions for an analytical solution, a step-by-step proof with a calculation example is provided. For the numerical solution, a specialized Metropolis-Hastings algorithm and an illustrative simulation example are provided to elaborate the stochastic processes of the method. An industrial case study, from a pipe fabrication company in Alberta, Canada, is presented to demonstrate the feasibility and applicability of the proposed credible interval estimation methods. Results of the case study indicate that both solutions can accurately and reliably serve the nonconforming quality inference purpose. This research can be implemented as a decision-making tool for credible interval estimation and will provide valuable support for understanding and improving quality performance of automated, nonconforming quality control processes.