Bayesian networks for statistical process control with attribute data

Abstract

Purpose Bayesian networks (BNs) are implemented for monitoring a process via statistical process control (SPC) where attribute data are available on output from the system. The paper aims to discuss this issue. Design/methodology/approach The BN provides a graphical and numerical tool to help a manager understand the effect of sample observations on the probability that the process is out-of-control and requires investigation. The parameters for the BN SPC model are statistically designed to minimize the out-of-control average run length (ARL) of the process at a specified in-control ARL and sample size. Findings The BN model outperforms adaptive np control charts in all experiments, except for some cases where only a large change in the proportion of sample defects is relevant. The BN is particularly useful when small sample sizes are available and when managers need to detect small changes in the proportion of defects produced by the process. Research limitations/implications The BN model is statistically designed and parameters are chosen to minimize out-of-control ARL. Future advancements will address the economic design of BNs for SPC with attribute data. Originality/value The BNs allow qualitative knowledge to be combined with sample data, and the average percentage of defects can be modeled as a continuous random variable. The framework of the BN easily permits classification of the system operation into two or more states, so diagnostic analysis can be performed simultaneously with statistical inference.

Designing acceptance single sampling plans: An optimization‐based approach under generalized beta distribution

“…The distribution function r D (D) of the number of defects in the lot is defined by Equation (13). It is supposed that p follows a generalized beta distribution p ∼ GB(p L , p U , 𝜇 X = 0.05, 𝜎 2 X = 0.00226), where the values 𝜇 X and 𝜎 2 X are derived from Equation (4) by choosing the Beta parameters a = 1 and b = 19.…”

“…8-10 Brush 11 and Sharma and Bhuttani 12 compared the risks of classical and Bayes producers and consumer, respectively. Recently, Cobb and Li, 13 among others, have suggested the use of Bayesian networks as an alternative to other approaches for Bayesian SPC with attributes, and Ouyang et al 14 proposed a Bayesian approach for online robust process design.…”

Worst Expected Best method for assessment of probabilistic network expected value at risk: application in supply chain risk management

“…A BBN model is a directed acyclic graph (DAG) comprising nodes (uncertain variables) where arcs indicate direct causal relationships between the connected nodes and the strength of interdependency between connected nodes is represented by conditional probability distributions (Cobb and Li, 2019). For a discrete BBN model, mutually exclusive discrete states are selected for individual variables, and network parameters representing the strength of interdependency between connected nodes can be evaluated using expert judgment.…”

On investigation of the Bayesian anomaly in multiple imprecise dependent information aggregation for system reliability evaluation

“…Cobb and Shenoy 14 proposed the piecewise linear (PL) approximation for nonlinear deterministic functions. Cobb and Li 15,16 further developed a Bayesian Network (BN) to monitor a production process where categorical attribute data are available. Lucas and coworkers 17,18 developed and generalized the theory of causal independence to allow a merging of continuous and discrete parameters.…”