Economic Design of an AttributenpControl Chart Using a Variable Sample Size

Bayesian networks for statistical process control with attribute data

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 adaptivenpcontrol 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.