Economical Quality Control Policies for a Single Cause System

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.

A power approximation model for the joint determination of X and R control chart parameters

Discusses the problem of the joint determination of the parameters for X and R control charts. A simple heuristic, called a power approximation, is presented. The power approximation is based on three regression equations which are used to estimate the sample size and the control limits for the X chart and the R chart. Thereafter, some developments and discussion about the proposed power approximation are presented and the method’s performance is tested and assessed using a set of problems previously studied in various scientific publications, and also using a specific set of data from a previously published study.

An optimal design of joint X‐ and S control charts using quadratic loss function

Cost models for the design of control charts based on Duncan’s approach have been studied in recent years. Presents a double assignable‐cause cost model, which is in terms of Taguchi’s loss imparted to society from the time a product is shipped, using renewal theory approach. The expression for the expected cycle length and the expected cost per cycle are easier to obtain by the proposed approach, and the cost model, including the customer’s voice, reveals the importance of quality. Sensitivity analysis performed on a large number of numerical examples illustrates that the cost of repair or replacement and customers’ tolerance, which are related to loss function, are critical when designing economically based on X‐ and S control charts.