A conjugate Bayesian approach to control chart for multi-batch and low volume production

Control chart could effectively reflect whether a manufacturing process is currently under control or not. The calculation of control limits of the control chart has been focusing on traditional frequency approach, which requires a large sample size for an accurate estimation. A conjugate Bayesian approach is introduced to correct the calculation error of control limits with traditional frequency approach in multi-batch and low volume production. Bartlett’s test, analysis of variance test and standardisation treatment are used to construct a proper prior distribution in order to calculate the Bayes estimators of process distribution parameters for the control limits. The case study indicates that this conjugate Bayesian approach presents better performance than the traditional frequency approach when the sample size is small.