Bayesian control charts based on predictive distributions

Control charts are statistical process control (SPC) tools that are widely used in the monitoring of processes, specifically taking into account stability and dispersion. Control charts signal when a significant change in the process being studied is observed. This signal can then be investigated to identify issues and to find solutions. It is generally accepted that SPC are implemented in two phases, Phase I and Phase II. In Phase I the primary interest is assessing process stability, often trying to bring the process in control by locating and eliminating any assignable causes, estimating any unknown parameters and setting up the control charts. After that the process move on to Phase II where the control limits obtained in Phase I are used for online process monitoring based on new samples of data. This thesis concentrate mainly on implementing a Bayesian approach to monitoring processes using SPC. This is done by providing an overview of some non-informative priors and then to specifically derive the reference and probability-matching priors for the common coefficient of variation, standardized mean and tolerance limits for a normal population. Using the Bayesian approach described in this thesis SPC is performed, including derivations of control limits in Phase I and monitoring by the use of runlengths and average run-lengths in Phase II for the common coefficient of variation, standardized mean, variance and generalized variance, tolerance limits for normal populations, two-parameter exponential distribution, piecewise exponential model and capability indices. Results obtained using the Bayesian approach are compared to frequentist results.