Bayesian process and profile monitoring

Linear profiles model many manufacturing process structures efficiently, but most profile-monitoring schemes assume that the explanatory variables and the process parameters are fixed, an assumption that changing technology and process conditions can violate by introducing parameter uncertainty and variability in the explanatory variables [1].

A related question is how the widely used CUSUM and EWMA charts behave when they are reconfigured within a Bayesian framework [2].

For linear profiles with a random explanatory variable, conjugate and non-conjugate priors are used to handle parametric uncertainty within double exponentially weighted moving average (DEWMA) charts, with separate univariate charts for the intercepts, slopes and error variances [1].

For count data, Bayesian CUSUM and EWMA charts are constructed from posterior and posterior predictive distributions obtained under three loss functions: squared error, precautionary and LINEX [2].

Bayesian DEWMA control charts for monitoring linear profiles when the explanatory variable is random [1].

Bayesian CUSUM and EWMA charts informed by posterior and posterior predictive distributions under different loss functions [2].

In average-run-length comparisons, the proposed Bayesian DEWMA charts detected out-of-control profiles earlier than competing charts, particularly for small shifts, and the charts based on conjugate priors were the quickest to signal [1].

Simulation studies examined sensitivity to the size of the out-of-control shift and to the choice of hyper-parameters, and the charts were also evaluated on real data [2].

Monitoring of manufacturing process structures, illustrated with a case study [1], and monitoring of processes that generate count data [2].