Computationally efficient Bayesian sequential function monitoring

In functional sequential process monitoring, a process is characterized by sequences of observations called profiles which are monitored over time for stability. The goal is to halt a process when the process generating these observations deviates from a specified in control standard. We propose a Bayesian sequential process control (SPC) methodology which uses wavelets to monitor the functional responses and detect out of control profiles. Our contribution is to propose a solution to the growing computational cost by constructing an efficient and accurate approximation to the posterior distribution of the wavelet coefficients, without recourse to Markov chain Monte Carlo.