Statistical process control and model monitoring.

This paper is concerned with model monitoring and quality control schemes, which are founded on a decision theoretic formulation. After identifying unacceptable weaknesses associated with Wald, sequential probability ratio test (SPRT) and Cuscore monitors, the Bayes decision monitor is developed. In particular, the paper focuses on what is termed a 'popular decision scheme' (PDS) for which the monitoring run loss functions are specified simply in terms of two indiff erence qualities. For most applications, the PDS results in forward cumulative sum tests of functions of the observations. For many exponential family applications, the PDS is equivalent to well-used SPRTs and Cusums. In particular, a neat interpretation of V-mask cusum chart settings is derived when simultaneously running two symmetric PDSs. However, apart from providing a decision theoretic basis for monitoring, sensible procedures occur in applications for which SPRTs and Cuscores are particularly unsatisfactory. Average run lengths (ARLs) are given for two special cases, and the inadequacy of the Wald and similar ARL approximations is revealed. Generalizations and applications to normal and dynamic linear models are discussed. The paper concludes by deriving conditions under which sequences of forward and backward sequential or Cusum chart tests are equivalent. [ABSTRACT FROM AUTHOR]