Setting policy for on-line process control with dynamic characteristics

In this article, we investigate a control policy for the choice of sampling interval and control limit by minimizing the expected quality cost. The study is based on the environment in which (i) the stochastic disturbances are assumed to follow an IMA (1, 1) process, ( ii) there is process dynamics between the input series and the output series, (iii) a feedback control scheme is imposed, and (iv) the expected quality cost contains off-target cost, adjustment cost, and inspection cost. Modeling and forecasting for ( i), ( ii), and ( iii) are performed according to the transfer function plus noise model. Minimizing the expected quality cost for ( iv) is carried out by a modified pattern search procedure. An example is given to demonstrate the advantage of using the pattern search method over the usual 3-sigma control scheme. The penalty of ignoring the process dynamics and for the case of choosing incorrect value of theta of an IMA (1, 1) disturbance is discussed. The pattern search method is also compared favorably with the modified Taguchi's method in quality cost for the cases considered therein.