Fixed point measurement, quality control

From a control standpoint, the most important variables are those which ultimately affect the end-use properties. These will be referred to as controlled variables affecting product quality. The most important of these are MW, MWD, monomer conversion, copolymer composition distribution, copolymer sequence distribution, and degree of branching. Most of these variables are not measurable on-line. The common approach is to control those variables which are measurable, to estimate those which are estimable and control based on the estimates, and to fix those which cannot be estimated by controlling the inputs to the process. Closed-loop control involves the adjustment of some manipulated variable(s) in response to a deviation of the associated control variable from its desired value. The purpose of closed-loop control is to bring the controlled variable to its desired value and maintain it at that point. Those variables which are not controllable in a closed-loop sense are maintained at their desired values (as measured by laboratory or other off-line measurement) by controlling all the identifiable input in order to maintain an unmeasured output at a constant value. 

It is evident that the distance between the inhouse and the specification limits is influenced by the quality of the calibration/measurement procedure a fixed relation, such as 2(j, 3(j, as has been proposed for control charts, might well be too optimistic or too pessimistic (for a single test result exactly on the 2(7 inhouse limit, the true value would have a = 16% chance of being outside the 3(7 SL). Note that it takes at least n - 6 (resp. n = 11) values to make a z = 2 (z = 3) scheme (see Figure 1.24) even theoretically possible. For n = 4, for instance, xmean would have to be > 1.5 a in order that the largest x could be beyond 3a run a series of simulations on program CONVERGE and concentrate on the first four data points to see that an OOS... 

---