The control rules

Figure 19-6 Relationship of process performance on the Sigma scale to the performance characteristics of commonly used laboratory QC procedures. Probability for rejection is plotted on the y-axis versus size of systematic error on the x-axis and the Sigma scale on the x-axis.The control rules and number of control measurements are given in the key at the right, where the 8 lines, top to bottom, correspond with the curves on the graph, top to bottom.

The different control procedures discussed here have different performance capabilities, depending on the control rules and the number of control observations chosen. These choices should be related to the quality goals set by the laboratory. Many of the procedures in use today have not been... 

Notice that this equation has the form of a straight line Y= a + bX), where the y-intercept a) is TE and the slope (b) depends on the sensitivity of the QC procedure. The value for ASE ont is obtained from power curves for the control rules and ns of interest and for specified probabilities, such as 90% and 50%, A plot of bias eas versus s eas will describe the allowable limits of imprecision and inaccuracy for different control rules and different numbers of control measurements. A QC procedure can be selected by plotting the observed inaccuracy and imprecision as the method s operating point, then identifying the control rules and n s of the lines above the operating point... 

Obtain power function graphs for the control rules and n s of interest, or OPSpecs charts for the defined TE . Power function graphs and OPSpecs charts for commonly used QC procedures with n s of 2, 3, 4, and 6 are available in the scientific literature, in workbook format, and also from computer programs (EZ Rules and QC Validator 2,0, Westgard QC, Inc., Madison, Wis.— http //vmw.westgard.com). 

When a run is out of control, determine the type of error occurring based on the control rule that has been violated. Look for sources of that type of error. Correct the problem, then reanalyze the entire run including both control and patient samples. 

When the output is close to the set point, the change of error must be properly taken into account in order to ensure stability and speed of response. The goal of the fuzzy controller is to achieve a satisfactory dynamic performance with small sensitivity to parameter variations. The control rules are as follows ... 

Figure 16.21 shows the main blocks of the fuzzy system which is the main part of the fuzzy logic controller (Lee, 1990 Passino and Yurkovich, 1998). The fuzzification block converts the inputs or physical variables, for instance the error signal, e(t), into suitable fuzzy sets, as was shown in the example of Figure 16.20. fuzzy inference process combines membership functions with the control rules to derive the fuzzy output, for example, the fuzzy controller output, u(t). This process is also often called fuzzy reasoning. Finally, these outputs of the fuzzy computations are translated into terms of real values using the defuzzification block. 

The form of the control rules with respect to the lead times depends on the situation. We may have a situation in which the firm uses rules to propose a lead time for every order, but we can also have a situation in which there are rules to accept or to refuse an order for which a certain lead time is asked by the client. According to the control roles for the production planning, the accepted orders are scheduled on the bottle-neck machine(s). In this monograph we want to find good control roles for situations in which the characteristics on market demand and on the production facilities are given. In particular, we are interested in the performance of these control roles in rather complex situations, for instance with different sorts of clients and a conq>lex... 

The situation we will consider is that of a firm, possibly in the process industry, manufacturing a wide variety of products on a make-to-ordo basis. We are particularly interested in those production processes which have exactly one bottleneck, not only because this situation is quite common, but also because it is the situation that can be analysed best. In our models we will only consider the bottleneck process and exclude the other processes. In a practical situation there will be a lot of aspects that have some importance for the production. We will ignore many of these aspects, because they would complicate the problem considerably, without being an essential element for the control rules for production planning and for the lead times. 

The fuzzy set of the elasticity of revenues is scaled from 0 to 1.4, as the S-curve shows a range from a straight line to a very steep slope around the inflection point within these upper and lower bounds. The control rules for the aggregation are depicted in... 

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