ADXMAMD: Construct McLean-Anderson Mixture Designs

Macros for the Design and Analysis of Experiments

ADXMAMD: Construct McLean-Anderson Mixture Designs

%adxmamd(ds, vlst)

where

ds is the name of the SAS data set to contain the constructed design. This data set contains variables for design factors. Default names are used. The default names for design factors are T1, T2, T3, and so on.

vlst is a list of mixture components and their constraints. Separate information for different components with a slash (/) and specify each component as follows:
name loval-hival
where name gives the name of the component, loval gives the low value for the component, and hival gives the high value for the component. If you omit loval or hival, the defaults are 0 and 1, respectively.

Use the ADXMAMD macro when your mixture factors are subject to constraints of the form

${low-value} & \leq & {component} & \leq & {high-value}$

In this situation, you cannot study a response over the entire mixture region, so you cannot use the ADXSCD or ADXSLD macros. You can use the ADXMAMD or the ADXXVERT macros. The ADXMAMD macro constructs a design composed of vertices of the feasible region, as described by McLean and Anderson (1966). If you do not specify any constraints, the McLean-Anderson design is the same as a simplex-lattice design of order 1.

For example, consider an experiment to study the effects of a lubricant additive on three-component lubricant blends. The additive and the three components are subject to restrictions as follows:

Mixture Component Range of Values

Additive (ADD) 7% to 18%

Component A (A) 0% to 30%

Component B (B) 37% to 70%

Component C (C) 0% to 15%

To construct the McLean-Anderson design and output it to the data set LUB, submit the following statements:

   %adxgen
   %adxmix
   %adxinit
   %adxmamd(lub,add .07-.18 /a -.3 /b .37-.7 /c -.15)

In the statements above, the low values for lubricant components A and C are omitted; since these low values are 0, you can use the defaults.

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ds	is the name of the SAS data set to contain the constructed design. This data set contains variables for design factors. Default names are used. The default names for design factors are T1, T2, T3, and so on.
vlst	is a list of mixture components and their constraints. Separate information for different components with a slash (/) and specify each component as follows: name loval-hival where name gives the name of the component, loval gives the low value for the component, and hival gives the high value for the component. If you omit loval or hival, the defaults are 0 and 1, respectively.

Mixture Component	Range of Values
Additive (ADD)	7% to 18%
Component A (A)	0% to 30%
Component B (B)	37% to 70%
Component C (C)	0% to 15%