Mixture Design

The following is an excerpt on DOE designed experiment techniques from Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller.

Formulations, blends, combinations, compounds, amalgams, and recipes are designs in which the factor levels in each run either all sum to a fixed quantity (volume, charge, load) or are restricted to a range of quantities.

Mixture designs differ from ordinary fractional factorial designs because the levels for the factors in a run cannot be chosen independently of one another. Each factor level must be measurable in some common unit of measure; the common measure need not be the units of measure of the experimental factors. The common unit may be cubic feet, with factor measures in gallons, pounds, and cubic inches. A factor level may have a minimum or maximum; in addition, the sum of all the factor levels in a run may be specified to not fall below some minimum or exceed some maximum quantity. Standardized designs are based on a non-dimensional unit, which may have upper and lower bounds on the sum of all factor levels in a run or which may have upper or lower bounds on the levels for each factor.

Mixture designs are usually special forms of response surface designs except for screening designs which have no center or other interior points. Mixture designs are usually constructed to estimate linear interactions only; that is, they estimate interactions such as ab or abc but cannot estimate ab2 , a2b2 or higher interaction forms.

Learn more about the DOE tools for designed experiments in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Intro. to DOE short course (only $99) or online Advanced Topics in DOE short course (only $139), or his online Black Belt certification training course ($875).