Department of Mathematics

Proposed Project for the MSU Industrial Math Students

Universal Forest Products, Inc.

Quantification of Wood-based Variability Compared to Process-based Variability Project for the MSU Industrial Math Students


Manufacturing pressure treated lumber used in residential construction is a batch chemical process in which lumber is infused with an aqueous solution containing EPA registered pesticides, which protect the lumber from attack by termites and wood destroying insects. The “treated wood” product is an important building material. It is economical, easy to work with, sustainable and few realize that from an environmental perspective, it proves out as superior to other possible building materials using Life Cycle Analysis in almost every compassion. It is the wood itself that drives these attributes but, as a natural material, wood also brings a great deal of variability which expresses itself in our quality control. Improved understanding of this variability could lead to improved quality and efficiency.


Each batch (called a “charge”) of treated wood is tested using a statistical sampling of randomly selected pieces. These samples are tested to evaluate the depth of preservative penetration into the lumber and then composited to test the concentration of the preservative. This concentration test is called the “assay.” The test results are compared to a set of industry standards and a determination is made as to whether the charge passes or fails to meet the standard. There are two sources of variability which are of particular interest. The first is the variability of the charge itself called “within charge variability”. This can be quantified by taking repeated samples from the same charge. The second is the variability from one charge to the next called “process variability” or “between charge variability” which includes within charge variability.

Documents Given to Students:

Universal Forest Products has been on the forefront of studying assay variability in the wood preservation industry. We have a large amount of test data in addition to a very large amount of production data. The test data would be made available to the students via Excel; the production data via Access. A treating plant visit to our facility in Lansing would be arranged early in the event to give the students a better understanding of the process and how the data is generated.

Project Goals:

  • Quantify within charge variability.
  • Assess the distribution of individual samples and the minimum number of composited samples needed to apply normal statistics (central limit theorem).
  • Quantify the between charge variability.
  • Propose strategies for improving quality and/or efficiency based on improved understanding of assay variability.


For any additional questions regarding the program curriculum and/or the extension deadline for the application to the MSIM program, contact us at


Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science