Statistical Modelling for Process Control in the Sawmill Industry

In soft-wood sawmills in the western U.S., the green lumber end-product is the result of several distinct sawing operations: an initial breakdown of large diameter logs by a headrig yields boards that are subsequently resawn one or more times by secondary saws of various types. Vibration of the saws contributes to irregularities in thickness of the final green lumber. Misalignment of the saws produces green boards that are systematically wedge-shaped or tapered or otherwise deformed. The green lumber is dried, either naturally or in a kiln, and is then planed to standard dimensions for the market. The green lumber must be sawn thick enough to offset random and systematic irregularities in shape and to allow for shrinkage when it dries. Boards too thin to meet market standards for thickness must be resawn wastefully. Shrinkage of green lumber is well-understood. However, because both systematic errors and random errors in thickness accumulate through a sequence of resawing operations, it has not been clear how to separate out the performance of secondary sawing machines. In a pilot study, boards selected “at random” as they came off a headrig were followed through one of more resawings. Initially and at each subsequent stage of the processing, the thickness of each green board was measured at standardized points along each edge. Using the data, this paper develops and validates a physically-based statistical model for the accumulation of systematic and random errors in resawing operations. The model quantifies how thickness variability in a batch of lumber accumulates through a sequence of resawing operations and thereby enables estimation of how much each resawing operation contributes to thickness errors in the end-product. Implications for process control in sequential resawing operations are noted.