Diagnostic analysis of board foot per ton of chips ratio for a small sawmill

The board foot to ton of chips (BFTC) ratio is a common lumber quality index used by small sawmills to gauge sawing efficiency. Producing too many chips, relative to board footage at any given time, is considered inefficient since a unit conversion into lumber is clearly more valuable than a unit conversion into ton of chips. Sawyers and managers thus assume normality and independence of the BFTC ratio when they attempt to identify outlying performance. The objectives of this study were to determine: a) the distributional properties of BFTC ratio; b) if a negative auto correlation exists between board footage and ton of chips; c) the appropriate diagnostics for BFTC ratio to determine abnormal deviation from mean process performance; and d) if differences in BFTC models between species exist. The results of this study demonstrate a skewed distribution. Also, the independence assumption was violated as a result of auto correlation between consecutive months. A residual plot versus time series chart from an auto regression model provided a better estimate of outlier boundaries, which was needed to detect process errors or changes. All processes appeared to follow a linear auto correlation model instead of the traditional least squares regression. Absence of significant auto regression for poplar was an indication of a process change at 18 months, which masked the ability to detect the auto regressive correlation. Identification of the process change and the creation of two models for poplar confirmed the auto regressive nature for all three species.

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