Anomaly Detection for Analysis of Annual Inventory Data: A Quality Control Approach

0 (assuming an unbiased model), as exploited thoroughly by Deming (1964). The remainder of this article is arranged as follows. First, we describe an annual forest inventory sample design and the construction of a control chart for this design. Next, we present an example of the use of the chart for consideration of the next measurement, and finally we give some recommendations for analysts of data arising from similar designs. An Annual Forest Inventory Design For illustrative purposes, we will use the US Forest Service’s FIA units’ temporally rotating, panelized forest inventory sampling design as an example. Here we give a brief explanation of the design, which is well documented in Reams et al. (2005). In this design, the sample plots are located in proximity to a systematic triangular grid consisting of g mutually exclusive interpenetrating panels. The panels are spatially balanced and contain an approximately equal number of sample plots. That is, if the total sample size is n, then each panel consists of approximately n/g plots. The sequence of panels is measured in order, with one panel measured each year, after which the panel measurement sequence reinitiates. Therefore, if panel 1 was measured in 2001, it will also be measured in 2001 g, 2001 2g, and so on. Panel 2 would then be measured in 2002, 2002 g, 2002 2g, etc. Scott et al. (2005) describe the estimation methods that FIA uses for within-panel estimates for this design. Patterson and Reams (2005) gives an introduction to methods of combining FIA panels for the establishment of time series. Since the initiation of the rotating panel design for FIA, there have been quite a few papers focusing on using trend models for the purpose of improving annual estimates, such as Van Deusen (1996, 1999), Roesch et al. (2003), Roesch (2007), Johnson et al. (2003), and Czaplewski and Thompson (2009). Without loss of generality, we will restrict this discussion to the case of five annual panels (g 5) sampling a defined area through time. One panel will be measured each year, and starting with year 6, 20% of the plots (i.e., one panel) will be remeasured each year. Roesch (2008) gives a useful explanation of this sample frame for the interested reader. Estimates of In-Control Variance Assume that a process that has not been determined to be out of control prior to time t is in control at time t. We can then estimate the in-control process variance using the g prior panels measured from time t g through time t 1: