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12.1 Overview - Control charts

Rationale

Suppose you have multivariate data (e.g., abundances of multiple species) sampled repeatedly through time. For example, annual surveys at a site would yield multiple time-points: year 1, year 2, year 3, ..., year $t$, and so on. With each new time point, one might ask - is the community (multivariate observation) at time $t$ unusual (significantly different) from what has been observed prior to that time? By using the Control chart routine in PRIMER 8, we are able to discern if a new sample point is 'in-control' or 'out-of-control', by comparison with a reference set of previous ('in-control') observations.

This is clearly a very useful tool in an environmental monitoring context. The control chart tool can also be used in virtually any cases where we want to identify outliers in multivariate space. We may wish to do this in a Euclidean space, or in the space of some other resemblance measure, such as Bray-Curtis.

This chapter begins with a brief description of a classical univariate control chart, as used historically in statistical process control-type settings ( Shewhart (1931) , Shewhart (1939) , Montgomery (2020) ). We then move to consider a classical multivariate control chart, which relies on the assumption of multivariate normality for the in-control set of samples (the 'reference' set). Building on this, we outline a dissimilarity-based multivariate control chart method, described in Adegoke (2019) , which is further generalised and extended via its implementation in PRIMER 8. This approach improves on the earlier work of Anderson & Thompson (2004) , because it accommodates anisotropy (non-spherical shapes / correlation structure) in the reference (in-control) set of multivariate samples. We provide details of how to set control-chart limits using either a parametric or a non-parametric criterion.

Finally, we demonstrate the use of the control-chart tool in PRIMER 8 by way of an example, analysing $N$ = 38 years of data on the abundances of $p$ = 156 species of birds observed at Grand Forks, British Columbia, Canada, from the North American Breeding Bird Survey (BBS).

'Flavours' of control chart

The Control chart routine in PRIMER 8 offers three different types (or 'flavours') of control chart that can be built for a given dataset. These types depend on the scale and size of the reference set of 'in-control' samples that is desired by the end-user. More specifically, the reference set can be comprised of:

  • all samples taken prior to the test sample ('progressive' control chart);
  • a specified number of initial samples ('baseline' control chart); or
  • a specified number of samples taken immediately prior to the test sample ('moving window' control chart).

Essentially, a progressive control-chart will be good at highlighting when there is a sudden change (a 'jump') in the multivariate time series. However, one should beware of interpreting results in the time series (e.g., at times $(t+1)$, $(t+2)$, ...) once an 'out-of-control' point has been identified at time $t$.

A baseline control chart will be good at tracking variation through time away from an original set of (reference) samples, and can detect either a sudden jump, or (eventually) a more gradual change, e.g., if samples drift over time and move away from the original (reference) set.

In contrast, the moving window option is designed to accommodate a certain amount of 'drift', under the rationale that we may expect a certain amount of natural change over time. A new sample point is only compared to a subset of recent samples (inside a chosen time-frame/window), so the moving-window control chart will be sensitive to sudden changes, but overall random drift at a broad scale will not necessarily be detected as significant.

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