threshold | R Documentation |

Calculate the non-parametric critical value threshold estimates for the SPE and T2 monitoring test statistics.

```
threshold(pca_object, alpha = 0.001, ...)
```

`pca_object` |
A list with class "pca" from the internal pca() function |

`alpha` |
The upper 1 - alpha quantile of the SPE and T2 densities from the training data passed to this function. Defaults to 0.001. |

`...` |
Lazy dots for additional internal arguments |

This function takes in a pca object returned by the pca() function and a threshold level defaulting to alpha = 0.1 percent of the observations. This critical quantile is set this low to reduce false alarms, as described in Kazor et al (2016). The function then returns a calculated SPE threshold corresponding to the 1 - alpha critical value, a similar T2 threshold, and the projection and Lambda Inverse (1 / eigenvalues) matrices passed through from the pca() function call.

This internal function is called by faultFilter().

A list with classes "threshold" and "pca" containing:

- SPE_threshold –
the 1 - alpha quantile of the estimated SPE density

- T2_threshold –
the 1 - alpha quantile of the estimated Hotelling's T2 density

- projectionMatrix –
a projection matrix from the data feature space to the feature subspace which preserves some pre-specified proportion of the energy of the data scatter matrix. This pre-specified energy proportion is user supplied as the var.amnt argument in the pca() function. See the pca() function's help file for more details.

- LambdaInv –
a diagonal matrix of the reciprocal eigenvalues of the data scatter matrix

- T2 –
the vector of Hotelling's T2 test statistic values for each of the n observations in "data"

- SPE –
the vector of SPE test statistic values for each of the n observations in "data"

Called by: `faultFilter`

. This function uses a port of
the `quantile.density()`

function from the now-orphaned BMS package.

```
nrml <- mspProcessData(faults = "NOC")
scaledData <- scale(nrml[,-1])
pca_obj <- pca(scaledData)
threshold(pca_object = pca_obj)
```

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