threshold: Non-parametric Threshold Estimation

In mvMonitoring: Multi-State Adaptive Dynamic Principal Component Analysis for Multivariate Process Monitoring

Non-parametric Threshold Estimation

Description

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

Usage

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

Arguments

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

Details

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().

Value

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"

See Also

Called by: faultFilter. This function uses a port of the quantile.density() function from the now-orphaned BMS package.

Examples

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

mvMonitoring documentation built on Nov. 22, 2023, 1:09 a.m.