Nomenclature
 ,  , c, d, ϑ,  |
Constants or correction terms |
 |
Correlation matrix for variable set z0 |
χ2,  |
Cumulative chi-squared distribution function and critical value for significance α |
 |
Projection matrix,  (PCA model) |
| δij | Kronecker delta, δij = 1 for i = j and 0 for i ≠ j |
| e, f, E, F | Residual vectors and matrices for input and output variables (PLS/MRPLS model) |
 ,  |
Error vector for input and variables (PLS/MRPLS model) |
| f( · ), F( · ) | Probability density and cumulative distribution function |
 ,  |
Cumulative distribution and critical value of an F distribution with m1 and m2 degrees of freedom and a significance α |
| g, G | Residual vector and matrix (PCA model) |
 |
Error vector for process variables (PCA model) |
| Γ(m) | Gamma function, m > 0 |
| H0,H1 | Null and alternative hypothesis |
| i, j | Variable indices, e.g. zi or xj |
| k, l | Sampling indices, e.g. z(k) is the kth sample of z |
 |
Index set |
K,  and  |
Number of reference samples, application delay for adapted MSPC models and length of moving window |
| Λ, λi | Diagonal matrix of eigenvalues, ith eigenvalue |
| n | Number of retained pairs of latent variables (PCA and PLS/MRPLS models) |
| nx, ny and nz | Number of input and output variables (PLS/MRPLS model), and number of process variables (PCA model) |
 |
Cumulative Gaussian distribution function of mean  and covariance matrix Szz |
| Ω, ω | General projection matrix and vector |
| p, P | Loading vector and matrix for process variables (PCA model) and input variable sets (PLS/MRPLS model) |
q,  , Q,  |
Weight and loading vectors and matrices for output variables (PLS/MRPLS model) |
| Q, Qα | Residual Q statistic and its control limit for significance α |
| rij | Correlation coefficient between ith and jth variable |
| r, w, R, W | Loading vectors and matrices for input variables (PLS/MRPLS model) |
| σ, Σ | Standard deviation and diagonal matrix storing standard deviations |
 |
Covariance matrix of source variables and its eigendecomposition |
| t, T | Score vector and matrix for data vector of PCA model and input vector of PLS/MRPLS model |
T2,  |
Hotelling's T2 statistic and control limit for significance α |
| u, U | Score vector and matrix for output vector (PLS model) |
 |
Fault subspace |
w,  , W |
Weight vectors and matrix for input variables (PLS/MRPLS model) |
| x, X | Input vector and matrix (PLS/MRPLS model) |
Ξ and ( ,  ) |
Parameter matrices (PCA and PLS/MRPLS models) |
| y, Y | Output vector and matrix (PLS/MRPLS model) |
| z, Z | Data vector and matrix (PCA model) |
 |
Parameter vector determining confidence interval for covariance matrix (Chapter 7) |
| Metric conversions | |
| 1lb/s | 0.453 kb/s |
| 1scf/s | 0.0283m3/s |
| 1psi/psia | 6894.75732Pa |
| Degrees in K | (80 × degrees in F − 32)/1.8 + 273.15 |
| 1 ICFM | 1.699 m3/h |
| degrees in C | (80 × degrees in F − 32)/1.8 |
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