Module iterative 

Iterative Phase I chart construction for SPM.

Repeatedly builds SPM charts and removes out-of-control observations until convergence, producing a cleaner in-control reference dataset. This addresses the common problem of Phase I data contamination where outliers distort the FPCA and control limits.

Convergence properties

The iterative Phase I procedure converges when no new outliers are removed between iterations. Convergence is guaranteed in at most n iterations (each iteration removes at least one outlier or terminates). In practice, 3–5 iterations suffice for typical contamination levels (5–15% outliers). Non-convergence (oscillation) can occur when the contamination fraction is near the breakdown point of the underlying T-squared / SPE statistics.

Breakdown point

The procedure’s breakdown point depends on the initial T-squared threshold. With alpha = 0.05 and chi-squared limits, the expected breakdown is roughly 50% for the T-squared statistic (Rousseeuw & Leroy, 1987, section 1.3, pp. 10–12). For contamination above the breakdown point, consider robust initialization via projection pursuit or minimum covariance determinant (MCD) before applying the iterative procedure.

References

• Sullivan, J.H. & Woodall, W.H. (1996). A comparison of multivariate control charts for individual observations. Journal of Quality Technology, 28(4), 398–408, section 3 (iterative Phase I procedure).
• Chenouri, S., Steiner, S.H. & Variyath, A.M. (2009). A multivariate robust control chart for individual observations. Journal of Quality Technology, 41(3), 259–271, section 2 (robust alternatives).
• Rousseeuw, P.J. & Leroy, A.M. (1987). Robust Regression and Outlier Detection. Wiley, section 1.3, pp. 10–12 (breakdown point), section 4.1, pp. 116–119 (iterative reweighting).

Structs

IterativePhase1Config

Configuration for iterative Phase I chart construction.

IterativePhase1Result

Result of iterative Phase I chart construction.

Functions

spm_phase1_iterative

Iteratively build a Phase I SPM chart by removing out-of-control observations.