An Improvement of the Hotelling 𝑇^𝟐 Statistic in Monitoring Multivariate Quality Characteristics

Table 1

The simulated UCLs for all of the 𝑇² statistics.

p	m	Empirical upper control limit (UCL)
		Empr			Med-Mad
		𝑇^2	𝑇^2mve	𝑇^2mcd	𝑇^2	𝑇^2mve	𝑇^2mcd
2	30	10.561	24.351	58.812	5.501	6.080	8.796
	50	12.302	21.042	34.615	5.666	6.289	7.967
	100	14.124	20.478	24.441	5.680	6.314	7.145
3	30	12.202	29.028	108.530	7.995	8.606	13.204
	50	13.976	25.145	50.430	8.266	8.883	11.985
	100	16.503	23.011	30.371	8.278	8.967	10.425
5	30	14.950	49.371	319.625	11.969	12.780	20.501
	50	17.581	33.792	111.725	12.482	13.160	19.823
	100	20.054	28.448	41.639	12.639	13.366	16.142
10	30	20.033	80.693	1555.711	19.541	19.812	25.827
	50	24.250	63.427	393.625	20.894	21.852	33.893
	100	27.964	44.287	84.655	21.470	22.287	29.604