Nonparametric Confidence Limits of Quantile-Based Process Capability Indices

Table 2

Simulation results the performance of various 95% interval estimates of 𝐶_𝑁𝑝(𝑢,𝑣) based sample quantile and interpolated quantile using Weibull process.

Size		Asymptotic	Sample quantile		Interpolated quantile
(𝑛)	PCI Type	PCI Var.	MSE[𝐶𝑁𝑝(𝝃)]	var𝑛[𝐶𝑁𝑝(𝝃)]	MSE[𝐶𝑁𝑝(𝜻)]	var𝑛[𝐶𝑁𝑝(𝜻)]
50	𝐶𝑁𝑝(0,0)	2.78004𝑒−07	0.1224934	6.833435𝑒−06	0.1281274	0.0003281428
	𝐶𝑁𝑝(1,0)	4.04514𝑒−06	0.09835884	0.0001175441	0.0991082	0.0005820965
	𝐶𝑁𝑝(0,1)	9.06451𝑒−07	0.07808902	0.001147389	0.0874771	0.001795696
	𝐶𝑁𝑝(1,1)	7.43255𝑒−06	0.08175114	0.0001861944	0.0976206	0.0005729443
100	𝐶𝑁𝑝(0,0)	1.39002𝑒−07	0.04463229	6.763005𝑒−06	0.0518551	4.923725𝑒−05
	𝐶𝑁𝑝(1,0)	2.02257𝑒−06	0.03884461	2.997771𝑒−05	0.0470966	0.0001031592
	𝐶𝑁𝑝(0,1)	4.53225𝑒−07	0.03483475	0.0001387058	0.0438483	0.0002384231
	𝐶𝑁𝑝(1,1)	3.71628𝑒−06	0.03572435	1.961133𝑒−05	0.0426112	7.817404𝑒−05
200	𝐶𝑁𝑝(0,0)	6.95009𝑒−08	0.01623415	8.483628𝑒−06	0.0205617	8.252656e-06
	𝐶𝑁𝑝(1,0)	1.01129𝑒−06	0.01489944	1.519576𝑒−05	0.0197595	1.852167e-05
	𝐶𝑁𝑝(0,1)	2.26613𝑒−07	0.01422966	3.028482𝑒−05	0.0177817	3.590338e-05
	𝐶𝑁𝑝(1,1)	1.85814𝑒−06	0.01422652	9.677983𝑒−06	0.0192691	1.137201𝑒−05
400	𝐶𝑁𝑝(0,0)	9.26679𝑒−08	0.00598806	1.319295𝑒−05	0.0091714	2.284677𝑒−06
	𝐶𝑁𝑝(1,0)	1.34838𝑒−06	0.00586153	1.430459𝑒−05	0.0077462	4.224512𝑒−06
	𝐶𝑁𝑝(0,1)	3.02150𝑒−07	0.00552098	1.616761𝑒−05	0.0076277	7.120676𝑒−06
	𝐶𝑁𝑝(1,1)	2.47752𝑒−06	0.00560132	1.155253𝑒−05	0.0076023	2.451394𝑒−06
1000	𝐶𝑁𝑝(0,0)	6.95009𝑒−08	0.00264029	3.57955𝑒−06	0.0029580	1.819142𝑒−06
	𝐶𝑁𝑝(1,0)	1.01129𝑒−06	0.00256571	4.026816𝑒−06	0.0029113	2.016832𝑒−06
	𝐶𝑁𝑝(0,1)	2.26613𝑒−07	0.00258448	4.102949𝑒−06	0.0028118	2.470318𝑒−06
	𝐶𝑁𝑝(1,1)	1.85814𝑒−06	0.00244308	3.640072𝑒−06	0.0027096	1.711628𝑒−06