Nonparametric Confidence Limits of Quantile-Based Process Capability Indices

Table 1

Point estimates and 95% asymptotic lower confidence limits of various 𝐶_𝑁𝑝(𝑢,𝑣).

	Sample quantile 𝝃			Interpolation-based qauntile 𝜻
Process	PCI Type	LCL	𝐶𝑁𝑝(𝝃)	s.e.	LCL	𝐶𝑁𝑝(𝜻)	s.e.
	𝐶𝑁𝑝(0,0)	0.911466	0.960000	0.02476212	0.918986	0.967761	0.02488492
Before	𝐶𝑁𝑝(1,0)	0.846163	0.920000	0.03767177	0.849286	0.927437	0.03987269
Adjust.	𝐶𝑁𝑝(0,1)	0.902110	0.953162	0.02604660	0.907308	0.960756	0.02726949
	𝐶𝑁𝑝(1,1)	0.824969	0.913447	0.04514164	0.827334	0.920725	0.04764796
	𝐶𝑁𝑝(0,0)	1.104678	1.142857	0.01947940	1.056493	1.142857	0.04406315
After	𝐶𝑁𝑝(1,0)	1.038113	1.095238	0.02914537	0.997961	1.095238	0.04963102
Adjust.	𝐶𝑁𝑝(0,1)	1.088776	1.131371	0.02173196	1.043063	1.131371	0.04505517
	𝐶𝑁𝑝(1,1)	1.011710	1.084230	0.03700042	0.977467	1.084230	0.05447085