Variability monitoring of multistage manufacturing processes using regression adjustment methods

Figures & data

Fig. 1 A multistage process for motor reducers.

Fig. 2 A two-step maching process: (a) front view of the workpiece; (b) drilling of the hole; and (c) non-perpendicular nature of the hole.

Fig. 3 Layout of a general multistage process.

Fig. 4 The graph representation of regressor selection results.

Fig. 5 A three-stage process.

Fig. 6 (a) FAR for different values of κ; and (b) MDR for different values of κ.

Fig. 7 (a) FAR for different values of β; and (b) MDR for different values of β.

Table 1 Phase I analysis results under different values of κ β= 2)

κ		UCL	CL	LCL
20	1.8993	1.5985	1.1140	0.6294
10	1.8440	1.7290	1.2049	0.6808
7	1.7443	1.8175	1.2666	0.7156
5	1.6891	1.9224	1.3396	0.7569

Table 2 Phase I analysis results under different values of β (κ = 10)

β		UCL	CL	LCL
1	0.8991	1.5663	1.0915	0.6167
2	1.8440	1.7290	1.2049	0.6808
3	2.7174	1.9430	1.3540	0.7650
6	5.4660	3.0158	2.1016	1.1874

Fig. 8 A four-stage process.

Fig. 9 FAR for the two considered adjustments: (a) FAR plotted against σ _{U 01} ²/σ _{U 1} ²; (b) FAR against σ _{U 02} ²/σ _{U 2} ²; (c) FAR against σ _{U 03} ²/σ _{U 3} ²; and (d) FAR against σ _{U 04} ²/σ _{U 4} ².

Table 3 Phase I analysis results for the two adjustment methods

Method	1	2	3	4	UCL	CL	LCL
Subset adjustment	—	4.7500	—	—	2.6374	1.8379	1.0384
All adjustment	0.3144	3.3971	−0.0193	0.6426	2.3479	1.6362	0.9244

Fig. 10 MDR for the two adjustment methods.