Question

	OBSERVATION
SAMPLE	1	2	3		5
1	1.20	1.42	1.05	1.06	1.40
2	1.81	1.76	1.46	1.23	1.88
3	1.28	1.17	1.15	1.76	1.92
4	1.11	1.43	1.41	1.06	1.41
5	1.79	1.66	1.18	1.21	1.67
6	1.54	1.34	1.84	1.34	1.49
7	1.02	1.54	1.47	1.94	1.09
8	1.20	1.86	1.05	1.64	1.82
9	1.22	1.52	1.98	1.74	1.83
10	1.06	1.61	1.06	1.52	1.72
11	1.06	2.00	1.41	1.59	1.40
12	1.80	1.85	1.77	1.27	1.08
13	1.87	1.08	1.70	1.59	1.52
14	1.21	1.29	1.80	1.15	1.11
15	1.96	1.58	1.64	1.79	1.92

Use the samples above to construct and determine the upper and lower limits the Bar-X and R-Charts.

Assume that the upper and lower tolerant limits of Pulley Engineering have been set at +/- 0.8 inches. Assess the process capability for Pulley.

A) Form the Correct construction of upper and lower limits for bar-R chart

B) Evaluate process capability using the information provided above.

Answer 1

Observation	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	X bar ( X⁻ )	Range R
1	1.2	1.42	1.05	1.06	1.4	1.226	0.37
2	1.81	1.76	1.46	1.23	1.88	1.628	0.65
3	1.28	1.17	1.15	1.76	1.92	1.456	0.77
4	1.11	1.43	1.41	1.06	1.41	1.284	0.37
5	1.79	1.66	1.18	1.21	1.67	1.502	0.61
6	1.54	1.34	1.84	1.34	1.49	1.51	0.5
7	1.02	1.54	1.47	1.94	1.09	1.412	0.92
8	1.2	1.86	1.05	1.64	1.82	1.514	0.81
9	1.22	1.52	1.98	1.74	1.83	1.658	0.61
10	1.06	1.61	1.06	1.52	1.72	1.394	0.66
11	1.06	2	1.41	1.59	1.4	1.492	0.94
12	1.8	1.85	1.77	1.27	1.08	1.554	0.77
13	1.87	1.08	1.7	1.59	1.52	1.552	0.79
14	1.21	1.29	1.8	1.15	1.11	1.312	0.69
15	1.96	1.58	1.64	1.79	1.92	1.778	0.32
						∑ X⁻ = 22.272	∑ R = 9.78

∑ X⁻ = 22.272 ,      ∑ R = 9.78

Grand mean = ∑ X⁻ / n

                       = 22.272 / 15

                       = 1.48

Range Mean R¯ = ∑ R / n

                              = 9.78 / 15

                              = 0.65

Control limits for Mean charts:

UCLx¯ = Grand mean + R¯ A₂

            = 1.48 + (0.65) ( 0.577)

= 1.85

Central Line CLx¯ = Grand mean = 1.48

LCLx¯ =  Grand mean - R¯ A₂

            = 1.48 - (0.65) ( 0.577)

= 1.10

Control Limits for Range charts:

UCL_R¯ = D₄R¯

= 2.114 (0.65)

= 1.37

Central Line =  R¯ = 0.65

LCL_R¯ = D₃R¯

= 0

Observation: No sample point is above UCL and below LCL .

Conclusion: The process is under control.