Question

Process Control at Polaroid (A)

1. Create and interpret SPC charts – Xbar and R charts for each work shift for finger height and pod weight. (provide step by step instructions on how you came up with the XBar, R, R bar, X double bar, UCL, and LCL)

Pod Weight (grams)
		Sample Number:
Day	Shift	1	2	3	4	5	6
3 August	A	2.800	2.799	2.760	2.802	2.805	2.803
	B	2.750	2.820	2.850	2.740	2.850	2.790
	C	2.768	2.807	2.807	2.804	2.804	2.803
4 August	A	2.841	2.802	2.802	2.806	2.807	2.807
	B	2.801	2.770	2.833	2.770	2.840	2.741
	C	2.778	2.807	2.804	2.804	2.803	2.804
5 August	A	2.760	2.804	2.804	2.806	2.805	2.806
	B	2.829	2.804	2.805	2.806	2.807	2.807
	C	2.741	2.850	2.744	2.766	2.767	2.808
6 August	A	2.814	2.804	2.803	2.805	2.807	2.804
	B	2.787	2.802	2.805	2.804	2.805	2.804
	C	2.766	2.805	2.804	2.802	2.804	2.806
7 August	A	2.774	2.801	2.805	2.805	2.805	2.804
	B	2.770	2.801	2.833	2.770	2.840	2.741
	C	2.832	2.836	2.794	2.843	2.813	2.743
10 August	A	2.829	2.846	2.760	2.854	2.817	2.805
	B	2.850	2.804	2.805	2.806	2.807	2.807
	C	2.803	2.803	2.773	2.837	2.808	2.808
11 August	A	2.815	2.804	2.803	2.804	2.803	2.802
	B	2.782	2.806	2.806	2.804	2.803	2.802
	C	2.779	2.807	2.808	2.803	2.803	2.803
12 August	A	2.815	2.815	2.803	2.864	2.834	2.803
	B	2.846	2.854	2.760	2.829	2.817	2.805
	C	2.767	2.804	2.834	2.803	2.803	2.803
13 August	A	2.850	2.804	2.804	2.804	2.804	2.804
	B	2.810	2.820	2.814	2.794	2.798	2.787
	C	2.850	2.820	2.750	2.740	2.850	2.790
14 August	A	2.750	2.765	2.850	2.760	2.790	2.840
	B	2.830	2.770	2.848	2.760	2.750	2.830
	C	2.740	2.770	2.833	2.770	2.840	2.800
17 August	A	2.753	2.807	2.805	2.804	2.802	2.804
	B	2.851	2.751	2.752	2.773	2.849	2.806
	C	2.845	2.804	2.803	2.806	2.805	2.806
18 August	A	2.844	2.777	2.754	2.791	2.833	2.811
	B	2.806	2.839	2.805	2.804	2.850	2.740
	C	2.849	2.801	2.804	2.762	2.814	2.791
19 August	A	2.820	2.793	2.812	2.833	2.853	2.812
	B	2.790	2.780	2.764	2.843	2.843	2.818
	C	2.850	2.806	2.805	2.814	2.807	2.807
20 August	A	2.767	2.831	2.808	2.793	2.836	2.811
	B	2.833	2.825	2.793	2.813	2.823	2.766
	C	2.824	2.799	2.790	2.764	2.817	2.805
21 August	A	2.778	2.775	2.799	2.805	2.833	2.772
	B	2.801	2.832	2.758	2.759	2.773	2.814
	C	2.770	2.787	2.744	2.766	2.807	2.803
Finger Height (mm)
		Sample Number:
Day	Shift	1	2	3	4	5	6
3 August	A	1.90	1.95	1.94	2.00	2.05	2.16
	B	2.15	2.17	2.11	2.13	2.02	2.03
	C	1.73	1.90	2.07	1.89	1.76	1.88
4 August	A	2.30	2.41	2.54	2.37	2.32	2.16
	B	2.28	2.16	2.19	2.08	2.25	2.24
	C	1.92	2.24	2.11	1.89	1.88	2.17
5 August	A	2.39	2.28	2.10	2.36	2.54	2.25
	B	2.11	2.21	2.24	2.21	2.17	2.24
	C	1.89	1.90	1.73	2.07	1.89	1.76
6 August	A	2.51	2.25	2.08	2.35	2.29	2.32
	B	2.22	2.19	2.22	2.24	2.01	2.23
	C	1.89	1.90	1.78	2.07	1.89	1.76
7 August	A	1.95	2.07	2.25	1.95	2.11	2.16
	B	2.08	2.03	2.27	2.23	2.24	2.13
	C	2.31	1.90	1.86	1.91	1.89	1.87
10 August	A	2.23	2.25	2.21	1.89	2.15	2.11
	B	2.23	2.21	2.05	2.19	2.07	2.16
	C	1.73	2.00	1.79	1.75	1.84	1.74
11 August	A	2.21	2.11	2.21	2.44	2.17	2.30
	B	2.17	2.19	2.15	2.04	2.07	2.22
	C	2.01	1.90	1.90	1.81	2.06	1.89
12 August	A	2.08	2.19	2.28	2.29	2.21	2.45
	B	1.93	2.09	1.90	1.95	2.04	2.09
	C	1.84	2.12	1.90	1.89	2.01	1.75
13 August	A	2.23	2.01	2.25	2.11	2.39	2.15
	B	2.19	2.22	2.18	2.15	2.23	2.04
	C	1.96	2.05	2.16	1.87	2.13	1.90
14 August	A	2.27	2.00	2.06	1.97	2.13	2.05
	B	1.92	1.78	1.76	1.77	1.78	1.87
	C	1.78	1.65	2.04	1.63	1.75	1.83
17 August	A	2.31	2.35	2.25	1.99	2.27	2.11
	B	2.02	1.97	1.81	1.73	1.77	1.82
	C	1.76	1.91	2.01	1.85	1.78	1.64
18 August	A	2.06	2.14	1.91	2.06	2.08	2.09
	B	1.76	1.83	1.79	1.79	1.77	1.94
	C	2.25	1.88	2.11	2.18	2.02	1.86
19 August	A	2.28	2.15	2.17	2.18	2.44	2.00
	B	2.31	2.27	2.16	2.10	2.24	2.28
	C	1.87	1.89	2.03	1.69	1.75	2.04
20 August	A	2.16	2.38	2.20	2.25	1.98	2.23
	B	2.06	2.08	2.14	2.24	2.26	2.18
	C	1.80	1.71	1.65	1.68	1.96	2.05
21 August	A	1.75	2.00	2.04	2.00	2.15	2.06
	B	1.90	1.90	1.81	1.86	1.98	1.81
	C	1.80	2.01	1.73	1.89	2.01	1.91

Answer 1

Pod weight:

Sample size (n) = 6
A2 = 0.483 (from table)
D3 = 0 (from table)
D4 = 2.004 (from table)

X-bar chart:

UCLx = X_double-bar + A2 * R-bar = 2.8025 + 0.483*0.064 = 2.8334
CLx = X_double-bar = 2.8025
LCLx = X_double-bar - A2 * R-bar = 2.8025 - 0.483*0.064 = 2.7716

Interpretation - the process is in statistical control.

R-chart:

UCLr = D4 * R-bar = 2.004*0.064 = 0.1283
CLr = R-bar = 0.064
LCLr = D3 * R-bar = 0*0.064 = 0.00

The process is in statistical control.

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Finger height:

Sample size (n) = 6
A2 = 0.483 (from table)
D3 = 0 (from table)
D4 = 2.004 (from table)

X-bar chart:

UCLx = X_double-bar + A2 * R-bar = 2.0487 + 0.483*0.2991 = 2.1932
CLx = X_double-bar = 2.0487
LCLx = X_double-bar - A2 * R-bar = 2.0487 - 0.483*0.2991 = 1.9043

The process is not in control.

R-chart:

UCLr = D4 * R-bar = 2.004*0.2991 = 0.5994
CLr = R-bar = 0.2991
LCLr = D3 * R-bar = 0*0.2991 = 0.00

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