Question

1. The data shown in Table 116.1 come from a production process with two observable quality characteristics: x1 and x2. The data are sample means of each quality characteristic, based on samples of size n = 25. Assume that mean values of the quality characteristics and the covariance matrix were computed from 50 preliminary samples: 200 1307 1 = 30s= 130 120 TABLE 11 E. 1 Data for Exercise 11.1 Sample Number 1 58 60 50 10 12 57 30 13 15 55 27 a) Construct a T 2 control chart using these data. Use the phase II limits.

Using minitab.

Answer 1

Solution :-

T 2 control chart for the given data with the explanation given below in details :

Sample Number	x1	x2	x1-mean	x2-mean	T2=(x1-mean,x2-mean)(S inverse)(x1-mean,x2-mean)
1	58	32	3	1.4666667	0.106528951
2	60	33	5	2.4666667	0.293758998
3	50	27	-5	-3.533333	0.169064163
4	54	31	-1	0.4666667	0.013571205
5	63	38	8	7.4666667	-0.023236307
6	53	30	-2	-0.533333	0.060895149
7	42	20	-13	-10.53333	0.631974961
8	55	31	0	0.4666667	-0.00398748
9	46	25	-9	-5.533333	0.738266041
10	50	29	-5	-1.533333	0.368688576
11	49	27	-6	-3.533333	0.35000313
12	57	30	2	-0.533333	0.063899844
13	58	33	3	2.4666667	0.03028482
14	75	45	20	14.466667	2.521082942
15	55	27	0	-3.533333	-0.228588419
Mean	55	30.53333			0.339480438
			S
			200	130
			130	120
			S inverse
			0.0169014	-0.01831
			-0.01831	0.028169

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