Question

2-1- Based on Initial Observation values, calculate the mean and standard deviation of the data. (You need to show your calculation for standard deviation calculation). Then calculate the Cp and Cpk of the process based on provided USL and LSL in the article.

USL=105 mm

LSL=75 mm

97.04
100.22
97.07
96.32
89.63
94.29
96.01
99.88
96.08
92.4
94.76
97.02
95.51
96.63
95.69
94.01
99.75
96.07
97.11
96.24
96.94
99.98
97.94
97.75
94.44
97.72
96.4
97.55
96.17
98.09

Answer 1

	x	(x-xbar)^2
	97.04	0.30217
	100.22	13.91066
	97.07	0.336052
	96.32	0.029002
	89.63	47.06372
	94.29	4.84132
	96.01	0.230688
	99.88	11.49007
	96.08	0.168346
	92.4	16.73055
	94.76	2.993938
	97.02	0.280582
	95.51	0.960988
	96.63	0.019516
	95.69	0.64048
	94.01	6.151888
	99.75	10.62564
	96.07	0.176652
	97.11	0.384028
	96.24	0.06265
	96.94	0.20223
	99.98	12.17801
	97.94	2.10163
	97.75	1.586844
	94.44	4.20373
	97.72	1.512162
	96.4	0.008154
	97.55	1.122964
	96.17	0.102592
	98.09	2.55904
sum=	2894.71
mean=	96.49033

USL=105

LSL=75

To find std dev =

=

142.9763

=142.9763 / (30-1)

std dev =4.9302

Cp=(USL-LSL)/6*

=(105-75) / 6*4.9302

= 30 /29.5813

Cp=1.0141

Cpk=

=min((105-96.4903)/3*4.9302 , (96.4903-75)/3*4.9302)

=min(8.5097/14.7906 , 21.4903/4.9302)

=min( 0.5753, 4.3589)

Cpk =0.5753

Anwers:

Cp=1.0141

Cpk=0.5753