Question

Q1. (b) Two operators have taken three measurements for each of 10 parts number during a gauge capability study as shown in Table 1.

(i)        Does the control chart analysis of the data indicate any potential problem in using the gauge?

  (ii)       Determine the standard deviation of the measurement error.                

Table 1

Part number	Operator 1 Measurements (mm)			Operator 2 Measurements (mm)
	1	2	3	1	2	3
1	50	49	50	50	48	51
2	52	52	51	51	51	51
3	53	50	50	54	52	51
4	49	51	50	48	50	51
5	48	49	48	48	49	48

Appendix A:

Table Q1[b]

Sample no.	x1	x2	x3	x4	x5	Xbar	R	Std. Dev.
1	-30	50	-20	10	30
2	0	50	-60	-20	30
3	-50	10	20	30	20
4	-10	-10	30	-20	50
5	20	-40	50	20	10
6	0	0	40	-40	20
7	0	0	20	-20	-10
8	70	-30	30	-10	0
9	0	0	20	-20	10
10	10	20	30	10	50

Answer 1

Answer:

Given that,

(b).

Two operators have taken three measurements for each of 10 parts number during a gauge capability study as shown in Table 1.

Part Number	Operator 1 Measurements/ Ukuran (mm)	Operator 2 Measurement Ukuran (mm)
1	2	3	1	2	3
1	50	49	50	50	48	51
2	52	52	51	51	51	51
3	53	50	50	54	52	51
4	49	51	50	48	50	51
548	48	49	48	48	49	48

(i).   

Does the control chart analysis of the data indicate any potential problem in using the gauge:

Part Number	Operator 1 Measurements/ Ukuran (mm)	Average1	Operator 2 Measurement Ukuran (mm)	Average-2
1	2	3	1	2	3
1	50	49	50	(50+49+50)/3=49.667	50	48	51	(50+48+51)=49.667
2	52	52	51	(52+52+51)/3=51.667	51	51	51	(51+51+51)/3=51
3	53	50	50	(53+50+50)/3=51	54	52	51	(54+52+51)/3=52.33
4	49	51	50	(49+51+50)/3=50	48	50	51	(48+50+51)/3=49.667
5	48	49	48	(48+49+48)/3=48.334	48	49	48	(48+49+48)/3=48.33

(ii).

Determine the standard deviation of the measurement error:

Part No.	Average 1	Average 2	Absolute Standard deviation of measurement error
1	49.667	49.667	0
2	51.667	51	0.667
3	51	51	0
4	50	51	1
5	48.334	48.334	0

Measurement of the part (2) and part (4) derivate by 0.667 and 1 mm tolerance respectively when parts were measured by a different- different operators.