PART 1: Control Charts Bobcat Manufacturing Company prides itself on the quality
ID: 389788 • Letter: P
Question
PART 1: Control Charts
Bobcat Manufacturing Company prides itself on the quality of its products. The company is engaged in competition for a very important project. A key element is a part that ultimately goes into precision testing equipment. Management is concerned that there may be an assignable cause of variation in the process. The following data were collected over the course of one shift. Use the “R and X-bar Charts” solver in OM Explorer [Note: make sure to adjust sample size before data copy/paste].
Observations (millimeters)
Sample
1
2
3
4
5
6
7
8
1
9.1
8.9
8.8
9.2
8.1
6.9
9.3
9.1
2
7.6
8
9
10.1
7.9
9
8
8.8
3
8.2
9.1
8.2
8.7
9
7
8.8
10.8
4
8.2
8.3
7.9
7.5
8.9
7.8
10.1
7.7
5
10
8.1
8.9
9
9.3
9
8.7
10
What are the upper and lower limits for the R-chart (UCL & LCL)? Is the R-chart in control?
What are the upper and lower limits for the X-bar chart (UCL & LCL)? Is the X-bar chart in control?
Should Bobcat Manufacturing continue operations with the current process?
Observations (millimeters)
Sample
1
2
3
4
5
6
7
8
1
9.1
8.9
8.8
9.2
8.1
6.9
9.3
9.1
2
7.6
8
9
10.1
7.9
9
8
8.8
3
8.2
9.1
8.2
8.7
9
7
8.8
10.8
4
8.2
8.3
7.9
7.5
8.9
7.8
10.1
7.7
5
10
8.1
8.9
9
9.3
9
8.7
10
Explanation / Answer
Please refer below table which calculates mean ( Xbar) and Range for each of the 5 samples
Sample
1
2
3
4
5
6
7
8
Xbar
Range
1
9.1
8.9
8.8
9.2
8.1
6.9
9.3
9.1
8.68
2.4
2
7.6
8
9
10.1
7.9
9
8
8.8
8.55
2.5
3
8.2
9.1
8.2
8.7
9
7
8.8
10.8
8.73
3.8
4
8.2
8.3
7.9
7.5
8.9
7.8
10.1
7.7
8.30
2.6
5
10
8.1
8.9
9
9.3
9
8.7
10
9.13
1.9
Average=
8.68
2.64
It is to be noted :
Xbar for a sample = sum of 8 sets of data/ 8
Range for sample = Highest value – Smallest value
Thus,
Xbar-bar = Average of Xbar values = Sum of Xbar values / 5 = 8.68
Rbar = Average of Range values = sum of Range values / 5 =2.64
Sample size = n = 8
Following are the relevant values of constants for n = 8 as derived from standard table for Xbar and Range values :
A2 = 0.373
D4 = 1.864
D3= 0.136
Xbar chart :
Upper control Limit ( UCLx ) = Xbar + A2 x Rbar = 8.68 + 0.373 x 2.64 = 8.68 + 0.984 = 9.664
Lower Control Limit ( LCLx) = Xbar – A2 x Rbar = 8.68 – 0.373 x 2.64 = 8.68 – 0.984 = 7.696
Range chart :
Upper control Limit ( UCLr) = D4.rbar = 1.864 x 2.64 = 4.92
Lower control Limit ( LCLr ) = D3.rbar = 0.136 x 2.64 = 0.359
It is to be noted that :
All calculated values of xbar ( for 5 samples ) are within control limit 7.696 - 9.664
All calculated values of rbar ( for 5 samples ) are within control limits 0.359 – 4.92
Therefore, process is fully in control and therefore Bobcat manufacturing continue operation with current process.
Sample
1
2
3
4
5
6
7
8
Xbar
Range
1
9.1
8.9
8.8
9.2
8.1
6.9
9.3
9.1
8.68
2.4
2
7.6
8
9
10.1
7.9
9
8
8.8
8.55
2.5
3
8.2
9.1
8.2
8.7
9
7
8.8
10.8
8.73
3.8
4
8.2
8.3
7.9
7.5
8.9
7.8
10.1
7.7
8.30
2.6
5
10
8.1
8.9
9
9.3
9
8.7
10
9.13
1.9
Average=
8.68
2.64
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