Question: Samples consisting of 4 parts each have been taken from a machining pr
ID: 378130 • Letter: Q
Question
Question: Samples consisting of 4 parts each have been taken from a machining process. The length of each part was measured in mm using a calibrated measuring device. The following data were obtained.
Time
Part 1 (Length, MM)
Part 2 (Length ,MM)
Part 3 (Length ,mm)
Part 3 (Length, MM)
8:00
20.10
19.97
20.03
20.05
9:00
20.00
20.11
19.98
20.09
10:00
20.10
20.06
19.99
20.03
11:00
19.94
20.09
20.02
20.01
12:00
20.08
20.08
20.00
20.12
13:00
20.06
20.10
19.95
20.05
14:00
20.11
20.03
20.09
20.00
15:00
20.06
20.09
20.08
20.00
16:05
19.88
19.94
20.02
19.96
17:00
20.03
20.01
19.98
19.92
18:00
19.88
20.01
19.98
19.96
19:00
19.87
19.97
19.96
19.99
20:00
20.01
19.97
19.96
19.89
21:00
19.92
20.01
19.97
19.97
22:00
19.96
20.00
19.90
19.90
23:00
20.05
20.02
19.96
20.00
Construct X-bar and Range charts for the process. Is the process in control? Discuss.
Time
Part 1 (Length, MM)
Part 2 (Length ,MM)
Part 3 (Length ,mm)
Part 3 (Length, MM)
8:00
20.10
19.97
20.03
20.05
9:00
20.00
20.11
19.98
20.09
10:00
20.10
20.06
19.99
20.03
11:00
19.94
20.09
20.02
20.01
12:00
20.08
20.08
20.00
20.12
13:00
20.06
20.10
19.95
20.05
14:00
20.11
20.03
20.09
20.00
15:00
20.06
20.09
20.08
20.00
16:05
19.88
19.94
20.02
19.96
17:00
20.03
20.01
19.98
19.92
18:00
19.88
20.01
19.98
19.96
19:00
19.87
19.97
19.96
19.99
20:00
20.01
19.97
19.96
19.89
21:00
19.92
20.01
19.97
19.97
22:00
19.96
20.00
19.90
19.90
23:00
20.05
20.02
19.96
20.00
Explanation / Answer
Please find the table below which includes Xbar ( men) and Range for each data set.
Following to be noted :
Xbar = ( Part 1 length + Part 2 length + Part 3 length + Part 4 length )/4
Range =( Maximum value – Minimum value ) of lengths of 4 parts
Accordingly ,
Sum of Xbar ( mean) = 320.08
Hence, Xbar-bar ( mean of means ) = 320.08 / 16 = 20.005
Rbar = Mean of range values = 1.83/16 = 0.114
Time
Part 1 ( mm)
Part 2 ( mm)
Part 3 (mm)
Part 4 ( mm)
Xbar
Range
08:00
20.1
19.97
20.03
20.05
20.04
0.13
09:00
20
20.11
19.98
20.09
20.05
0.13
10:00
20.1
20.06
19.99
20.03
20.05
0.11
11:00
19.94
20.09
20.02
20.01
20.02
0.15
12:00
20.08
20.08
20
20.12
20.07
0.12
13:00
20.06
20.1
19.95
20.05
20.04
0.15
14:00
20.11
20.03
20.09
20
20.06
0.11
15:00
20.06
20.09
20.08
20
20.06
0.09
16:00
19.88
19.94
20.02
19.96
19.95
0.14
17:00
20.03
20.01
19.98
19.92
19.99
0.11
18:00
19.88
20.01
19.98
19.96
19.96
0.13
19:00
19.87
19.97
19.96
19.99
19.95
0.12
20:00
20.01
19.97
19.96
19.89
19.96
0.12
21:00
19.92
20.01
19.97
19.97
19.97
0.09
22:00
19.96
20
19.9
19.9
19.94
0.04
23:00
20.05
20.02
19.96
20
20.01
0.09
SUM =
320.08
1.83
Given,
Sample size = n = 4,
The relevant values of constants as derived from standard table for Xbar and Range chart as follows :
A2 = 0.729
D4 = 2.282
D3 = 0
Thus control chart limits as follows :
CONTROL LIMITS FOR Xbar CHART :
Upper Control Limit = UCL = Xbar-bar + A2.Rbar = 20.005 + 0.729 x 0.114 = 20.005 + 0.083 = 20.088 MM
Lower Control Limit = LCL = Xbar – A2.Rbar = 20.005 – 0.729 x 0.114 = 20.005 – 0.083 = 19.922 MM
CONTROL LIMITIS FOR R CHART :
Upper Control Limit = D4.Rbar = 2.282 x 0.114 = 0.26
Lower Control Limit = D3.Rbar = 0
For a process to be in control , all data of Xbar and Range ( R) are to be within control limits. That means ,
Xbar to be in the range of = 19.922 MM – 20.088 MM
Range to be in the range of = 0 – 0.26 MM
All data pertaining to Xbar and R values as calculated and presented in above table are within above stipulated limits. Therefore, it can be concluded that the Process is in Control
Time
Part 1 ( mm)
Part 2 ( mm)
Part 3 (mm)
Part 4 ( mm)
Xbar
Range
08:00
20.1
19.97
20.03
20.05
20.04
0.13
09:00
20
20.11
19.98
20.09
20.05
0.13
10:00
20.1
20.06
19.99
20.03
20.05
0.11
11:00
19.94
20.09
20.02
20.01
20.02
0.15
12:00
20.08
20.08
20
20.12
20.07
0.12
13:00
20.06
20.1
19.95
20.05
20.04
0.15
14:00
20.11
20.03
20.09
20
20.06
0.11
15:00
20.06
20.09
20.08
20
20.06
0.09
16:00
19.88
19.94
20.02
19.96
19.95
0.14
17:00
20.03
20.01
19.98
19.92
19.99
0.11
18:00
19.88
20.01
19.98
19.96
19.96
0.13
19:00
19.87
19.97
19.96
19.99
19.95
0.12
20:00
20.01
19.97
19.96
19.89
19.96
0.12
21:00
19.92
20.01
19.97
19.97
19.97
0.09
22:00
19.96
20
19.9
19.9
19.94
0.04
23:00
20.05
20.02
19.96
20
20.01
0.09
SUM =
320.08
1.83
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