A process that is considered to be in control measures an ingredient in ounces.
ID: 343801 • Letter: A
Question
A process that is considered to be in control measures an ingredient in ounces. Below are the last 10 samples (each of size n = 5) taken. The population process standard deviation is1.20
Samples
1
2
3
4
5
6
7
8
9
10
1010
1414
1414
99
1313
1010
1010
1414
77
1010
1010
1111
88
99
1010
99
1212
1010
88
1111
1010
1212
1111
1010
88
99
99
77
1212
99
99
1414
1010
1010
1010
1313
77
99
1313
77
1111
1111
88
1111
1010
99
88
99
99
1212
a) Standard deviation of the sampling means =
b) With z = 3 ,the control limits for the mean chart are
UCL Subscript x overbarUCLx= _____
LCL Subscript x overbarLCLx= _____
c) The control limits for the R-chart are:
UCL Subscript Upper RUCLR= _____
LCL Subscript Upper RLCLR= _____
d) Based on the
x overbarx -chart,
is one or more samples beyond the control limits? Yes or no
.
Based on the R-chart, is one or more samples beyond the control limits? Yes or no
.
Samples
1
2
3
4
5
6
7
8
9
10
1010
1414
1414
99
1313
1010
1010
1414
77
1010
1010
1111
88
99
1010
99
1212
1010
88
1111
1010
1212
1111
1010
88
99
99
77
1212
99
99
1414
1010
1010
1010
1313
77
99
1313
77
1111
1111
88
1111
1010
99
88
99
99
1212
Explanation / Answer
Below is the filled up table for 10 sample with each sample having 5 sets of data.
Sample
1st
2nd
3rd
4th
5th
Xbar
Range
1
10
10
10
9
11
10
2
2
14
11
12
14
11
12.4
3
3
14
8
11
10
8
10.2
6
4
9
9
10
10
11
9.8
2
5
13
10
8
10
10
10.2
5
6
10
9
9
13
9
10
4
7
10
12
9
7
8
9.2
5
8
14
10
7
9
9
9.8
7
9
7
8
12
13
9
9.8
6
10
10
11
9
7
12
9.8
5
AVERAGE:
10.12
4.5
The mean ( Xbar) and Range for each sample has been calculated and have been presented.
The mean for each sample = Xbar = Sum of 5 data / 5
Range for each sample = Range = Highest value – Lowest value in that sample
The average of mean values for each sample
= Xbar-Bar = Sum of all Xbar /10 = 10.12
Rbar = Average of Range values for each sample = 4.5
Sample size = n = 5
Corresponding values of constants for n = 5 as derived from standard table for Xbar and Range chart are :
A2 = 0.577
D4 = 2.114
D3 = 0
Control Limit for Mean chart :
Upper Control Limit = UCLx= Xbar-bar +A2.Rbar = 10.12 + 0.577 x 4.5= 10.12 + 2.596=12.716
Lower Control Limit = LCLx = Xbar-bar – A2.Rbar = 10.12 – 0.577x4.5= 10.12-2.596= 7.524
Control Limits for range chart :
Upper Control Limit = D4.Rbar = 2.114 x4.5 = 9.504
Lower Control Limit = D3.Rbar = 0
It can be seen that all values of Xbar are within 7.524 – 12.716 range
Therefore , NO SAMPLES ARE BEYOND THE CONTROL LIMITS
It can be seen that all values of Range are within control limits 0 – 9.504
Therefore , NO SAMPLES ARE BEYOND THE CONTROL LIMITS
Sample
1st
2nd
3rd
4th
5th
Xbar
Range
1
10
10
10
9
11
10
2
2
14
11
12
14
11
12.4
3
3
14
8
11
10
8
10.2
6
4
9
9
10
10
11
9.8
2
5
13
10
8
10
10
10.2
5
6
10
9
9
13
9
10
4
7
10
12
9
7
8
9.2
5
8
14
10
7
9
9
9.8
7
9
7
8
12
13
9
9.8
6
10
10
11
9
7
12
9.8
5
AVERAGE:
10.12
4.5
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