COURSE-Quality Management-
ASSIGNMENT #3: CONTROLLIG A PROCESS
Sample
TR1
TR2
TR3
TR4
Average, x̅
Range, R
Process check 1
79
86
96
109
92.5
30
Process check 2
99
118
97
91
101.25
27
Process check 3
92
105
101
96
98.5
13
Process check 4
92
105
110
103
102.5
18
Process check 5
93
97
99
93
95.5
6
Process check 6
112
101
89
100
100.5
23
Process check 7
110
92
92
87
95.25
23
Process check 8
102
111
84
90
96.75
27
Process check 9
102
104
100
118
106
18
Process check 10
89
110
96
91
96.5
21
Day 1
97
106
104
90
99.25
16
Day 2
91
98
100
85
93.5
15
Day 3
108
100
89
100
99.25
19
Day 4
107
101
108
103
104.75
7
Day 6
116
110
79
85
97.5
37
Day 7
97
90
104
89
95
15
Day 8
102
87
88
92
92.25
15
Day 9
104
113
96
94
101.75
19
Day 10
115
117
92
88
103
29
Day 11
107
100
91
116
103.5
25
Day 12
119
119
92
104
108.5
27
Day 13
84
94
99
92
92.25
15
Day 14
104
94
89
115
100.5
26
Day 15
92
114
113
105
106
22
Day 16
113
100
108
95
104
18
Day 17
104
104
132
116
114
28
Day 18
102
119
79
99
99.75
40
Day 19
102
113
107
117
109.75
15
Day 20
93
105
111
96
101.25
18
Day 21
112
107
114
126
114.75
19
Day 22
110
100
90
109
102.25
20
Day 23
110
107
130
94
110.25
36
Day 24
123
92
114
106
108.75
31
Day 25
99
92
95
91
94.25
8
Day 26
131
111
117
104
115.75
27
Day 27
102
108
82
90
95.5
26
Day 28
106
103
114
106
107.25
11
Day 29
112
106
103
106
106.75
9
Day 30
109
103
103
102
104.25
7
Factors for control limits
n
A2
D4
d2
3/d2
Am
2
1.88
3.268
1.128
2.659
0.779
3
1.023
2.574
1.693
1.722
0.749
4
0.729
2.282
2.059
1.457
0.728
5
0.577
2.114
2.326
1.29
0.713
6
0.483
2.004
2.534
1.184
0.701
R bar = ΣR/k = 20.5
x̿= Σ x̅/k = 101.72
σ = √[Σ(x- x̅)2/n] (population std dev) = 10.553
Geometric σ =
x-bar chart
UCLx̅=130.
88
Averages
LCLx̅=72.60
145
125
105
85
65
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
R chart
UCLRbar =
46.781
50
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
X-Bar Chart

Used to detect the process mean when counting the subgroups
R Chart

Used to detect the process variability as per range when measuring the small groups
historically
Target
165
USL=125
Averages 115
Target
LSL=75
65
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
CUSUM Chart
CUSUM
UCL=21.1
60
50
40
30
20
10
0
-10
-20
-30
CL=0
CL
UCL
LCL
SH
SL
LCL=-21.1
σ = 10.553
Time
Advantages of using CUSUM Chart


Best way to detect small shift in the process mean.
Easy to identify visually shift in process mean.

It responds fast and finds out the process of control chart when it is modified
Disadvantages of using CUSUM Chart


Complicated to prepare and maintain.
Slower in detecting large shift in process mean.

the underlying data is lost
CUSUM
UCL=2.2
100
80
60
40
20
0
-20
-40
GESUM Chart
CL=0
CL
UCL
LCL
SH
LCL=-2.2
SL
Time
Advantages of using GESUM Chart
More reliable in detecting out of control situations.
Geometric σ= 1.1091
Process capability:
σ
10.586
USL
125
LSL
75
µ=
101.72
Cpu = (USL-µ)/3σ
0.7331
Cpl = (µ-LSL)/3σ
0.8413
Cpk = Min
{Cpl,Cpu)
0.7331
Shewhart Chart
Advantages

Control limits are evaluated from the data by specified values for known standards

Numeric or character values are acceptable

Save chart statistics and control limits in output data sets
Disadvantages

It can be used incorrect based on the sample group or output chosen

Wrong decisions can be made by not analyzing the variation related to the measurement.