OPSM 451 Service Operations Management
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Transcript OPSM 451 Service Operations Management
Koç University
OPSM 301 Operations Management
Class 22:
Quality: Statistical process control
Zeynep Aksin
[email protected]
Statistical Process Control
Detect and eliminate assignable variation
(statistical process control)
– If there is no assignable variation, Process is
in control
– We use Process Control charts to maintain
this
Natural Variations
Also called common causes
Affect virtually all production processes
Expected amount of variation, inherent due to:
- the nature of the system
- the way the system is managed
- the way the process is organised and operated
can only be removed by
- making modifications to the process
- changing the process
Output measures follow a probability distribution
For any distribution there is a measure of central tendency
and dispersion
Assignable Variations
Also called special causes of variation
Exceptions to the system
Generally this is some change in the process
Variations that can be traced to a specific reason
considered abnormalities
often specific to a
certain operator
certain machine
certain batch of material, etc.
The objective is to discover when assignable causes are
present
Eliminate the bad causes
Incorporate the good causes
Process Measure
Process Control Chart
Time
Information: Monitor process variability
over time
Control Limits: Average + z Normal Variability
Decision Rule:
Ignore variability within limits as “normal”
Investigate variation outside “abnormal”
Errors:
MBPF
Type I - False alarm (unnecessary investigation)
Control and
Capability
TypeProcess
II - Missed
signal
(to identify and correct)
5
X-bar – Chart
Shows sample means over time
Means of the values in a sample
Monitors process mean
X Bar Chart
UCL
Average
86
84
82
80
LCL
78
19
17
15
13
9
11
7
5
3
1
76
Day
Average X bar = 82.5 kg
Standard Deviation of X bar = 1.6 kg
Control Limits
= Average X bar + 3 Std of X bar
= 82.5 + (3)(1,6) = [77.7, 87.3]
Process is “In Control” (i.e., the mean is stable)
7
R – Chart
Type of variables control chart
Shows sample ranges over time
Difference between smallest and
largest values in sample
Monitors process variability
Independent from process mean
Range
Range (R) Chart
UCL
20
15
10
5
0
LCL
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Day
Average Range R = 10.1 kg
Standard Deviation of Range = 3.5 kg
Control Limits: 10.1 + (3)(3.5) = [0, 20.6]
Process Is “In Control” (i.e., variation is stable)
MBPF
Process Control and Capability
9
Setting Control Limits
Control Chart
for sample of
9 boxes
Variation due
to assignable
causes
Out of
control
17 = UCL
Variation due to
natural causes
16 = Mean
15 = LCL
| | | | | | | | | | | |
1 2 3 4 5 6 7 8 9 10 11 12
Sample number
Out of
control
Variation due
to assignable
causes
Mean and Range Charts
(a)
(Sampling mean is
shifting upward but
range is consistent)
These
sampling
distributions
result in the
charts below
UCL
(x-chart detects
shift in central
tendency)
x-chart
LCL
UCL
(R-chart does not
detect change in
mean)
R-chart
LCL
Mean and Range Charts
(b)
These
sampling
distributions
result in the
charts below
(Sampling mean
is constant but
dispersion is
increasing)
UCL
(x-chart does not
detect the increase
in dispersion)
x-chart
LCL
UCL
(R-chart detects
increase in
dispersion)
R-chart
LCL
Process Control and Improvement
Out of Control
UCL
LCL
In Control
Improved
Important points to remember
Control charts are used to differentiate normal
variability from assignable/abnormal variability
X-bar chart monitors control of process mean
R-chart monitors control of process variability
An improvement in the process implies lower
normal variability