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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