Transcript Statistical Process Control

Mata kuliah : J0444 - Manajemen Operasional
Tahun
: 2010
Quality Control
Pertemuan 12
Learning Objectives
•
•
•
•
•
List and briefly explain the elements of the control
process.
Explain how control charts are used to monitor a
process, and the concepts that underlie their use.
Use and interpret control charts.
Use run tests to check for nonrandomness in process
output.
Assess process capability.
Phases of Quality Assurance
Inspection of lots
before/after
production
Acceptance
sampling
The least
progressive
Inspection and
corrective
action during
production
Process
control
Quality built
into the
process
Continuous
improvement
The most
progressive
Inspection
• How Much/How Often
• Where/When
• Centralized vs. On-site
Inputs
Acceptance
sampling
Transformation
Process
control
Outputs
Acceptance
sampling
Where to Inspect in the Process
• Raw materials and purchased parts
• Finished products
• Before a costly operation
• Before an irreversible process
• Before a covering process
Examples of Inspection Points
Type of
business
Fast Food
Inspection
points
Cashier
Counter area
Eating area
Building
Kitchen
Hotel/motel Parking lot
Accounting
Building
Main desk
Supermarket Cashiers
Deliveries
Characteristics
Accuracy
Appearance, productivity
Cleanliness
Appearance
Health regulations
Safe, well lighted
Accuracy, timeliness
Appearance, safety
Waiting times
Accuracy, courtesy
Quality, quantity
Statistical Control
• Statistical Process Control:
Statistical evaluation of the output of a
process during production
• Quality of Conformance:
A product or service conforms to specifications
Control Chart
• Control Chart
– Purpose: to monitor process output to see if it is
random
– A time ordered plot representative sample
statistics obtained from an on going process (e.g.
sample means)
– Upper and lower control limits define the range of
acceptable variation
Control Chart
Abnormal variation
due to assignable sources
Out of
control
UCL
Mean
Normal variation
due to chance
LCL
Abnormal variation
due to assignable sources
0
1
2
3
4
5
6
7
8
Sample number
9
10 11 12 13 14 15
Statistical Process Control
• The essence of statistical process control is to assure
that the output of a process is random so that future
output will be random.
Statistical Process Control Steps
Start
Produce Good
Provide Service
Take Sample
No
Assign.
Causes?
Yes
Inspect Sample
Stop Process
Create
Control Chart
Find Out Why
Statistical Process Control
• Variations and Control
– Random variation: Natural variations in the output
of a process, created by countless minor factors
– Assignable variation: A variation whose source can
be identified
Sampling Distribution
Sampling
distribution
Process
distribution
Mean
Normal Distribution
Standard deviation



Mean
95.44%
99.74%

Control Limits
Sampling
distribution
Process
distribution
Mean
Lower
control
limit
Upper
control
limit
SPC Errors
• Type I error
– Concluding a process is not in control when it
actually is.
• Type II error
– Concluding a process is in control when it is not.
Type I and Type II Errors
In control
Out of control
In control
No Error
Out of
control
Type II Error
(consumers risk)
Type I error
(producers risk)
No error
10-17
Type I Error
/2
/2
Mean
Probability
of Type I error
LCL
UCL
Observations from Sample Distribution
UCL
LCL
1
2
Sample number
3
4
Control Charts for Variables
Variables generate data that are measured.
• Mean control charts
– Used to monitor the central tendency of a process.
– X bar charts
• Range control charts
– Used to monitor the process dispersion
– R charts
Mean and Range Charts
(process mean is
shifting upward)
Sampling
Distribution
UCL
Detects shift
x-Chart
LCL
UCL
R-chart
LCL
Does not
detect shift
Mean and Range Charts
Sampling
Distribution
(process variability is increasing)
UCL
x-Chart
LCL
Does not
reveal increase
UCL
R-chart
Reveals increase
LCL
Control Chart for Attributes
• p-Chart - Control chart used to monitor the proportion
of defectives in a process
• c-Chart - Control chart used to monitor the number of
defects per unit
Attributes generate data that are counted.
Use of p-Charts
• When observations can be placed into two
categories.
–
Good or bad
–
Pass or fail
–
Operate or don’t operate
• When the data consists of multiple samples of
several observations each
Use of c-Charts
• Use only when the number of occurrences per unit of
measure can be counted; non-occurrences cannot be
counted.
– Scratches, chips, dents, or errors per item
– Cracks or faults per unit of distance
– Breaks or Tears per unit of area
– Bacteria or pollutants per unit of volume
– Calls, complaints, failures per unit of time
Use of Control Charts
• At what point in the process to use control charts
• What size samples to take
• What type of control chart to use
– Variables
– Attributes
Run Tests
• Run test – a test for randomness
• Any sort of pattern in the data would suggest a nonrandom process
• All points are within the control limits - the process
may not be random
Nonrandom Patterns in Control charts
•
•
•
•
•
Trend
Cycles
Bias
Mean shift
Too much dispersion
Counting Runs
Counting Above/Below Median Runs
B A
A
B
A
B
B
B A
(7 runs)
A
B
Counting Up/Down Runs
U
U
D
U
(8 runs)
D
U D
U U
D
NonRandom Variation
• Managers should have response plans to investigate
cause
• May be false alarm (Type I error)
• May be assignable variation
Process Capability
• Tolerances or specifications
– Range of acceptable values established by
engineering design or customer requirements
• Process variability
– Natural variability in a process
• Process capability
– Process variability relative to specification
Process Capability
Lower
Specification
Upper
Specification
A. Process variability
matches specifications
Lower
Specification
Upper
Specification
B. Process variability
Lower
Upper
well within specifications Specification Specification
C. Process variability
exceeds specifications
Process Capability Ratio
If the process is centered use Cp
specification width
Process capability ratio, Cp =
process width
Cp =
Upper specification – lower specification
6
If the process is not centered use Cpk
C pk
 X  LTL
UTL - X 

= min 
or

3

3



Limitations of Capability Indexes
1. Process may not be stable
2. Process output may not be normally distributed
3. Process not centered but Cp is used
Example
Standard Machine
Machine Deviation Capability
Cp
A
0.13
0.78
0.80/0.78 = 1.03
B
0.08
0.48
0.80/0.48 = 1.67
C
0.16
0.96
0.80/0.96 = 0.83
Cp > 1.33 is desirable
Cp = 1.00 process is barely capable
Cp < 1.00 process is not capable
10-35
The End