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Statistical Process Control
What is Quality?
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History of the Quality Movement
Total Quality Management
Control Charts
x bar and R charts
p charts and c charts
Process Capability
What is Quality?
Perfection
Consistency
Waste elimination
Speed of delivery
Provide a good and usable product
Compliance with policies and procedures
Doing it right the first time
Delighting or pleasing customers
Total customer service and satisfaction
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Quality from Manufacturing Point of View
Fitness for use
Extent to which customer expectations are met
Types of quality
Quality of design
Quality of conformance
Quality of performance
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Quality from Customers’ Perspective
Operation- Does the product do what it is designed to do?
Reliability and Durability- this reflects the probability of a products’ failing or deteriorating
Conformance- the degree to which the product meets specifications
Serviceability- speed and accuracy of repair
Appearance- perceived quality (subjective) the look, the touch, and the feel of the product
Perceived Quality- brand name, or image of the product
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1924 Statistical Quality Control/Control Charts, Shewart/Bell Labs
Late 20’s Statistical Acceptance Sampling, Bell Labs
1946 American Society for Quality Control created
1950 W. Edwards Deming introduces statistical quality control in Japan
1951 established in Japan
1980’s Total Quality Management (TQM)
1988 National Quality Awards established in the U.S.
1990’s ISO 9000, international quality standards adopted
History of the Quality Movement
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
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1915 – 1989
1904 – 2008
W. Edwards Deming 1900-1993
Influential Figures of Quality Control
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– Quality Trilogy
Movement toward proactive prevention, process oriented, etc.
Improvement
Improvement
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Create constancy of purpose toward improvement of product and service with a plan to become competitive, stay in business, and provide jobs
Adopt a new philosophy
Cease dependence on mass inspection
End the practice of awarding business on the basis of price tag
Improve constantly and forever the system of production
and service to improve quality and productivity
Institute training
Institute leadership
Drive out fear, so that everyone may work more effectively
for the company
W. Edwards Deming’s 14 Points
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Break down organizational barriers
Eliminate slogans, exhortations and arbitrary numerical goals and targets for the workforce which urge the workers to achieve new levels of productivity and quality without providing methods
Eliminate work standards and numerical quotas
Remove barriers that rob employees of their pride of workmanship
Institute vigorous program of education and self-improvement
Take action to accomplish the transformation
W. Edwards Deming’s 14 Points continued
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
A cause-and-effect diagram for “long line at convenience store”
Also known as fishbone chart
Ishikawa’s Cause-and-Effect Concentration Diagram
Cash register not working
Gas pump not accepting credit cards
Slow credit card terminal connection
Low on cash for making change
Training new employee
Not enough staff
High turnover
Employees don’t care
Poor morale
Poor store layout
Sale and promotion
Physical Environment
Long line at convenience store
Procedures
Adapted from Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
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Series of international quality standards
Establishes structures and processes for quality control systems at every step of the production process – design, raw materials, in-process monitoring, and so on
Imposes quality discipline
Broad acceptance internationally
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
First presented in 1988
Presented by the U.S. Commerce Department
Named for late
Established to
Promote quality awareness
Recognize quality achievements by US companies
Publicize successful quality strategies
Past winners include Motorola, Federal Express, 3M, Ritz-Carlton.
National Quality Awards
Adapted from Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
TQM is comprised of
Statistical Process Control
Shewhart Charts
Control Charts
Total Quality Management (TQM)
Natural variation is normal random variation versus a cause or reason to make an adjustment to the process.
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Historical inspection approach
Inspection of output
Action on output
Scrap, rework, downgrade (expensive!)
Statistical Process Control (SPC)
Monitor and study process variation
Goal: Continuous process improvement
Quality Control (QC)
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Assignable variation: caused by material, tools, worker related problems.
Common variation (random variation): caused by type of process, equipment etc.
If we eliminate assignable variation, we will bring the process within control. The process itself may still produce the variation due to common causes.
Back to statistics again
Process Variability
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We estimate these parameters ( and ) using random samples. From samples we can calculate sample mean ( ) and standard deviation ( ).
Products from any process have variability and a dimension of the product we are interested in may have certain probability distribution with mean and standard deviation .
Process Variability continued
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When a process is influenced only by common cause variation, the process will be in statistical control.
Common and Assignable Causes
2. When a process is influenced by one or more assignable causes, the process will not be in statistical control; such as an overused pattern, worn-out or broken part, defective materials, change in operator.
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Must decide which process variables to study
Best to study a quantitative variable (meaning we employ measurement data)
We will take a series of samples over time
Usually called subgroups
Usually of size two to six
Usually observed over a short period of time
Want to observe often enough to detect important process changes. Control charts are used to audit the processes.
Sampling a Process and Rational Subgrouping
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
A control chart employs a center line, upper control limit and lower control limit
The center line represents average performance
The upper and lower control limits are established so
that when in control almost all plot points will be between the limits
Control Charts
Adapted from Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Red line: control line. Out of red line: out of control
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stands for proportions, i.e., proportion that pass
or fail, material faults, percentage of phone calls not answered within 5 rings, percentage of dissatisfied customers, etc.
Variables and Attributes
Control charts for variables – things that we can measure
are in continuous units, i.e. diameter, time, length, height, or weight
measures of range
Control charts for attributes – things that we count
stands for things that we can count, i.e., number of defects, complaints, data entry errors, etc.
Average of sample mean
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Control Chart example
Now we calculate the grand mean and average range
x bar 31.8 46.8 27.4 36.4 … 27.2 32.8 33.8 29.6
Range 4 22 25 3 … 3 6 6 2
Now we calculate sample mean for 20 samples
Now we calculate sample range for 20 samples
We have collected 20 samples of size 5 each
1 2 3 4 … 17 18 19 20
1 30 55 19 36 … 27 29 30 30
2 30 51 25 36 … 27 32 34 31
3 34 47 21 37 … 26 34 34 29
4 33 33 44 35 … 29 35 35 29
5 32 48 28 38 … 27 34 36 29
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
20 Samples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 30 55 19 36 36 34 32 42 29 29 36 20 33 27 27 36 27 29 30 30
2 30 51 25 36 35 38 31 40 24 28 35 22 37 24 29 23 27 32 34 31
3 34 47 21 37 36 36 39 42 26 34 39 21 26 22 26 45 26 34 34 29
4 33 33 44 35 31 29 37 46 25 33 32 20 29 25 28 35 29 35 35 29
5 32 48 28 38 36 36 24 44 29 32 26 21 38 31 31 31 27 34 36 29
Mean 31.8 46.8 27.4 36.4 34.8 34.6 32.6 42.8 26.6 31.2 33.6 20.8 32.6 25.8 28.2 34.0 27.2 32.8 33.8 29.6
R 4 22 25 3 5 9 15 6 5 6 13 2 12 9 5 22 3 6 6 2
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Sample Number
We start with samples of size each. We are dealing with the distribution of the average , (normally distributed).
Most observations should be within 3 std. dev. from the mean.
So we set up control limits at these points.
We turn around this figure by 90˚ before plotting.
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
An observation beyond the control limits indicates the presence of an assignable cause
Other types of patterns also indicate the presence of an assignable cause
These patterns are more easily described in terms of control chart zones of A, B, and C.
Pattern Analysis
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Out of Control Patterns
(a) A run on one side of the
center line
(b) A run up
(c) A run down
(d) A trend
(here, increasing)
(e) Fanning out
(f) Funneling In
(g) A cycle
(h) An alternating pattern
Adapted from Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
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In Control Patterns
(a) A control chart with A, B, and C zones
(.135%) Zone Boundaries x Chart R Chart
Upper Control Limit:
Upper A-B Boundary:
Upper B-C Boundary:
(b) Calculating zone boundaries for and charts in the hole location case
Lower B-C Boundary:*
Center Line:
Lower A-B Boundary:*
Lower Control Limit:*
Adapted from Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
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Any of the following patterns is evidence of the likely presence of an assignable cause of variation
One point beyond zone A (three standard deviation limits)
Two of three consecutive points in zone A (the two standard deviation warning limits, or beyond) on one side of the center line
Four of five consecutive points in zone B (the one standard deviation limits, or beyond) on one side of the center line
A run of eight consecutive points (runs up, down or on the same side of center line)
Any nonrandom pattern – trend, fanning out, cycle or alternating pattern
Otherwise, the process is in statistical control
Pattern Analysis for and Charts
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Two of Three in A or Beyond
Observation
Adapted from Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Four of Five in B or Beyond
Observation
Adapted from Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
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Limits for this chart are given by
Use A2 values from Table of Control Chart Constants
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Control Charts: Stage 1
Sample # 1 2 3 4 5 6 7 8 9 10
Mean 31.8 46.8 27.4 36.4 34.8 34.6 32.6 42.8 26.6 31.2
Range 4 22 25 3 5 9 15 6 5 6
Stage 1: to establish the control limits
Which points outside ?
Which points outside ?
Sample # 11 12 13 14 15 16 17 18 19 20
Mean 33.6 20.8 32.6 25.8 28.2 34 27.2 32.8 33.8 29.6
Range 13 2 12 9 5 22 3 6 6 2
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Chart : Trial Control Limits
Points 2 (46.8), 8 (42.8), 9 (26.6), 12 (20.8), 14 (25.8)
are outside limits.
Find assignable cause and eliminate these points.
Find new control limits.
Chart: Trial Control Limits
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Revised Chart
Revision 1,
All points are within limits. The process is now in control and the limits become stable.
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
We have samples of size each and plot sample range values. So we are dealing with the distribution of .
Distribution of is not normal.
We need control limits:
Estimates for limits are:
Use D3 and D4 values from Table of Control Chart Constants
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Chart: Trial Control Limits
Points 2, 3, 16 are outside limits.
Find assignable cause and eliminate these points.
Find new control limits.
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Point 7 is outside limits
Perform revision 2
Chart: Revised Control Limits
Chart revision 1 (
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Chart revision 2 ( )
Point 11 is outside limits
Perform revision 3
Chart: Control Limits (revision 2)
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Chart revision 3 ( )
Point 13 is outside limits.
Perform revision 4
Chart: Control Limits (revision 3)
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Chart revision 4 ( )
All points are in control now!
Chart: Control Limits (revision 4)
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UCL LCL Out of Control UCL LCL Out of Control Eliminate
Trial 37.36 26.98 2,8,9,12,14 19.04 0 2,3,16 2,3,8,9,12,14,16
Rev. 1 36.20 28.30 4,15,17 14.48 0 7 4,7,15,17
Rev. 2 36.79 28.72 None 14.81 0 None None
Using and Charts Simultaneously
Chart: Trial Control Limits
Chart: Trial Control Limits
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Control Charts: Stage 2
Stage 2: To maintain control limits
Keep on taking new samples as per established procedure and plot
new points.
If process goes out of control, take corrective action (but do not recalculate control limits).
Revise limits whenever major changes occur.
Stable Control Limits
Trial Control Limits
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Population of all subgroup means
in any given time period
Population of all individual process
measurements in any given time period
Time period
Center line
Subgroup means observed over time
Adapted from Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
and Chart: Control Limits
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Reduce common cause variation in order to create leeway between the natural tolerance limits and the specification limits
Use control charts to establish statistical control and to monitor the process
When the control charts give out-of-control signals, take immediate action on the process to reestablish control before out-of-specification product is produced
Prevention Using Control Charts
Bowerman, B. L., O’Connell, R. T., & Murphree, E. S., (2010). Business Statistics in Practice (6th Ed.), Copyright © McGraw-Hill Education
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Variables and Attributes
Control charts for variables – things that we can measure
are in continuous units, i.e. diameter, time, length, height, or weight
measures of range
stands for proportions, i.e., proportion that pass
or fail, material faults, percentage of phone calls not answered within 5 rings, percentage of dissatisfied customers, etc.
Control charts for attributes – things that we count
stands for things that we can count, i.e., number of defects, complaints, data entry errors, etc.
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
Control Limits for Attributes
Control Limits and Center Line for a Chart
Control Limits and Center Line for a Chart
Johns Hopkins School _ Statistical Process Control_ Slide ‹#›
A company that makes slacks controls its production process by periodically taking a sample of 100 slacks from the production line. Each pair of slacks is inspected for defective features. Control limits are developed using three standard deviations from the mean as the limit. During the last 16 samples taken, the proportion of defective items per sample was recorded as follows:
Control Chart
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