1. business and industrial
2. manufacturing

Control Charts
for Attributes
 p-chart: A chart used for controlling the
proportion of defective services or
products generated by the process.
p =
p(1 – p)/n
Where
n = sample size
p = central line on the chart, which can be either the historical
average population proportion defective or a target value.
–
Control limits are: UCLp = p+zp and LCLp = p−zp
–
z = normal deviate (number of standard deviations from the average)
Hometown Bank
Example
The operations manager of the booking services department of Hometown Bank
is concerned about the number of wrong customer account numbers recorded by
Hometown personnel.
Each week a random sample of 2,500 deposits is taken, and the number of
incorrect account numbers is recorded. The results for the past 12 weeks are
shown in the following table.
Is the booking process out of statistical control? Use three-sigma control limits.
Hometown Bank
Using a p-Chart to monitor a process
n = 2500
p=
p =
p =
147
= 0.0049
12(2500)
p(1 – p)/n
0.0049(1 – 0.0049)/2500
p = 0.0014
UCLp = 0.0049 + 3(0.0014)
= 0.0091
LCLp = 0.0049 – 3(0.0014)
= 0.0007
Sample
Number
Wrong
Account #
Proportion
Defective
1
2
3
4
5
6
7
8
9
10
11
12
15
12
19
2
19
4
24
7
10
17
15
3
0.006
0.0048
0.0076
0.0008
0.0076
0.0016
0.0096
0.0028
0.004
0.0068
0.006
0.0012
Total
147
Hometown Bank
Using a p-Chart to monitor a process
Example
In class Problem
Control Charts
Two types of error are possible with control
charts
• A type I error occurs when a process is
thought to be out of control when in fact
it is not
• A type II error occurs when a process is
thought to be in control when it is
actually out of statistical control
These errors can be controlled by the choice
of control limits
Process Capability
• Process capability is the ability of the
process to meet the design specifications
for a service or product.
• Nominal value is a target for design
specifications.
• Tolerance is an allowance above or below
the nominal value.
Process Capability
Nominal
value
Process distribution
Lower
specification
20
Upper
specification
25
Process is capable
30
Process Capability
Nominal
value
Process distribution
Lower
specification
20
Upper
specification
25
Process is not capable
30
Process Capability Ratio, Cp
Process capability ratio, Cp, is the tolerance width divided by 6 standard
deviations (process variability).
Cp =
Upper specification - Lower specification
6
Process Capability Index, Cpk
Process Capability Index, Cpk, is an index that measures the potential
for a process to generate defective outputs relative to either upper
or lower specifications.
Cpk = Minimum of
=x – Lower specification
3
Upper specification – x=
,
3
We take the minimum of the two ratios because it gives the worstcase situation.
Intensive Care Lab
Example
The intensive care unit lab process has an average turnaround time
of 26.2 minutes and a standard deviation of 1.35 minutes.
The nominal value for this service is 25 minutes with an upper
specification limit of 30 minutes and a lower specification limit of 20
minutes.
The administrator of the lab wants to have three-sigma performance
for her lab. Is the lab process capable of this level of performance?
Upper specification = 30 minutes
Lower specification = 20 minutes
Average service = 26.2 minutes
 = 1.35 minutes
Intensive Care Lab
Assessing Process Capability
Example
Cpk = Minimum of
Cpk =
Upper specification = 30 minutes
Lower specification = 20 minutes
Average service = 26.2 minutes
 = 1.35 minutes
=
x – Lower specification
3
3(1.35)
Cpk =
Minimum of
1.53, 0.94
3
,
26.2 – 20.0
Minimum of
=
Upper specification – x
,
= 0.94
30.0 – 26.2
3(1.35)
Process
Capability
Index
Intensive Care Lab
Assessing Process Capability
Example
Cp =
Cp =
Upper specification - Lower specification
6
30 - 20
6(1.35)
= 1.23
Process Capability Ratio
Does not meet 3 (1.00 Cpk) target due to a shift in mean
(Note variability is ok since Cp is over 1.0)
Before Process Modification
Upper specification = 30.0 minutes Lower specification = 20.0 minutes
Average service = 26.2 minutes
 = 1.35 minutes Cpk = 0.94 Cp = 1.23
In Class Problem
In Class Problem
Effects of Reducing
Variability on Process Capability
Nominal value
Six sigma
Four sigma
Two sigma
Lower
specification
Upper
specification
Mean
What it means to operate at 6-sigma
Range
Population in range
Expected frequency outside
range
Approx. frequency for daily
event
μ ± 1σ
0.682689492137
1 in 3
Twice a week
μ ± 2σ
0.954499736104
1 in 22
Every three weeks
μ ± 3σ
0.997300203937
1 in 370
Yearly
μ ± 4σ
0.999936657516
1 in 15,787
Every 43 years (twice in a
lifetime)
μ ± 5σ
0.999999426697
1 in 1,744,278
Every 5,000 years (once in
history)
μ ± 6σ
0.999999998027
1 in 506,842,372
Every 1.5 million years
Six Sigma
• 3.4 defects per million
• Cpk = 2
• Impact of number of parts or production steps
on yield:
– 6 sigma
•
•
•
•
1 100%
5 100%
10 100%
100 99.97%
4 sigma
3 sigma
99%
97%
94%
54%
99%
71%
50%
0%
Designing in 6-sigma
• Reduce the number of parts in a product
• Reduce the number of steps in a process
Six Sigma
• Six Sigma is a comprehensive and flexible system for
achieving, sustaining, and maximizing business success
by minimizing defects and variability in processes.
• It relies heavily on the principles and tools of TQM.
• It is driven by a close understanding of customer needs;
the disciplined use of facts, data, and statistical analysis;
and diligent attention to managing, improving, and
reinventing business processes.
Six Sigma
Improvement Model
1. Define Determine the current process
characteristics critical to customer satisfaction
and identify any gaps.
2. Measure Quantify the work the process does
that affects the gap.
3. Analyze Use data on measures to perform
process analysis.
4. Improve Modify or redesign existing methods to
meet the new performance objectives.
5. Control Monitor the process to make sure high
performance levels are maintained.
Six Sigma Implementation
 Top Down Commitment from corporate leaders.
 Measurement Systems to Track Progress
 Tough Goal Setting through benchmarking bestin-class companies.
 Education: Employees must be trained in the
“whys” and “how-tos” of quality.
 Communication: Successes are as important to
understanding as failures.
 Customer Priorities: Never lose sight of the
customer’s priorities.
Six Sigma Education
• Green Belt: An employee who achieved the first level of
training in a Six Sigma program and spends part of his or
her time teaching and helping teams with their projects.
• Black Belt: An employee who reached the highest level
of training in a Six Sigma program and spends all of his
or her time teaching and leading teams involved in Six
Sigma projects.
• Master Black Belt: Full-time teachers and mentors to
several black belts.
International Quality
Documentation Standards
ISO
9000
ISO
14000
A set of standards governing documentation
of a quality program.
Documentation standards that require participating
companies to keep track of their raw materials use
and their generation, treatment, and disposal of
hazardous wastes.
Malcolm Baldrige National Quality
Award
Named after the late secretary of commerce, a strong proponent of
enhancing quality as a means of reducing the trade deficit. The
award promotes, recognizes, and publicizes quality strategies and
achievements.
1.
2.
3.
4.
Category 1 ─ Leadership
Category 2 ─ Strategic Planning
Category 3 ─ Customer and Market Focus
Category 4 ─ Measurement, Analysis, and
Knowledge Management
5. Category 5 ─ Human Resource Focus
6. Category 6 ─ Process Management
7. Category 7 ─ Business Results
120 points
85 points
85 points
90 points
85 points
85 points
450 points