The document discusses statistical control charts, particularly p-charts, which are used to monitor the proportion of defective services or products. It emphasizes the importance of process capability, explaining metrics like the process capability ratio (Cp) and index (Cpk) to measure a process's ability to meet specifications. Additionally, it outlines the Six Sigma methodology for improving processes through a structured approach and highlights standards for quality documentation such as ISO 9000 and 14000.

1. Control Charts
for Attributes
p-chart: A chart used for controlling the
proportion of defective services or
products generated by the process.

p
p =
= p
p(1 –
(1 – p
p)/
)/n
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.
z = normal deviate (number of standard deviations from the average)
Control limits are: UCLp = p+z
p
p and LCLp = p−zp
– –

2. Hometown Bank
Hometown Bank
Example
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.

3. Sample Wrong Proportion
Number Account # Defective
1 15 0.006
2 12 0.0048
3 19 0.0076
4 2 0.0008
5 19 0.0076
6 4 0.0016
7 24 0.0096
8 7 0.0028
9 10 0.004
10 17 0.0068
11 15 0.006
12 3 0.0012
Total 147
Hometown Bank
Hometown Bank
Using a p-Chart to monitor a process
Using a p-Chart to monitor a process
n = 2500
p =
147
12(2500)
= 0.0049

p
p =
= p
p(1 –
(1 – p
p)/
)/n
n

p
p =
= 0.0049
0.0049(1 –
(1 – 0.0049
0.0049)/
)/2500
2500

p
p = 0.0014
= 0.0014
UCLp = 0.0049 + 3(0.0014)
= 0.0091
LCLp = 0.0049 – 3(0.0014)
= 0.0007

4. Hometown Bank
Hometown Bank
Using a p-Chart to monitor a process
Using a p-Chart to monitor a process
Example

5. In class Problem

6. 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

7. 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.

8. 20
20 25
25 30
30
Upper
Upper
specification
specification
Lower
Lower
specification
specification
Nominal
Nominal
value
value
Process Capability
Process is capable
Process distribution
Process distribution

9. Process is not capable
Process is not capable
20
20 25
25 30
30
Upper
Upper
specification
specification
Lower
Lower
specification
specification
Nominal
Nominal
value
value
Process distribution
Process distribution
Process Capability

10. Process capability ratio, Cp, is the tolerance width divided by 6 standard
deviations (process variability).
Process Capability Ratio, Cp
C
Cp
p =
=
Upper specification - Lower specification
Upper specification - Lower specification
6
6


11. Cpk = Minimum of Upper specification – x
3
x – Lower specification
3
,
= =
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.
Process Capability Index, Cpk
We take the minimum of the two ratios because it gives the worst-
case situation.

12. Intensive Care Lab
Example
Upper specification = 30 minutes
Upper specification = 30 minutes
Lower specification = 20 minutes
Lower specification = 20 minutes
Average service = 26.2 minutes
Average service = 26.2 minutes

 = 1.35 minutes
= 1.35 minutes
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?

13. Cpk = Minimum of Upper specification – x
3
x – Lower specification
3
,
= =
Upper specification = 30 minutes
Lower specification = 20 minutes
Average service = 26.2 minutes
 = 1.35 minutes
Intensive Care Lab
Assessing Process Capability
C
Cpk
pk =
= Minimum of
Minimum of 26.2
26.2 – 20.0
– 20.0
3(
3(1.35
1.35)
) ,
,
30.0 –
30.0 – 26.2
26.2
3(
3(1.35
1.35)
)
C
Cpk
pk =
= Minimum of 1.53, 0.94
Minimum of 1.53, 0.94 = 0.94
= 0.94
Process
Capability
Index
Example

14. Cp =
=
Upper specification - Lower specification
6
Cp
p =
=
30 - 20
6(1.35)
= 1.23 Process Capability Ratio
Before Process Modification
Upper specification = 30.0 minutes Lower specification = 20.0 minutes
Average service = 26.2 minutes
 = 1.35 minutes Cpk = 0.94 C
Cp
p = 1.23
Intensive Care Lab
Assessing Process Capability
Does not meet 3 (1.00 Cpk
pk) target due to a shift in mean
(Note variability is ok since Cp
p is over 1.0)
Example

15. In Class Problem

16. In Class Problem

17. Lower
Lower
specification
specification
Mean
Mean
Upper
Upper
specification
specification
Nominal value
Nominal value
Six sigma
Six sigma
Four sigma
Four sigma
Two sigma
Two sigma
Effects of Reducing
Variability on Process Capability

18. 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
What it means to operate at 6-sigma

19. Six Sigma
• 3.4 defects per million
• Cpk = 2
• Impact of number of parts or production steps
on yield:
– 6 sigma 4 sigma 3 sigma
• 1 100% 99% 99%
• 5 100% 97% 71%
• 10 100% 94% 50%
• 100 99.97% 54% 0%

20. Designing in 6-sigma
• Reduce the number of parts in a product
• Reduce the number of steps in a process

21. 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.

22. 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.

23. Six Sigma
Implementation
 Top Down Commitment from corporate leaders.
 Measurement Systems to Track Progress
 Tough Goal Setting through benchmarking best-
in-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.

24. 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.

25. International Quality
International Quality
Documentation Standards
Documentation Standards
ISO
ISO
9000
9000
A set of standards governing documentation
of a quality program.
ISO
ISO
14000
14000
Documentation standards that require participating
companies to keep track of their raw materials use
and their generation, treatment, and disposal of
hazardous wastes.

26. 1. Category 1 ─ Leadership
120 points
2. Category 2 ─ Strategic Planning
85 points
3. Category 3 ─ Customer and Market Focus
85 points
4. Category 4 ─ Measurement, Analysis, and
Knowledge Management
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.