lect 6 - process capability

7/28/2019 Lect 6 - Process Capability

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Control Charts

for Attributes

p-chart: A chart used for controlling theproportion of defective services orproducts generated by the process.

p = p(1p)/nWhere

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+zp and LCLp= pzp


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Hometown BankExample

The operations manager of the booking services department of Hometown Bankis 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.


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Sample Wrong Proportion

Number Account # Defective

1 15 0.006

2 12 0.0048

3 19 0.00764 2 0.0008

5 19 0.0076

6 4 0.0016

7 24 0.0096

8 7 0.00289 10 0.004

10 17 0.0068

11 15 0.006

12 3 0.0012

Total 147

Hometown BankUsing a p-Chart to monitor a process

n = 2500

p =147

12(2500)= 0.0049

p = p(1p)/n

p = 0.0049(10.0049)/2500

p = 0.0014

UCLp = 0.0049 + 3(0.0014)

= 0.0091

LCLp = 0.0049 3(0.0014)

= 0.0007


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Hometown BankUsing a p-Chart to monitor a process

Example


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In class Problem


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Control Charts

Two types of error are possible with controlcharts

A type I error occurs when a process is

thought to be out of control when in factit is not

A type II error occurs when a process is

thought to be in control when it isactually out of statistical control

These errors can be controlled by the choice

of control limits


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Process Capability

Process capability is the ability of theprocess to meet the design specificationsfor a service or product.

Nominal value is a target for designspecifications.

Tolerance is an allowance above or below

the nominal value.


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20 25 30

Upper

specification

Lower

specification

Nominal

value

Process Capability

Process is capable

Process distribution


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Process is not capable

20 25 30

Upper

specification

Lower

specification

Nominal

value

Process distribution

Process Capability


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Process capability ratio, Cp, is the tolerance width divided by 6 standard

deviations (process variability).

Process Capability Ratio, Cp

Cp =Upper specification - Lower specification

6


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Cpk= Minimum ofUpper specificationx

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.


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Intensive Care Lab

Example

Upper specification = 30 minutesLower specification = 20 minutes

Average service = 26.2 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?


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Cpk= Minimum ofUpper specificationx

3

x Lower specification

3 ,= =

Upper specification = 30 minutes

Lower specification = 20 minutes


= 1.35 minutes

Intensive Care Lab

Assessing Process Capability

Cpk= Minimum of26.2 20.0

3(1.35) ,30.026.2

3(1.35)

Cpk= Minimum of 1.53, 0.94 = 0.94Process

Capability

Index

Example


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Cp =Upper specification - Lower specification

6

Cp =30 - 20

6(1.35)

= 1.23 Process Capability Ratio

Before Process ModificationUpper specification = 30.0 minutes Lower specification = 20.0 minutes


= 1.35 minutes Cpk = 0.94 Cp = 1.23

Intensive Care LabAssessing Process Capability

Does not meet 3 (1.00 Cpk) target due to a shift in mean

(Note variability is ok since Cp is over 1.0)

Example


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In Class Problem


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In Class Problem


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Lower

specification

Mean

Upper

specification

Nominal value

Six sigma

Four sigma

Two sigma

Effects of Reducing

Variability on Process Capability


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Range Population in rangeExpected frequency outside

range

Approx. frequency for daily

event

1 0.682689492137 1 in 3 Twice a week

2 0.954499736104 1 in 22 Every three weeks

3 0.997300203937 1 in 370 Yearly

4 0.999936657516 1 in 15,787Every 43 years (twice in a

lifetime)

5 0.999999426697 1 in 1,744,278Every 5,000 years (once in

history)

6 0.999999998027 1 in 506,842,372 Every 1.5 million years

What it means to operate at 6-sigma


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Six Sigma

3.4 defects per million

Cpk = 2

Impact of number of parts or production stepson yield:

6 sigma 4 sigma 3 sigma

1 100% 99% 99%

5 100% 97% 71%

10 100% 94% 50%

100 99.97% 54% 0%


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Designing in 6-sigma

Reduce the number of parts in a product

Reduce the number of steps in a process


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Six Sigma

Six Sigma is a comprehensive and flexible system forachieving, sustaining, and maximizing business successby 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.


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Six SigmaImprovement Model

1. Define Determine the current processcharacteristics critical to customer satisfactionand identify any gaps.

2. Measure Quantify the work the process doesthat affects the gap.

3. Analyze Use data on measures to performprocess analysis.

4. Improve Modify or redesign existing methods tomeet the new performance objectives.

5. Control Monitor the process to make sure highperformance levels are maintained.


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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 thecustomers priorities.


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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 levelof 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.


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International QualityDocumentation Standards

ISO

9000

A set of standards governing documentation

of a quality program.

ISO

14000

Documentation standards that require participating

companies to keep track of their raw materials use

and their generation, treatment, and disposal of

hazardous wastes.


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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 90 points

5. Category 5 Human Resource Focus 85 points

6. Category 6 Process Management 85 points

7. Category 7 Business Results 450 points

Malcolm Baldrige National QualityAward

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.

lect 6 - process capability

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