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# Control Charts for Attributes - PowerPoint PPT Presentation

 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: UCL p = p+z  p and LCL p = p−z  p. Control Charts for Attributes.

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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

Control Charts for Attributes

• p-chart: A chart used for controlling the proportion of defective services or products generated by the process.

z = normal deviate (number of standard deviations from the average)

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.

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

= 0.0049

147

12(2500)

p =

p = p(1 – p)/n

p = 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

Hometown Bank

Using a p-Chart to monitor a process

n = 2500

Using a p-Chart to monitor a process

Example

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 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.

value

Process distribution

Lower

specification

Upper

specification

20

25

30

Process Capability

Process is capable

value

Process distribution

Lower

specification

Upper

specification

20

25

30

Process Capability

Process is not capable

6

Cp =

Process Capability Ratio, Cp

Process capability ratio, Cp, is the tolerance width divided by 6 standard deviations (process variability).

x – Lower specification

3s

=

Upper specification – x

3s

Cpk = Minimum of

,

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.

We take the minimum of the two ratios because it gives the worst-case 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

=

x – Lower specification

3s

Upper specification – x

3s

Cpk = Minimum of

,

Cpk = Minimum of

Cpk = Minimum of 1.53, 0.94

26.2 – 20.0

3(1.35)

,

Process Capability Index

30.0 – 26.2

3(1.35)

= 0.94

Intensive Care Lab Assessing Process Capability

Example

Upper specification = 30 minutes

Lower specification = 20 minutes

Average service = 26.2 minutes

 = 1.35 minutes

6(1.35)

Process Capability Ratio

Cp =

= 1.23

Upper specification - Lower specification

6

Cp =

Intensive Care Lab Assessing Process Capability

Example

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= 0.94Cp = 1.23

Six sigma

Four sigma

Two sigma

Lower

specification

Upper

specification

Mean

Effects of Reducing Variability on Process Capability

• 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%

• Reduce the number of parts in a product

• Reduce the number of steps in a process

• 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

Define Determine the current process characteristics critical to customer satisfaction and identify any gaps.

Measure Quantify the work the process does that affects the gap.

Analyze Use data on measures to perform process analysis.

Improve Modify or redesign existing methods to meet the new performance objectives.

Control Monitor the process to make sure high performance levels are maintained.

• 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.

• 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.

9000

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.

ISO

14000

International Quality Documentation Standards

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.

Category 1 ─ Leadership 120 points

Category 2 ─ Strategic Planning 85 points

Category 3 ─ Customer and Market Focus 85 points

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