TN7: Basic Forms of Statistical Sampling for Quality Control

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TN7: Basic Forms of Statistical Sampling for Quality Control. Acceptance Sampling: Sampling to accept or reject the immediate lot of product at hand. Statistical Process Control (SPC): Sampling to determine if the process is within acceptable limits. Acceptance Sampling. Purposes

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TN7: Basic Forms of Statistical Sampling for Quality Control
• Acceptance Sampling: Sampling to accept or reject the immediate lot of product at hand.Statistical Process Control (SPC): Sampling to determine if the process is within acceptable limits.
Acceptance Sampling
• Purposes
• Determine quality level
• Ensure quality is within predetermined level

Sample selected and analyzed

Results compared with acceptance criteria

Accept the lot

Reject the lot

Send to production or to customer

Decide on disposition

Basic Forms of Variation - SPC
• Assignable variation is caused by factors that can be clearly identified and possibly managed.
• Common variation is inherent in the production process.
Control Limits are based on the Normal Curve

x

m

z

-3

-2

-1

0

1

2

3

Standard deviation units or “z” units.

x

LCL

UCL

Control Limits

If we establish control limits at +/- 3 standard deviations, then

we would expect 99.7% of our observations to fall within these limits

StatisticalProcessControl

See Exhibit S6.3 for other evidence prompting investigation

Statistical Process Control (SPC) Charts

UCL

Normal Behavior

LCL

1 2 3 4 5 6

Samples over time

UCL

Possible problem, investigate

LCL

1 2 3 4 5 6

Samples over time

UCL

Possible problem, investigate

LCL

1 2 3 4 5 6

Samples over time

Statistical Sampling--Data

Attribute (Go no-go information)

• Defectives
• Defects
• Typically use sample size of 50-100

Variable (Continuous)

• Usually measured by the mean and the standard deviation
• Typically use sample size of 2 to 10

Where Z is equal to the number of Standard Deviations

2. Calculate the average of the sample proportions.

3. Calculate the sample standard deviation.

4. Calculate the control limits (where Z=3).

p-Chart (Continued)

5. Plot the individual sample proportions, the average

of the proportions, and the control limits

Matching Action to the Type of Variation

• If you treat special causes like common causes, you lose an opportunity to track down and eliminate something specific that is increasing variation in your process.
• If you treat common causes like special causes, you will most likely end up increasing variation (called “tampering”).
• Taking the wrong action not only doesn’t improve the situation, it usually makes it worse.
Quarterly Audit Scores

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Quarter

Quarterly Audit Scores

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Quarter

Quarterly Audit Scores

Score

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1 2 3 4 5

Process Capability
• Process limits (The “Voice of the Process” or The “Voice of the Data”) - based on natural (common cause) variation
• Tolerance limits (The “Voice of the Customer”) – customer requirements
• Process Capability – A measure of how “capable” the process is to meet customer requirements; compares process limits to tolerance limits

(a)

(b)

specification

specification

natural variation

natural variation

(c)

(d)

specification

specification

natural variation

natural variation

Process Capability

Evans and Lindsay The Management and Control of Quality, Southwestern Books.

Process Capability Index, Cpk

Capability Index - shows how well parts being produced fit into design limit specifications.

Interpreting the Cpk

Cpk < 1 Not Capable

Cpk = 1 Capable at 3

Cpk = 1.33 Capable at 4

Cpk = 1.67 Capable at 5

Cpk = 2 Capable at 6

Process Capability Index, Cpk

Find the Cpk for the following:

A process has a mean of 50.50 and a variance of 2.25. The product has a specification of 50.00 ± 4.00.

Is 99% Good Enough?
• 22,000 checks will be deducted from the wrong bank accounts in the next 60 minutes.
• 20,000 incorrect drug prescriptions will be written in the next 12 months.
• 12 babies will be given to the wrong parents each day.
Motorola’s Initial Six SigmaMeasurement Process
• Cycle time; e.g., 81 minutes  27 minutes  9 minutes  3 minutes  1 minute  20 seconds
• Defects; e.g., 81 defects  27 defects  9 defects  3 defects 1 defect  0.3 defects

REDUCE BOTH SIMULTANEOUSLY!

Six Sigma Quality

The objective of Six Sigma quality is 3.4 defects per million opportunities!

100K

10K

1K

100

10

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But is Six Sigma Realistic?

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(66810 ppm)

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Restaurant Bills

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Doctor Prescription Writing

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Payroll Processing

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Average

Company

Order Write-up

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Journal Vouchers

Wire Transfers

Air Line Baggage Handling

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Defects Per Million Opportunities (DPMO)

Purchased Material

Lot Reject Rate

(233 ppm)

Best in Class

Domestic Airline

Flight Fatality Rate

(3.4 ppm)

(0.43 ppm)

SIGMA

• Coca-Cola
• Home Depot
• SunTrust Banks
• Bank of America
• Delta Airlines
• Atlantic Envelope Company
• GE Capital
• Lithonia Lighting