A General EXCEL Solution for LTPD Type Sampling Plans

David C. Trindade, Ph.D.Sun Microsystems

David MeadeAMD

1999 Joint Statistical Meetings Baltimore, MD

Lot Acceptance Sampling

• Assume single random sample of size n from a process or a very large lot.

• Binomial distribution is appropriate.

• Refer to as type B sampling.

Sampling Plan

• Specifies – the sample size n– the acceptance number c

• An operating characteristic (OC) curve shows the probability of lot acceptance for a given level of incoming lot percent defective p

n = 50 c = 3

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%

Lot Percent Defective

Pro

bab

ility

of

Acc

ep

tan

ceOC Curve

LTPD Plans

• The quality level at 10% probability of acceptance (consumer’s risk) is called the LTPD.

• This rejectable quality level (RQL) is highest percent defective (poorest quality) tolerable in a small percentage of product.

• Borderline of distinction between a satisfactory lot and an unsatisfactory one.

• LTPD plans are used for many product qualification plans to assure consumer protection.

Common Sampling Problem in Industry

• There are constraints on sample size based on limited time, money, or other resources.

• There is often the need to adjust sample size and corresponding acceptance number while holding LTPD constant.

LTPD Tables

Limitations of Tables

• LTPD values restricted to only those listed.

• There are finite ranges of sample sizes and acceptance numbers.

Example Case

• Reliability qualification plan for integrated circuits calls for stressing a sample of 300 units for 1000 hours. Pass requirement is no more than three failures.

• Early samples are precious, costing approximately $10,000 each and are needed for other evaluations.

• How can the engineer reduce the sample size and allowed failures while holding the LTPD constant?

Approaches by Engineer

• First, the LTPD value must be determined.

• Then, LTPD tables may be consulted to see if n = 300 and c = 3 are tabulated.

• Approximation may be necessary:– Checking LTPD table, we see n = 333 and c = 3

for LTPD = 2%.– For c = 1, LTPD = 2%, we need n = 195.

Graphical Techniques*

*Applied Reliability, 2nd ed., P. Tobias and D. Trindade

Graphical Results

• For n = 300, c = 3, LTPD = 2.2%.

• For LTPD = 2.2%, c = 1, n ~ 180.

There is a limitation in these graphs to

only c = 0, 1, 2, or 3.

EXCEL Solution (Add-In)

Find LTPD for Given Sampling Plan

Find LTPD for a Given sampling Plan: Output

Find Alternative LTPD Sampling Plan

Find Alternative Sampling Plan: Output

Find Sample Size for Given c

Find Sample Size for Given c: Output

Final Comments

• Description and theory presented in paper.

• LTPD add-in and paper available for download from www.trindade.com/LTPD.html

• Questions to:– david.trindade@eng.sun.com– david.meade@amd.com (VB programming)