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Reliability test sample size and LTPD calculator

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KEY POINTS

The sample size needed to demonstrate reliability R at confidence level CL with zero failures is n = ln(1−CL)/ln(R): 230 units for 99% reliability at 90% confidence, and 2,302 units for 99.9%. The "3 lots × 77 units = 231 units with 0 failures" plan common in JEDEC HTOL testing corresponds to an LTPD of about 1% at 90% confidence.

Sample size needed to demonstrate a target reliability

Reliability to demonstrate (good-unit rate) R (%)Confidence level CLAllowed failures c (units)

Required sample size n230units

Pass criterionTest 230 units; with 0 or fewer failures, reliability is at least 99% at 90% confidence

Upper bound on the defect rate from test results (LTPD)

Units tested (units)Failures (units)

Upper bound on defect rate (90% confidence)0.992%

Lower bound on reliability99.008%

The "3 lots × 77 units = 231 units with 0 failures" plan often used for HTOL and other tests in JEDEC JESD47 corresponds to an LTPD of about 1% at 90% confidence.

Test size needed to demonstrate a failure rate (FIT) target

Target failure rate (FIT)Test duration (hours)Acceleration factor AFAllowed failures (units)

Required sample size591units

Required equivalent device hours N·t·AF4.605×10⁷hours

χ² (90%, 2 degrees of freedom)4.605

Failures are assumed to follow an exponential distribution (constant failure rate). Derive the acceleration factor from the test conditions (temperature, voltage, humidity) and the use conditions.

Reliability and sample size with zero failures

Reliability R	CL 60%	CL 90%	CL 95%	CL 90%, up to 1 failure
90%	9	22	29	38
95%	18	45	59	77
99%	92	230	299	388
99.5%	183	460	598	777
99.9%	916	2,302	2,995	3,889

Zero failures does not mean 100% reliability

Even if a sample test shows zero failures, you cannot conclude that the population defect rate is zero. All you can say is that if the defect rate were p or higher, the chance of all n units passing would be no more than 1 − CL. Demonstrating 99% reliability at 90% confidence with zero failures takes 230 units, and 99.9% takes 2,302; each extra nine of reliability multiplies the sample size by roughly ten.

Semiconductor reliability qualification draws samples from at least three lots to capture lot-to-lot variation. Failure rate (FIT) claims rely on tests accelerated by temperature or voltage, converted to use conditions with an acceleration factor. A larger acceleration factor means fewer samples and shorter tests, but test conditions are capped so they do not trigger failure modes that never occur in use.

FAQ

Why 77 units per lot?

Three lots of 77 units give 231 units. With zero failures, that demonstrates an LTPD of about 1% at 90% confidence, which is why the plan appears in JEDEC JESD47 qualification.

Does zero failures prove 100% reliability?

No. It only shows that if the defect rate were above a certain level, passing every unit would have been unlikely. Each extra nine of reliability needs roughly ten times as many units.

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Last updated: October 23, 2026