Example Data Table
| Method |
Target |
Confidence |
Allowed failures |
Input hours |
Typical use |
| Binomial |
95% reliability |
90% |
0 |
100 per unit |
Pass or fail mission test |
| Binomial |
97% reliability |
95% |
1 |
80 per unit |
Lot acceptance planning |
| Exponential |
1,000 MTBF |
90% |
0 |
100 per unit |
Life test hour planning |
Formula Used
Binomial Attribute Test
Confidence = 1 − Σ C(n, x) × qx × Rn−x,
where x runs from 0 to c. R is target reliability.
q is 1 − R. c is allowed failures.
Zero Failure Shortcut
n = ln(1 − confidence) ÷ ln(R).
This applies when allowed failures equal zero.
Exponential MTBF Test
Required total time = MTBF × χ²(2c + 2, confidence) ÷ 2.
Required units = ceiling(required total time ÷ hours per unit).
Mission Reliability From MTBF
Reliability = e−mission time ÷ MTBF.
The calculator uses the lower MTBF bound for this estimate.
How to Use This Calculator
- Select the reliability test method.
- Enter target reliability and required confidence.
- Enter the maximum allowed failures.
- Add mission time, MTBF, and unit test hours.
- Enter cost values for planning estimates.
- Press calculate to show the result above the form.
- Use CSV or PDF buttons to save the result.
Reliability Sample Size Planning
Reliability testing protects buyers, engineers, and budgets. A sample that is too small may approve weak parts. A sample that is too large may waste time and money. This calculator helps plan a balanced test before units enter the lab. It supports attribute testing and exponential life testing. Each method uses confidence, allowed failures, and a target reliability goal.
Why Sample Size Matters
A reliability claim needs evidence. Teams often state that a product must reach a target reliability, such as 95 percent. They also need confidence in that claim. More confidence usually needs more tested units or more total test time. Allowing some failures can reduce harsh zero failure rules, but it can also increase the required sample size.
Attribute Test Approach
The binomial method fits pass or fail tests. Each unit either survives the mission or fails during it. The calculator finds the smallest number of units that can demonstrate the selected reliability at the chosen confidence level. It also reports the acceptance rule. For example, a plan may require testing 59 units and accepting the lot only when failures are not above one.
Exponential Life Approach
The MTBF method fits time based reliability planning. It uses total accumulated test hours. More units can shorten calendar duration when they run in parallel. Longer tests can reduce unit count. The lower MTBF bound is checked against the target. This is useful for electronics, machines, pumps, and repairable systems.
Using the Result
Treat the output as a planning estimate. Real programs may need stress factors, censoring rules, warranty risk, and supplier agreements. Always define the failure mode before testing. Use the same mission profile for every unit. Keep records of run hours, removals, and observed failures. Export the CSV or PDF for review meetings. A clear plan avoids disputes and gives managers a repeatable basis for quality decisions.
Important Practical Checks
Review the test environment before approval. Confirm that samples represent normal production. Remove special builds unless the plan allows them. Define how replacement units are handled. Decide whether cosmetic issues count as failures. Document every assumption. These checks make the sample size meaningful. They also help auditors understand why the plan supports the reliability statement.
FAQs
What is a reliability sample size?
It is the number of units needed to support a reliability claim at a chosen confidence level. The required number depends on target reliability, confidence, allowed failures, and test method.
When should I use the binomial method?
Use it when each tested unit has a pass or fail result. It fits mission tests, lot acceptance tests, and demonstrations where survival during a defined period matters.
When should I use the exponential MTBF method?
Use it when reliability is measured by accumulated operating hours. It is common for electronics, machines, systems, pumps, and repairable products.
What does allowed failures mean?
Allowed failures means the maximum failures permitted while still accepting the test. Higher allowance may need more samples or more test time to keep the same confidence.
Why does higher confidence require more testing?
Higher confidence needs stronger evidence. That usually means more tested units, more total test hours, or a stricter failure acceptance rule.
Can this replace a formal reliability plan?
No. It supports planning estimates. Formal programs may also require environmental profiles, failure definitions, censoring rules, warranty limits, and customer approval.
Why is mission time included?
Mission time defines the period over which reliability is claimed. In MTBF mode, it helps convert the lower MTBF bound into a mission reliability estimate.
What should I export after calculating?
Export the result table for review. The CSV is useful for spreadsheets. The PDF is useful for audit files, reports, and quality planning meetings.