Executive answer
Separate the task, the unit and the statistical claim
- Report what each identified specimen completed before making a population claim.
- A zero-failure confidence bound uses eligible independent units, not a sum of cycles or an unreviewed count of keys.
- A larger sample cannot repair a changed failure rule, a biased selection or an unsupported transfer to field conditions.
Current guidance context
The buyer question is about the claim, not just the counter
A membrane-switch report can truthfully say that five identified samples completed a recorded test with no observed failure. Whether it can also support a population reliability statement is a different question. A quotation that offers more cycles on the same samples has not necessarily offered stronger evidence about variation between manufactured units.
ASTM's catalog lists F1578-24, Contact Closure Cycling of a Membrane Switch, as active, last updated May 29, 2024. Use the existing HYR cycle-test guide to define the test conditions. This page instead applies NIST's binomial and exact-confidence-limit context to a clearly labeled sample-count example. It does not reproduce the ASTM procedure or claim that ASTM specifies the example's sample quantity.
Define one task outcome per eligible unit
NIST describes a binomial model with two possible outcomes and a success probability fixed across trials. For the worksheet here, define one trial as one independently selected specimen completing one fixed task. R is the common probability of success at that task. The population, unit, task and failure definition must be meaningful before the arithmetic is used.
Assume, only for illustration, that five independently selected panels each complete an invented 100,000-cycle task under identical defined conditions. The five complete outcomes give n = 5. The total 500,000 cycles is exposure, not 500,000 independent manufactured specimens. Continuing those panels to a longer task changes the task being assessed; it does not manufacture additional independent units.
Several keys on one panel may share materials, processing, support and environment. Do not count them as independent panel-level samples merely because the counter has separate channels. If key-level reliability is the actual question, define that population and address within-panel dependence with the reliability owner. This guide supplies no effective-sample-size correction.
Worked example: five passes are not a 95% reliability demonstration
Hypothetical HYR editorial calculation—not measured product data. Assume a fixed sample count, independent units with the same R, appropriate representation of the stated population, complete observation of the agreed task and zero failures. The probability that all n units pass is R^n. For the chosen one-sided 95% exact lower confidence bound, set alpha = 0.05 and solve R_L^n = alpha. Thus R_L = 0.05^(1/n).
With n = 5, the lower bound is approximately 0.5493, or 54.93%. With n = 30, it is approximately 90.50%. These are lower confidence bounds under the stated model, not estimates that the switches are only that reliable. The observed pass fraction is 100% in both examples; it is not a proof that every unit in the population will pass.
Confidence describes the repeated-sampling coverage of the chosen statistical procedure under its assumptions. It is not a 95% posterior probability that this particular population parameter lies above the calculated bound, and it is not a 95% chance that the next device or project will succeed. Specify one-sided confidence explicitly: a two-sided 95% interval allocates tail probability differently and does not use the same bound.
Work backward from a stated target before testing
For an invented target R_target = 0.95 at one-sided 95% confidence, with acceptance requiring zero failures in a fixed complete sample, the smallest integer n satisfies 0.95^n ≤ 0.05. Calculating n = ceil[ln(0.05) / ln(0.95)] gives 59. Here ceil means round upward to the next integer. This is a property of the assumed plan, not a default membrane-switch sample requirement.
The boundary matters: 58 complete passes give a lower bound of approximately 94.97%, while 59 give approximately 95.05%. Rounding a result to 95% must not turn the 58-unit case into a pass against the exact target. At a true R of 0.95, the probability of 59 passes is approximately 4.8495%, which is below the chosen 5% tail probability.
Agree on the target, confidence, model and acceptance rule before releasing the test. Increasing n after inspecting favorable results, discarding a failed unit or stopping when a desired bound first appears can change the statistical plan. Ask the reliability owner to evaluate such changes; do not reuse the fixed-plan calculation as though nothing changed.
Keep incomplete runs and field-life questions visible
A specimen removed before completing the task is not a complete pass. Retain its actual exposure and reason for removal. If a failure occurs, the zero-failure formula no longer applies; the full outcomes need a suitable analysis. A replacement specimen does not erase the original event. Keep mechanical, electrical and observation records linked so a missed intermittent failure is not silently classified as success.
The formula does not decide whether convenient prototypes represent future production. Record revision, lot origins and selection method. Shared process effects or a deliberately selected set can undermine the simple model or limit the population claim. Stratification, dependence and finite-lot sampling may require a different plan; merely increasing the displayed count does not resolve them.
NIST also explains that few failures provide limited information for failure-mode and life-model assessment, and that transferring high-stress results to use conditions requires an acceleration model. Passing the fixed laboratory task therefore does not establish a time-to-failure distribution, calendar life or service-life equivalence in a different enclosure or environment. Keep those questions separate.
Five report errors that can overstate the evidence
These are review scenarios, not reported HYR defects. Each changes what the buyer can conclude.
- Cycles are relabeled as independent samples: retain specimen count and exposure as separate fields.
- Multiple keys from one panel are pooled without an independence argument: define the unit and dependence boundary first.
- An incomplete or failed specimen disappears from the denominator: preserve every enrolled unit and its outcome.
- A rounded bound, unstated sidedness or changed stopping rule creates a passing headline: retain the exact method and predeclared rule.
- A laboratory-task bound is advertised as field life, lot acceptance or finished-equipment approval: keep the population, task and approval scopes explicit.
What OEM engineering and sourcing should agree in the RFQ
Start with the claim the evidence must support. Identify the membrane-switch construction and revision, the target population, the unit being counted and the complete task. Freeze the mounted support, keys, environment, electrical monitoring and failure definition in the linked test plan. Then ask the reliability and quality owners to justify the sampling and analysis, rather than requesting an unexplained reliability percentage.
Compare quotations on the same basis: eligible independent specimens, exposure per specimen, observation coverage, handling of failures and incomplete runs, reporting and the named decision owner. More total cycles or a lower test price cannot answer a sample-representation question. If the available budget supports only exploratory prototypes, describe that evidence honestly instead of relaxing the conclusion after the test.
Send HYR the controlled drawing, proposed task and sample-evidence request through the existing secure RFQ. Keep component supply review separate from approval of the statistical plan and the finished equipment. The next useful output is a traceable proposed evidence scope, not a promised sample count, reliability rating, cost or completion date.