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A passing acceptance sample is a decision under a sampling plan, not proof that every untested ceramic circuit conforms. The plan’s operating characteristic describes how often lots with different nonconforming fractions would be accepted. Reviewing that curve before inspection makes the risk visible and helps the buyer decide whether the proposed sampling arrangement answers the intended lot-release question.
Measurement purpose
Evaluate whether a proposed attribute acceptance plan provides the intended discrimination between satisfactory and unsatisfactory ceramic-circuit lots.
Specimens and conditions
- Lot and unit
- Defined lot size, traceability boundary and binary nonconforming-unit criteria
- Sample selection
- Approved selection method with retained unit identities and relevant clustering information
Equipment and records required
- Inspection method: Validated classification of the defects represented by the plan
- Probability calculation: Independently checked binomial or finite-population implementation appropriate to the sample design
Method sequence
- Risk definition
Agree good and poor quality points and acceptable decision risks
Record: Sampling objectives
- Plan assessment
Evaluate the operating characteristic and model assumptions
Record: Acceptance-probability table or curve
- Execution
Apply the fixed approved procedure and record rejected-lot handling
Record: Lot sample and disposition record
Decision and uncertainty
Use an agreed sampling plan whose operating characteristic and applicability are understood; a passing sample does not prove every untested unit conforms.
Finite population, clustering, selection bias and classification errors can invalidate a simple binomial curve.
The buyer and designated quality owner approve the plan and lot-disposition consequences.
Traceable outputs
| Record | Required contents |
|---|---|
| Plan assessment | n, c, model, quality points, acceptance probabilities and limitations |
| Lot result | Sample identities, observed classifications, decision and any rejection action |
Method review decisions
- Define the nonconforming unit before counting sample outcomes.
- Evaluate the plan at both good and poor lot-quality levels.
- Separate lot acceptance probability from confidence about an observed sample.
Specify the unit, defect classification and lot boundary
Identify what counts as one unit: individual ceramic circuit, panel or completed assembly. Define the characteristic or combined defect classification used by the plan. Counting three defects on one circuit as three nonconforming units changes the analysis. Keep critical failure categories separate where the governing quality arrangement requires different treatment.
Define the lot and its traceability boundary before selecting the sample. A mixture of unrelated material revisions or process histories may not support the same sampling model. Sampling cannot repair an uncontrolled lot definition. It also does not replace mandatory individual tests or safety-related requirements specified for the product.
Write the decision procedure before observing the sample
A single-sample attribute plan specifies sample size n and acceptance number c. Inspect the selected n units using the defined method; accept the lot under that plan when the number of nonconforming units does not exceed c. Also define the treatment of invalid measurements and the disposition of rejected lots.
Do not continue drawing extra parts until the result becomes favourable unless the approved procedure is explicitly a sequential or multiple-sampling plan with its own decision logic. Repeatedly restarting a failed sample changes the probability of acceptance. The curve for the original fixed plan no longer describes that improvised procedure.
Calculate acceptance probability for the proposed plan
For independent binary outcomes with a common nonconforming probability p, the sample count follows a binomial model. The probability of lot acceptance is the sum of the probabilities of observing zero through c nonconforming units. This is a forward question: if the lot quality were p, how often would this plan accept it?
The binomial model is often an approximation for sampling without replacement from a large finite lot. If the sampled fraction is appreciable, use the appropriate finite-population calculation with the actual lot size and number of nonconforming units. Keep the modelling assumptions beside the curve rather than treating every sample as automatically independent.
Paccept(p) = Σ(k=0 to c) C(n,k) p^k (1−p)^(n−k)
- n is the fixed number of inspected units; c is the maximum accepted nonconforming count.
- p is the hypothetical nonconforming probability in the binomial population model.
Independent, identically distributed binary outcomes and correct classification. Finite sampling without replacement may require the hypergeometric model.
Examine a worked curve rather than one pass percentage
For illustration, take n equal to twenty and c equal to one. The acceptance probability is the probability of observing zero failures plus the probability of observing exactly one. The table shows four points on that curve. This invented plan is not a recommended sampling standard or an approved ChipSimple release rule.
Even when the hypothetical lot has ten percent nonconforming units, this plan accepts about 39.17 percent of such lots. At one percent nonconforming, it accepts about 98.31 percent. Whether those risks are suitable depends on the consequence, contractual plan and quality objectives; a small sample that often passes may simply have limited discrimination.
| Hypothetical nonconforming fraction | Probability of acceptance | Probability of rejection |
|---|---|---|
| 1% | 98.31% | 1.69% |
| 5% | 73.58% | 26.42% |
| 10% | 39.17% | 60.83% |
| 20% | 6.92% | 93.08% |
Choose two quality points to express the intended protection
The buyer and supplier can identify a satisfactory quality level at which rejection should be uncommon and an unsatisfactory level at which acceptance should be uncommon. Evaluate the proposed plan at both points. Tightening one risk objective may require a larger sample or a different acceptance number.
Do not describe the acceptance number as permission to manufacture that many defects. It is a rule applied to the selected sample. Likewise, an acceptable-quality label does not mean every accepted lot has that quality or better. The curve describes probabilities across hypothetical lots under the model; it does not reveal the exact composition of the particular lot on the bench.
Keep operating characteristics separate from confidence intervals
After observing a sample, a confidence analysis asks what population fractions are compatible with the data under a stated procedure. That is different from calculating the probability of acceptance at a specified p before sampling. A zero-failure demonstration and an acceptance-plan curve can use related probability mathematics while answering different questions.
If twenty inspected parts all pass, the finding does not establish a zero defect fraction in the untested remainder. Report the observed sample result and the plan decision accurately. Do not reinterpret a plan’s high acceptance probability for good lots as the probability that the observed accepted lot is good; that reversal requires additional population information and a different analysis.
Check selection and measurement assumptions in practice
A convenient sample from one tray corner is not necessarily representative of the defined lot. Preserve the randomization or justified selection method and the unit identities. If defect mechanisms cluster by panel, firing position or material sublot, investigate that structure rather than assuming independent units because the arithmetic is simpler.
The operating characteristic also assumes that the inspection classifies units according to the stated definition. Missed defects and false rejections change its effective behaviour. A sampling plan cannot compensate for an optical method that cannot resolve the relevant defect or an electrical fixture that misattributes results. Verify the measurement route separately.
Retain the plan and rejected-lot disposition with the result
The release record should show lot identity, selected units, actual sample outcomes, n, c, the approved procedure and the resulting decision. Define what happens after rejection: containment, investigation, authorized screening or another specified action. Do not remove failed sampled units and relabel the unchanged remainder as a newly proven conforming lot without the required process.
ChipSimple can review drawing-specific inspection and lot evidence requirements with the buyer. The sampling plan must be selected for the actual product and acceptance obligations. Its value is a transparent risk-based lot decision, not a blanket reliability or defect-free claim for every ceramic circuit shipped under a passing sample.
Specify the lot sampling objective
State the required protection and inspection boundary before choosing a sample count.
- Lot definition, size and unit identity
- Nonconforming classifications and any mandatory individual tests
- Good and poor quality points with intended decision risks
- Proposed sampling procedure and selection method
- Rejected-lot containment, screening and reporting requirements
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