Effect of Approximate Probability Distributions on Single and Double Acceptance Sampling Plans for Attributes
Bibliographic record
Abstract
An acceptance sampling plan is a statement of the sample size to be used and the associated acceptance or rejection criteria for sentencing individual lots. An important measure of the performance of an acceptance sampling plan, such as the operating characteristic curve, is related to probability distributions. This research investigates the effect of binomial, Poisson and normal approximations to single and double acceptance sampling plans for attributes. For single-sampling plans, type-A OC curves show that the binomial approximation tends to overestimate the probability of acceptance Pa of the true hypergeometric distribution when the lot size is at most 10 times the sample size. The single-sampling plan with type-B OC curve displays that the Pa from Poisson is a slight overestimate of the true Pa for the binomial distribution with small n and large p, moreover, the Pa from normal approximation can be a significant underestimation, exact value, or overestimation of the binomial, even with small p. On double-sampling plans, the Poisson approximation results in a tiny overestimation, while the normal approximation appears to be a major underestimation of the binomial. In rectifying inspection, the characteristics of AOQL are very similar to the sampling plan.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.047 | 0.158 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".