ISO 28598-2:2017 – Acceptance Sampling Based on Allocation of Priorities Principle (APP) — Part 2: Coordinated Single Sampling Plans for Acceptance Sampling by Attributes

Coordinated Sampling Plans for the APP Framework

ISO 28598-2:2017 provides the pretabulated single sampling plans that operationalize the APP framework described in Part 1. While Part 1 establishes the methodology for determining priority weights, Part 2 provides the actual sample size tables and acceptance/rejection numbers that translate those weights into actionable inspection plans. The plans are “coordinated” in the sense that they are designed to work together across different priority levels, maintaining consistent consumer and producer risks.

The coordinated nature of these plans means that when priority shifts between characteristics, the OC curves remain consistent — a characteristic inspected at “enhanced” level always provides the same consumer risk regardless of which product family or supplier it belongs to.

Sample Size Tables and Acceptance Numbers

The standard includes master tables for coordinated single sampling at three inspection levels: reduced (priority score ≤ 8), normal (priority score 9-27), and enhanced (priority score > 27). For normal inspection at AQL = 0.65%, the sample size for lot size 10,001-35,000 is J (500 units) with Ac = 7, Re = 8. For enhanced inspection, the sample size increases to L (1,250 units). The consistency across priority levels is maintained by using the same AQL and lot size code letters as ISO 2859-1, with the priority score determining which inspection level table is used.

Lot Size	Code Letter	Normal n/Ac/Re	Reduced n/Ac/Re	Enhanced n/Ac/Re
91 – 150	E	13 / 1 / 2	8 / 0 / 1	20 / 1 / 2
151 – 280	F	20 / 1 / 2	13 / 0 / 1	32 / 2 / 3
281 – 500	G	32 / 2 / 3	20 / 0 / 1	50 / 3 / 4
501 – 1,200	H	50 / 3 / 4	32 / 1 / 2	80 / 5 / 6
1,201 – 3,200	J	80 / 5 / 6	50 / 1 / 2	125 / 7 / 8
3,201 – 10,000	K	125 / 7 / 8	80 / 2 / 3	200 / 10 / 11
10,001 – 35,000	L	200 / 10 / 11	125 / 3 / 4	315 / 14 / 15

The enhanced inspection plans use approximately 1.6 times the normal sample size, while reduced plans use approximately 0.6 times the normal sample size. This geometric scaling ensures that the total inspection load remains relatively constant when priority scores are balanced across characteristics — the savings from reduced plans fund the additional cost of enhanced plans.

Statistical Properties and OC Curve Families

The coordinated plans are designed so that the producer’s risk (α) at the AQL is approximately 5% across all three inspection levels, while the consumer’s risk (β) at the LQL varies: 10% for enhanced, 10% for normal, and 15% for reduced. This asymmetry — allowing higher consumer risk at reduced levels while maintaining producer risk — reflects the APP philosophy that lower-priority characteristics can tolerate slightly higher acceptance risk. The OC curves for the three levels are provided in the annex for easy reference.

When aggregating inspection results across multiple characteristics with different priority levels, the overall lot acceptance decision follows a “weakest link” rule: the lot is accepted only if all characteristics meet their respective acceptance criteria. A single characteristic at enhanced level can reject an entire lot even if all other characteristics pass at reduced level.

Practical Implementation for Multi-Characteristic Products

For products with 20+ inspected characteristics (common in electronic assemblies and precision mechanical components), the APP coordinated plans offer significant efficiency advantages. Using traditional standards, each characteristic would require its own sample, often leading to impractical total inspection quantities. Under APP, characteristics share the same physical sample units but with different acceptance criteria per characteristic, dramatically reducing the total inspection burden while maintaining appropriate quality assurance across all priority levels.

The sharing of sample units across characteristics assumes independence of characteristics. If two characteristics are physically correlated (e.g., surface finish and coating thickness on the same part), the acceptance/rejection decisions are not independent, and the coordinated plan’s statistical properties no longer hold. In such cases, treat correlated characteristics as a single composite characteristic.

Plan Selection and Implementation Guidelines

The coordinated single sampling plans in ISO 28598-2 are designed for direct use in quality management systems without requiring the full APP scoring framework if the organization chooses to determine priority levels through other means. The standard provides master tables for AQL values ranging from 0.01% to 10% across all three inspection levels (reduced, normal, enhanced), with acceptance numbers (Ac) and rejection numbers (Re) for each combination. The sample size for a given lot size and AQL is determined using the same code letter system as ISO 2859-1, with the priority level determining which column of the master table is used. For example, for a lot of size 10,000 with AQL = 0.65% at normal inspection, the code letter is L (sample size 200, Ac = 5, Re = 6). At enhanced inspection, the code letter increases to M (sample size 315, Ac = 7, Re = 8), while at reduced inspection, the code letter decreases to K (sample size 125, Ac = 2, Re = 5). Note that the reduced plan acceptance number is lower than normal for the same lot size, reflecting that the accept-zero philosophy is partially carried forward — the reduced plan has tighter acceptance criteria per unit sampled, offsetting the reduced sample size to maintain adequate consumer protection.

The geometric scaling of sample sizes (enhanced ≈ 1.6× normal, reduced ≈ 0.6× normal) is calibrated so that the total inspection load remains approximately constant when priority scores are balanced across characteristics or products. This means that implementing APP does not necessarily increase total inspection costs — rather, it redistributes the existing inspection budget to where it provides the greatest quality assurance benefit.

Statistical Properties and Risk Analysis

The coordinated plans’ statistical properties have been carefully calibrated to maintain consistent producer and consumer risks across all three inspection levels. For normal inspection, the producer’s risk (α) is approximately 5% at the AQL, while the consumer’s risk (β) at the limiting quality level (LQL = approximately 5× AQL) is approximately 10%. For enhanced inspection, the consumer’s risk decreases to approximately 5% at the same LQL due to the larger sample size, providing additional protection for high-priority characteristics. For reduced inspection, the consumer’s risk increases to approximately 15%, reflecting the acceptance of slightly higher risk for lower-priority items. The producer’s risk at the AQL remains at approximately 5% for all three levels, ensuring fairness to suppliers regardless of how the characteristic is classified. The operating characteristic curves for all three levels are provided in the annex, enabling quality engineers to verify that the selected plan provides the desired level of discrimination for their specific application. The standard also provides tables of average outgoing quality limit (AOQL) values for each plan, enabling estimation of the maximum long-term average fraction nonconforming in the accepted product stream under the combined effect of sampling and corrective action.

A critical consideration when using the coordinated plans for multi-characteristic products: the overall lot acceptance probability is the product of acceptance probabilities across all independent characteristics. For a product with 10 characteristics each at normal inspection with 95% acceptance probability (at AQL), the overall lot acceptance probability is 0.95¹⁰ ≈ 0.60 (60%). This means that even at the AQL, there is a 40% probability of lot rejection due to the combination of sampling variation across multiple characteristics. Quality engineers must account for this multi-characteristic effect when setting AQL values and planning production quality targets.

FAQ

Q: Can ISO 28598-2 plans be used without implementing the full APP framework?
A: Yes, the coordinated single sampling plans can be used independently as an alternative to ISO 2859-1 for situations where consistency across different inspection levels is desired.

Q: How are switching rules applied in the APP coordinated system?
A: The switching rules from ISO 2859-1 (normal-tightened-reduced) apply within each priority level independently. However, the priority scores themselves should be reviewed quarterly, which provides an additional mechanism for adjusting inspection intensity.

Q: What AQL values are supported?
A: The standard supports the full AQL series: 0.01%, 0.015%, 0.025%, 0.065%, 0.10%, 0.15%, 0.25%, 0.40%, 0.65%, 1.0%, 1.5%, 2.5%, 4.0%, 6.5%, and 10%.