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ISO 28591:2017 — Sequential Sampling Plans for Inspection by Attributes
Minimizing inspection costs through sequential probability ratio testing for attribute quality characteristics.
Introduction to ISO 28591
ISO 28591:2017 specifies sequential sampling plans for inspection by attributes, indexed by producer’s risk quality (PRQ) and consumer’s risk quality (CRQ). The standard replaced ISO 8422:2006 as part of the ISO/TC 69/SC 5 renumbering initiative that consolidated several acceptance sampling standards under the 28590-28599 numbering range. Sequential sampling offers the smallest average sample size among all sampling plan types with equivalent statistical properties — achieving up to 85 % reduction compared to single sampling plans for very good quality lots while maintaining rigorous control of both producer’s and consumer’s risks.
For expensive or destructive testing, sequential sampling according to ISO 28591 can dramatically reduce the number of items that need to be inspected while maintaining rigorous statistical control of both producer’s and consumer’s risks.
Principles of Sequential Sampling
Unlike single sampling (fixed sample size), sequential sampling draws items one at a time, updating the cumulative count of nonconforming items after each inspection. After each item, one of three decisions is made: accept the lot, reject the lot, or continue sampling. The decision boundaries are defined by two parallel lines on a graph of cumulative nonconforming items versus cumulative sample size, calculated from the specified PRQ, CRQ, and the associated risk levels. This approach minimizes the amount of inspection needed by continuously evaluating whether sufficient evidence has accumulated for a decision.
| Plan Type | Sample Size Flexibility | Avg. Sample Size (good quality) | Admin. Complexity |
|---|---|---|---|
| Single | Fixed | 100 % | Low |
| Double | Two stages | ~63 % | Medium |
| Multiple | Multiple stages | ~25 % | Medium-High |
| Sequential | Item-by-item | ~15 % | High |
Curtailment and Practical Implementation
A key feature of the sequential plans in ISO 28591 is the introduction of a curtailment rule — an upper limit nₜ on the number of items inspected. Without curtailment, the sequential process could theoretically continue indefinitely if quality hovers near the indifference zone, which is the region where the cumulative count remains between the acceptance and rejection lines. The operating characteristics of the plans are computed with curtailment factored in, so it is an integral component rather than an afterthought. Two implementation methods are provided: the numerical method using an acceptability table where pre-calculated acceptance and rejection numbers are listed for each sample size, and the graphical method using an acceptability chart where the cumulative results are plotted against decision lines.
The curtailment limit prevents the pathological case where a sequential plan continues indefinitely. However, if the curtailment limit is reached, the decision is based on a pre-determined acceptance/rejection rule that may have different statistical properties than the pure sequential plan.
Engineering Design Insights
ISO 28591 is particularly valuable in high-cost testing scenarios and regulatory compliance contexts where both producer’s and consumer’s risks must be strictly controlled. The standard explicitly contrasts its plans with those in ISO 2859-5: ISO 2859-5 plans are designed for the continuing-series AQL system and rely on switching rules for consumer protection, whereas ISO 28591 plans control both risks directly — making them suitable for isolated lots, regulatory testing, and hypothesis testing applications where each lot must be evaluated independently.
Practical Considerations
The standard acknowledges several practical challenges: sequential rules are more easily misunderstood by inspectors than single sampling; scheduling is difficult because sample size is not known in advance; if drawing samples at different times is expensive, the savings may be offset; and if tests are time-consuming and items can be tested simultaneously, sequential plans may take longer overall. These factors must be weighed against the sample size reduction when selecting a sampling plan type.
Frequently Asked Questions
Q: What is the maximum possible sample size reduction with sequential sampling?
A: Up to 85 % compared to single sampling plans for very good quality lots, with average savings typically in the range of 50-85 %.
A: Up to 85 % compared to single sampling plans for very good quality lots, with average savings typically in the range of 50-85 %.
Q: What is curtailment and why is it needed?
A: Curtailment is an upper limit on the number of items inspected. It prevents the sequential plan from continuing indefinitely when quality is borderline.
A: Curtailment is an upper limit on the number of items inspected. It prevents the sequential plan from continuing indefinitely when quality is borderline.
Q: What is the difference between ISO 28591 and ISO 2859-5?
A: ISO 2859-5 provides sequential plans within the AQL system for continuing series of lots. ISO 28591 provides plans that directly control both producer’s and consumer’s risks, suitable for isolated lots and regulatory testing.
A: ISO 2859-5 provides sequential plans within the AQL system for continuing series of lots. ISO 28591 provides plans that directly control both producer’s and consumer’s risks, suitable for isolated lots and regulatory testing.
Q: Which implementation method is recommended — numerical or graphical?
A: The numerical method (acceptability table) is generally preferred for routine use as it is less prone to reading errors. The graphical method is useful for training and visualization.
A: The numerical method (acceptability table) is generally preferred for routine use as it is less prone to reading errors. The graphical method is useful for training and visualization.
