Sampling

Sampling is the process of selecting a subset of items (parts, documents, people, etc) from a larger group (called a population or lot) to inspect or test, so you can make judgments about the entire group without checking every item.

It is useful for determining whether to accept an entire group (based on the results of a subset of that group), improving a process (checking to see if results are getting better or worse), or ensure consistent quality (compare differences from previous results).

It can be based on one or more binary outcomes (either pass/fail or good/bad) or measurements (numeric or continuous data such as 14.7 or 0.344) that must fall within a specification range (above, below or between).

Key Terms:

• Lot: The full group of items you’re sampling from.
• Sample: The smaller group you actually inspect.
• Sampling Plan: A set of rules that tells you how many items to inspect and how to decide if the lot passes or fails.
• Acceptance Number: The maximum number of defects allowed in the sample for the lot to be accepted.
• Rejection Number: If defects exceed this number, the lot is rejected.

For example, you receive a shipment of 1,000 batteries. Instead of checking all 1,000, you randomly select and inspect 50 batteries:

• If 2 or more bulbs are defective (if Rejection Number = 1), you reject the entire shipment.
• If 0 or 1 battery is defective, accept the shipment.

Here is a summary of sampling plans for checking the quality conformance or acceptance of items during a test or inspection. The result of each item selected in these sampling approaches would be binary

1. Single Sampling Plans

• Most basic form of sampling plan.
• A single sample is taken from the lot and the number of nonconforming items is counted.
• If the count is within the acceptance number, the lot is accepted; otherwise, it is rejected.
• Often used when testing is destructive or costly, or when simplicity is preferred.

2. Double Sampling Plans

• Involves two sequential samples:
• If the result from the first sample is inconclusive (not clearly acceptable or rejectable), a second sample is taken.
• The combined result determines acceptance or rejection.
• Reduces average sample size when the process quality is very good or very poor.

3. Multiple Sampling Plans

• Similar to double sampling but involves more than two samples.
• Useful in scenarios where decisions can be made earlier (after fewer samples) for very good or very poor quality lots.
• Provides flexibility and efficiency but is more complex to administer.

4. Sequential Sampling Plans

• Items are inspected one at a time, and the decision to accept, reject, or continue sampling is made after each inspection.
• Highly efficient in terms of minimizing sample sizes.
• Requires real-time analysis and clear decision boundaries (often graphically presented).

5. Skip-Lot Sampling Plans (abbreviated as S-lot sampling)

• Not every lot is inspected, based upon a set of rules that encourages less sampling as quality improves.
• Inspection is reduced or waived for some lots based on prior performance and history.
• Suitable for stable, high-quality processes.
• Can have significant reduction in time and resources with minimal impact on defective items getting through.

Links

• MIL-STD-105 – United States defense standard for sampling with binary or attribute outcomes. Developed from the work by Walter Shewhart, Harry Romig, and Harold Dodge.
• Replaced by ASTM E2234, MIL-STD-1916, “DoD Preferred Methods for Acceptance of Product”, or ANSI/ASQ Z1.4, “Sampling Procedures and Tables for Inspection by Attributes” and ISO 2859 “Sampling procedures for inspection by attributes.”
• ANSI/ASQ Z1.4 and ISO 2859-1 both originated from the MIL-STD-105