c=0 Sampling Plans (Zero Acceptance Number)

A c=0 sampling plan is an acceptance sampling plan whose acceptance number is zero: inspect a sample, accept the lot only if it contains zero defectives, and reject the lot on the very first defective found. The most common version is Nicholas Squeglia's Zero Acceptance Number Sampling Plans, derived from ANSI/ASQ Z1.4 but engineered to give equal or better consumer protection with a smaller sample. In exchange, a single defect rejects the lot, which raises the producer's risk at the stated AQL.

c=0 plans are popular in regulated manufacturing, medical devices, pharmaceuticals, aerospace, where "accept on zero defects" reads cleanly against a quality system and where smaller samples cut inspection cost. But the appeal hides a trap: the AQL printed on a c=0 table is an index, not a promise about what quality you are accepting. This guide explains what c=0 plans do, how they compare to Z1.4, how to read the table, and when they actually fit.

What is a c=0 sampling plan?

A c=0 plan is an attribute single-sampling plan defined by two numbers: a sample size n and an acceptance number of zero. You draw n pieces at random from the lot, inspect them against pass/fail criteria, and apply the simplest possible rule, zero defectives, accept; one or more, reject. There is no double sampling, no acceptance number to remember, and in Squeglia's system no normal/tightened/reduced switching rules. That plainness is much of why floors like it.

The plans come from Nicholas Squeglia, whose Zero Acceptance Number Sampling Plans (now in its fifth edition, published by ASQ) tabulates a sample size for each combination of lot size and AQL. Squeglia derived those sample sizes from the ANSI/ASQ Z1.4 plans, but with a specific design goal: match the consumer's risk the protection against accepting bad quality, that the corresponding Z1.4 plan provides, while shrinking the sample. The result is a table you enter with lot size and AQL and leave with a single number, n.

How does c=0 compare to ANSI/ASQ Z1.4?

Z1.4 lets the acceptance number be greater than zero. A Z1.4 plan might say "sample 80, accept if 2 or fewer defectives, reject if 3 or more," and it layers on switching rules that tighten or relax inspection based on the supplier's recent history. c=0 throws all of that out: acceptance number fixed at zero, no double sampling, no switching. For the same AQL and lot size, the c=0 sample is smaller, often much smaller, than the Z1.4 sample, because a plan that rejects on any defect can protect the consumer with fewer pieces.

The catch lives in the operating characteristic (OC) curve, which plots the probability of accepting a lot against the lot's true fraction defective. Squeglia matched his plans to Z1.4 at the consumer's-risk point the poor quality level that should almost always be rejected, not at the AQL. So the two curves pass through roughly the same low point, but the c=0 curve is a different shape: for a plan of sample size n, the probability of acceptance is (1 − p) raised to the n, a curve that starts dropping immediately as defect rate rises. A Z1.4 plan with acceptance number above zero stays near 100% acceptance longer before falling. The practical consequence: at the AQL, a c=0 plan rejects good lots more often than the matched Z1.4 plan. That is the higher producer's risk you trade for the smaller sample.

Laid side by side, the two systems trade simplicity and sample size against producer protection and built-in adaptivity:

Neither column is "better" in the abstract. Z1.4's switching rules make it well suited to a steady supplier relationship where inspection effort should track demonstrated performance. c=0's plainness and small samples make it well suited to gate checks on strong quality, or to inspections where every tested piece is expensive or destroyed.

How do you read a c=0 table?

Reading a Squeglia table is four steps, and the fourth is the one people skip.

1. Determine your lot size. The tables are banded by lot size (for example, 51–90, 91–150, 151–280, and so on). Larger lots draw larger samples.
2. Choose the AQL to index on. The columns are labeled by AQL (0.010 up through 10). Pick the AQL your specification, customer, or standard calls for. Treat this as the row-and-column address, not as the quality you are guaranteed.
3. Read the sample size, n. The cell at the intersection of lot-size band and AQL gives the number of pieces to inspect. The acceptance number is always zero, so there is nothing else to look up.
4. Apply the accept-on-zero rule and record it. Inspect the n pieces; accept the lot if all pass, reject if any fail. Because rejecting on one defect is a strong action, document the plan (lot size, AQL index, n) so the decision is traceable and repeatable.

A worked feel for the OC curve, using round numbers: a c=0 plan with a sample of 30 accepts a lot with probability (1 − p) to the 30th power. At 1% true defective that is about 0.74, so even a fairly good lot gets rejected about a quarter of the time. At 5% defective it is about 0.21, and the 10%-acceptance (consumer's-risk) point lands near 7.4% defective. Those numbers are the mechanics of (1 − p) to the n; a real table entry will differ, but the shape is always this: acceptance falls off from the very first bit of defect rate.

When do c=0 plans fit, and when do they hurt?

c=0 plans fit when two conditions hold together: your process quality runs comfortably better than the AQL, and the cost or risk of one defect reaching the customer is high. That is exactly the profile of much FDA-regulated production, which is why zero-acceptance plans are common in device and pharmaceutical incoming and finished inspection, the philosophy of "we do not knowingly accept any defect" aligns with the regulatory posture, and the smaller sample lowers destructive-test and inspection cost.

They hurt when quality sits near the AQL. Because the OC curve drops immediately, a process producing at or just below its AQL will see good lots rejected often, driving needless rework, re-inspection, and supplier friction. c=0 is not a license to accept marginal quality with less looking; it is a tool for confirming quality that is already strong. Two more cautions:

• The AQL is an index, not an acceptance quality. Squeglia's plans are matched on consumer risk, so the AQL column is a lookup key. Reading "AQL 1.0" as "1% defective is fine" misreads the plan.
• No switching rules means no built-in memory. Z1.4 rewards good suppliers with reduced inspection and punishes bad ones with tightened inspection. c=0 has none of that, so pair it with your own supplier history and supplier quality management to decide when a plan should change.

The standards behind zero-acceptance sampling

Zero-acceptance sampling is well documented and tied to the mainstream sampling standards. The facts worth keeping straight:

• The definitive tables are Nicholas Squeglia's Zero Acceptance Number Sampling Plans, fifth edition published by ASQ Quality Press (ASQ, H1331).
• They are derived from and indexed to ANSI/ASQ Z1.4 the standard for attribute acceptance sampling by AQL, matching its consumer's-risk protection with a smaller sample and acceptance number zero (ANSI/ASQ Z1.4).
• For a single-sampling c=0 plan of size n the probability of accepting a lot with fraction defective p is (1 − p) to the n, the OC curve that falls from the first defective onward.

Where c=0 sits in your inspection strategy

A c=0 plan is an acceptance decision at a gate, most often incoming material inspection or final lot release, not a monitoring tool. That distinction matters: acceptance sampling judges lots pass/fail, while a c-chart or the wider practice of statistical process control watches the process over time. The two work together, and the sampling choice also depends on whether you are counting defects or measuring dimensions, which is the attribute versus variable inspection question. Sitting underneath all of it is the AQL you index on; the companion guide to the acceptable quality level and the walkthrough of ANSI/ASQ Z1.4 cover where that number comes from and how the parent standard behaves.

The operational weak point of any sampling plan is the same one that hurts a control chart: the record. A c=0 rejection is a strong, traceable action, and it needs to travel with the lot, the supplier, and the disposition. Capturing the inspection result at the receiving dock, the way Harmony's live capture and shop-floor visibility tooling does, keeps the plan, the sample size, and the accept-or-reject decision searchable instead of buried on a clipboard, so the next audit, and the next supplier conversation, has the evidence already assembled. c=0 is a simple plan. Keeping its decisions honest and findable is where the work actually is.