Acceptance Number
Understanding the Acceptance Number (Ac)
If a massive factory in Taiwan builds 10,000 RF amplifiers in a single day, it is economically and physically impossible to test every single one of them. To guarantee quality without testing all 10,000, the factory relies on Statistical Sampling (AQL). The absolute core of this process is the Acceptance Number.
The Mathematics of the Sample
The factory uses a massive, standardized mathematical chart (like the ANSI Z1.4 tables) to determine exactly how many units they need to test.
- For a batch of 10,000 amplifiers, the chart dictates they must randomly pull exactly 200 units off the assembly line.
- The chart also provides the golden numbers based on the strictness of the contract. It provides the Acceptance Number (Ac) and the Rejection Number (Re).
- For a standard enterprise contract, the chart might say: Ac = 5, Re = 6.
The Pass/Fail Guillotine
The engineers put the 200 amplifiers onto the test benches and blast them with radio waves.
- If they find 4 broken amplifiers, the number is below the Acceptance Number (5). The factory mathematically guarantees the overall quality of the batch. The 4 broken units are thrown away, and the remaining 9,996 units are immediately shipped to the customer.
- If they find exactly 6 broken amplifiers, the number hits the Rejection Number. The mathematical sample has failed. The entire batch of 10,000 amplifiers is instantly locked down. The factory must halt the assembly line, find exactly which robotic arm is malfunctioning, and physically test every single one of the remaining 9,800 amplifiers by hand.
Key Equations
Maximum defectives allowed in sample for lot acceptance
Binomial probability:
P(X ≤ c) = Σk=0c C(n,k)pk(1−p)n−k
Poisson approximation (np < 5):
P(X ≤ c) = Σk=0c (np)ke−np/k!
Comparison
| c | n=50 AQL=1% | n=100 AQL=1% | Producer risk | Notes |
|---|---|---|---|---|
| 0 | P(acc)=0.61 | P(acc)=0.37 | 39–63% | Very strict |
| 1 | P(acc)=0.91 | P(acc)=0.74 | 9–26% | Strict |
| 2 | P(acc)=0.99 | P(acc)=0.92 | 1–8% | Standard |
| 3 | P(acc)=1.00 | P(acc)=0.98 | <2% | Lenient |
| 5 | P(acc)=1.00 | P(acc)=1.00 | <0.1% | Very lenient |
Frequently Asked Questions
Can the Acceptance Number be Zero?
Yes, this is called a C=0 (Zero Acceptance Number) sampling plan. It is heavily utilized in mission-critical aerospace and medical RF engineering. If the contract mandates C=0, the engineers pull the random sample of 200 units. If even a single, solitary unit fails the test, the entire batch of 10,000 is instantly quarantined. This forces the factory to maintain absolute perfection on the assembly line.
Who decides what the Acceptance Number is?
The customer and the manufacturer negotiate the AQL (Acceptable Quality Limit) percentage in a legally binding contract before manufacturing begins. If the customer is buying cheap $10 plastic routers, they might agree to a loose 2.5% AQL (allowing a high Acceptance Number). If the customer is the US Military buying $50,000 missile radar chips, they will legally demand an astronomically strict 0.01% AQL.
What happens to the 10,000 units if the batch is rejected?
It depends on the cost of the hardware. For cheap consumer electronics, the entire batch is literally thrown into a massive shredder, because paying human engineers to test all 10,000 by hand is more expensive than the plastic. For expensive telecom hardware, the batch is put into '100% Sorting.' Every single unit is manually tested, the broken ones are scrapped, and only the flawless ones are allowed to ship.