SORT EFFECTIVENESS
& OUTGOING PPM
What a 100% sort actually proved, and what is still going out the door.
A full sort feels like a clean answer. It is not one. Human visual inspection misses parts, and a second and third pass miss more of what is left, not less, because they are working the population the first pass already failed on. This calculator shows the escape rate after inspection and the outgoing PPM after one, two and three passes, then says how many passes your customer's PPM target would really take. Every figure is a band, because the number driving all of it — inspection effectiveness — is almost never measured. PLI Sorting runs documented sorting and containment across Ohio and the industrial Midwest — 216.440.6060.
WHAT THE SORT REALLY LEAVES.
Loaded with a typical suspect lot so there is a number on screen before you touch anything. Change any field and every line below updates. Nothing is sent anywhere; the arithmetic runs in your browser.
After one 100% sort
Pass by pass
Each figure is a band from the effectiveness range you entered. There is no point estimate here on purpose — a single hard number gets pasted into an 8D and defended later.
| Pass | ek | Defectives left | Outgoing PPM | P(≥1 per shipment) |
|---|
Scroll the table sideways →
The arithmetic, line by line
Both ends of the band, worked out in full. Check it against your own numbers before it goes anywhere.
Passes needed to hit the target
—
What the customer's dock sees
Outgoing PPM is a rate across the lot. This is the chance that one individual shipment contains at least one defective part — the number the receiving plant actually experiences.
Reverse check — a clean sample
—
Inputs used on this run
Inputs are within normal ranges. Nothing was clamped.
Disclosure: PLI Sorting sells sorting, containment and inspection. Every extra pass this page counts is a pass we would be paid to run, so we have a direct commercial interest in you concluding that more sorting is the answer. That is exactly why the model here is the pessimistic one: each pass is degraded by ρ, effectiveness is reported as a band rather than a flattering point estimate, and the formula that would make our 200 % and 300 % quotes look good — 1 − (1 − e)ⁿ — is named on this page and refused.
It is also built to say no. Because each pass is weaker than the last, this model has a floor: a PPM the sort converges on and never gets below, however many passes are bought. When that floor sits above your target, the honest answer is that no amount of our labour reaches it, and the money belongs upstream at the process or in a detection method that is not a human eye. The worked example below is exactly that case. If a quote we send you disagrees with the numbers on this page, argue with the numbers.
HOW THIS IS CALCULATED.
Every figure above comes from one of these six steps. No hidden coefficients, no proprietary multiplier, and one formula deliberately not used.
- 1. Each pass is weaker than the last
- The effectiveness of pass k is the first-pass effectiveness knocked down by the degradation factor, once for every pass already run. At e₁ = 0.80 and ρ = 0.65 that is 0.80, then 0.52, then 0.34.
e_k = e₁ × ρ^(k − 1) - 2. Defectives left after n passes
- Start with the defectives in the lot, D₀ = Q × p. Multiply by the fraction surviving each pass, one pass at a time. What is left is the expected escapes.
D_n = D₀ × (1 − e₁) × (1 − e₂) × … × (1 − e_n) - 3. The formula this tool refuses to use
- Treating every pass as an independent draw at full first-pass effectiveness systematically overstates the payoff of 200 % and 300 % sorting, and it errs in the sorting vendor's favour. It is the first thing a customer-side supplier quality engineer checks.
caught after n passes = 1 − (1 − e)^n - 4. Outgoing PPM
- Parts per million defective in what ships. Because D_n is itself Q × p × the survival product, the Q cancels: outgoing PPM turns on the incoming rate and the effectiveness assumptions, not on lot size. A bigger lot means more escaped pieces at the same PPM.
outgoing PPM = (D_n ÷ Q) × 1,000,000 - 5. At least one defect in a shipment
- For a shipment of s pieces drawn from the sorted lot. This is what the customer experiences, and it is usually far more alarming than the PPM behind it: a lot at 1,300 PPM shipped 500 at a time carries a defect in roughly half of all shipments.
P = 1 − (1 − D_n ÷ Q)^s - 6. What a zero-defect sample proves
- Inspect n pieces, find zero defects, and the Clopper-Pearson one-sided upper bound collapses to a closed form. At n = 200 and C = 95 % the bound is 1.487 %. Report it as “with 95 % confidence the defect rate is below 1.487 %” — never as “the lot is good”.
p_UCB = 1 − (1 − C)^(1 ÷ n)
This tool is for planning only. It is not a release or disposition authority. It does not certify stock, does not close a containment, does not clear a lot for shipment, and does not substitute for your customer's procedure. Release and disposition of suspect material stay with the part owner, under their own quality system, their customer's requirements and any active controlled shipping level. A long visual sort does not catch everything — that is the entire point of the numbers above.
Every field marked EST is an assumption we have loaded so the page is useful on arrival. They are typical of sorting work in the Midwest, not measurements from your line. Replace them with PLI's own job data or your own study before the output goes in front of a customer. First-pass effectiveness and the degradation factor move the answer more than anything else on the page — and if the answer comes back “no realistic number of passes reaches the target”, that is the finding, and the fix belongs upstream at the process or in a detection method that is not a human eye.
WHAT THE DEFAULTS
ARE AND AREN'T.
Three inputs above are assumptions rather than measurements. They are marked EST in the form, they are editable, and they should be replaced the moment real data exists.
Incoming defect rate — default 3 %
A placeholder. If containment has already run, use the rate it measured. If it has not, the whole output is only as good as this one guess, and it should be presented that way.
First-pass effectiveness — default 0.70 to 0.85
Commonly cited in the 0.6–0.9 range for human visual inspection. It varies with defect type, part, lighting, cycle time, shift length and crew. Virtually no plant has measured its own, which is exactly why this is a range.
Pass degradation — default ρ = 0.65
A working assumption that later passes are meaningfully weaker, because they only see the parts earlier passes already failed on. Set it to 1.00 and the tool will show you the optimistic answer instead.
How to make these real
Seed a known population of defects into a sample lot and measure what one pass actually catches. That single exercise replaces the two biggest guesses on this page. Until it is done, quote a band and say where it came from.
WHEN NO NUMBER OF PASSES
GETS THERE AND WE LOSE THE JOB.
A tool published by a sorting company is worth nothing if it never says “do not buy another pass.” Here is the shape of job we turn down, with the arithmetic in full. Press Load the 25 PPM target case in the calculator above to run it yourself.
40,000 pieces, 2.0 % incoming defective, customer target 25 PPM. Effectiveness at the same 0.70–0.85 band, degradation at the same ρ = 0.65. That is 800 defective pieces to start, and a target that allows one of them to reach the customer.
A 100 % sort leaves 120 to 240 pieces in the lot. A 300 % sort — three full passes, 120,000 piece touches — leaves 34 to 92. That is 860 to 2,303 PPM against a target of 25: still 34× to 92× over, after touching every piece three times.
The number that ends the argument is the floor. Push the passes out to infinity and the surviving fraction converges: this sort bottoms out at 17 to 51 pieces left in the lot, 418 to 1,283 PPM. The target needs 1 piece. There is no number of passes that reaches 25 PPM on this lot, and every pass after the third is billable labour buying a rounding error.
So the honest recommendation is: run one documented pass for containment if the customer needs product moving today, and put the rest of the budget on the process that is making 2 % defective parts, or on a gauge, a poka-yoke or an automated check that does not depend on a human eye at the end of a shift. We would rather lose the 200 % and 300 % passes than sell you three of them and watch the escalation continue.
The arithmetic
| Stage | Pieces left | Outgoing PPM |
|---|---|---|
| D₀, before any sort | 800 | 20,000 |
| After pass 1 (100 % sort) | 120 – 240 | 3,000 – 6,000 |
| After pass 2 (200 % sort) | 53.7 – 130.8 | 1,343 – 3,270 |
| After pass 3 (300 % sort) | 34.4 – 92.1 | 860 – 2,303 |
| Floor, unlimited passes | 16.7 – 51.3 | 418 – 1,283 |
| What 25 PPM requires | 1.0 | 25 |
Effectiveness by pass: 0.700–0.850, then 0.455–0.553, then 0.296–0.359. Each figure is a band because e₁ is an assumption, not a measurement. The low end of each PPM band is the optimistic e₁ = 0.85; the high end is the conservative 0.70.
The floor is the limit of D₀ × ∏(1 − e₁ρ^(k−1)) as k runs to infinity. It is positive for any ρ < 1, which is the whole argument: degrading passes cannot converge on zero.
FAQ.
How effective is 100 percent visual inspection?
Human visual inspection effectiveness is commonly cited in the 0.6 to 0.9 range, meaning a single 100 % sort finds roughly 60 % to 90 % of the defects that are present. Almost no plant has measured the figure for its own part, its own defect mode and its own crew, so any single number quoted for a specific job is an assumption rather than a measurement. That is why this calculator takes a range and reports a band rather than one hard figure.
Is a 200 percent sort twice as effective as a 100 percent sort?
No. The second pass runs only against the parts the first pass already failed on, which is by definition the harder population, and inspectors are re-examining parts they have already accepted once. Modelling 200 % sort effectiveness as two independent passes at full first-pass effectiveness overstates the payoff. This calculator degrades each pass by a factor ρ, defaulting to 0.65, so pass two is worth substantially less than pass one.
What is the escape rate after inspection?
Escapes are the defective parts that survive the sort. After n passes the expected number remaining is the starting defective count multiplied by the product of (1 − e_k) across every pass, where e_k is that pass's effectiveness. Divide by the lot quantity and multiply by one million and that is the outgoing PPM.
Does a zero-defect inspection sample prove the lot is good?
No. Inspecting 200 pieces and finding nothing supports a statement of the form: with 95 % confidence the defect rate is below 1.487 %. That is an upper confidence bound, not a clearance. On a lot of 20,000 pieces the same clean sample is consistent with roughly 297 defective parts still being in the boxes. Use the reverse check above with your own sample size.
Can this calculator be used to release a lot?
No. It is a planning tool. It estimates outcomes from assumptions you supply, several of which are not measured anywhere. Release and disposition of suspect material remain the responsibility of the part owner under their own quality system, their customer's requirements and any active controlled shipping level.
Why would a sorting company publish a tool that says buy fewer passes?
Because a tool that always recommends the seller is worth nothing to the buyer, and supplier quality engineers check arithmetic for a living. PLI Sorting is paid to run the passes this page counts, so it uses the pessimistic degrading-pass model rather than the independent-pass formula that would flatter a 200 % or 300 % quote, reports effectiveness as a band instead of a point estimate, and publishes a worked example in which no number of passes reaches the customer target and the honest recommendation is to spend the money upstream instead. If a quote from us disagrees with this page, argue with the page.
Why does outgoing PPM not change when I change the lot quantity?
PPM is a rate. Doubling the lot doubles both the defectives that start in it and the defectives that escape, so the ratio is unchanged. Lot quantity does change the piece counts, and it changes how many defective parts reach the customer in absolute terms — which is usually the number that gets escalated.
NEED THE SORT
ACTUALLY RUN?
If the numbers above say you need containment, a documented sort, or an independent third party your customer will accept, that is what PLI Sorting does. We tell you what we find, document what we do, and hand you data you can put in front of your customer.
sales@phillipslightindustrial.com
Lines answered 24 hours a day, 7 days a week.