Line read rate and reject analysis
Enter the totals: first-read successes, second-attempt successes and rejects. The tool calculates the first-pass, final read and reject rates, the distance to your target rate and the extra reads needed to reach it, and shows confidence intervals for the rates. If you paste shift or day rows it also summarises the trend.
The calculation runs in your browser; the numbers you enter are not sent anywhere.
Result
| Result | Rate | 95% confidence interval |
|---|---|---|
| First-pass read rate11,760 items | 98.00% | 97.73 – 98.24 |
| Final read rate11,910 items | 99.25% | 99.08 – 99.39 |
| Reject rate90 items | 0.75% | 0.61 – 0.92 |
Recovered by second attempt: 1.25% (150)
Target
- Target
- 99.50%
- Distance to target
- -0.25 percentage points
Below target.
Extra successful reads needed to reach the target: 30
Most rejects that still meet the target at this total: 60
The upper bound of the interval is below the target: you are very likely below target.
first-pass = first / total · final = (first + second) / total · reject = rejected / total · extra needed = ⌈target × total⌉ − successes · Wilson: (p + z²/2n ± z√(p(1−p)/n + z²/4n²)) / (1 + z²/n)
The tool processes the numbers you enter; it cannot say what causes read failures (print quality, light, position, camera settings). The confidence interval shows sampling uncertainty, not the error of the measuring system itself; items are assumed to be independent and read under the same conditions, and differences between shifts can break this assumption. Target rates must come from your company's, your customer's or the relevant regulation's specification; this calculation is not legal or technical advice.
Let's measure print quality, camera position and lighting on the line together to bring the read rate to target.
Request a conversation01
How to use it
A
Enter the total, first-read successes, second-attempt successes and rejects; add a target rate if you wish.
B
Read the first-pass, final and reject rates, their confidence intervals and the extra reads needed to reach the target.
C
For several shifts or days switch to "list" mode; paste the rows, see the trend and download the CSV.
02
First pass or final read?
The first-pass read rate is the share of items read successfully on the first read, with no retry. The final read rate also counts those recovered on a second attempt. The gap between them shows how much of the line depends on retries (a second camera, a reprint, a manual scan).
A line with a high final rate but a low first-pass rate seems to work; it still loads retry capacity, line speed and labour. Watch both.
03
Why a confidence interval?
A read rate is calculated from a sample; 99.5% on 200 items is not as reliable as 99.5% on 20,000. The Wilson interval gives the plausible range for the observed rate, and stays useful even when rates are close to zero or one hundred percent.
If the target lies inside this interval, this sample cannot decide whether you are below or above target; reading more items narrows the interval. If the whole interval is below the target, improvement is needed.
04
Distance to target and improvement needed
When you enter a target rate, the tool shows how many percentage points the observed rate is from the target, the most rejects that still meet the target at the same total, and the extra reads needed to reach it. The extra count is a point estimate: it says how many of the rejects in a total would have to be recovered.
For shift or day rows the tool also calculates a linear slope and a two-proportion test between the first and second half. With few rows the slope is unreliable; the half comparison looks at whether the difference could be chance.
FAQ
- Why must the total equal first + second + rejected?
- Each item falls into exactly one of three outcomes: read on the first attempt, read on the second attempt or rejected. If the total is not the sum of the three, one of the numbers is missing or counted twice; the tool reports the difference and does not calculate.
- What is the difference between the Wilson interval and a simple approximate interval?
- The simple (Wald) interval misleads when the rate is near zero or one hundred percent and the sample is small, and can even give impossible values (above 100%). The Wilson interval is more reliable in these cases; it is preferred because read rates are usually above 99%.
- What should I enter as the target rate?
- The value your company, your customer or the relevant specification asks for. The tool does not propose a target. If the target applies to the first pass or to the final rate, choose that with "Apply the target to".
- What does the confidence level mean?
- If the same line were measured many times under the same conditions, the chosen percentage of the calculated intervals would contain the true rate. 95% is a common choice; 99% gives a wider and 90% a narrower interval.
- How far can I trust the trend result?
- The slope takes the rows to be in time order and is unstable with few rows. The comparison of the first and second half catches a big difference but does not know outside factors such as shift order, product mix and maintenance. Interpret the finding together with line records.
Let's improve the read rate on your line together
We carry out print quality grading, camera position and lighting tuning and the classification of reject causes on site, and measure until you reach the target rate.