Losses multiply, they do not add
Five stages that each pass 97 per cent do not pass 85 per cent. They pass 0.97 to the fifth, which is 85.87 per cent, and the difference is small enough that adding them is a fair rough answer. That is the boring half of the arithmetic and it is not where the money is.
The money is in the ordering. Every stage a unit survives, it becomes more expensive to throw away, because it has picked up another input on the way. A container rejected off the pallet has cost you a container. The same container rejected at the final check has cost you the container, the product inside it, the closure and the label, and the labour of putting all four together. Two identical one per cent reject rates at opposite ends of a line are not the same number in any sense that matters.
Which is why inspection moves to the front
| Unit dies at | What has gone into it | Who notices |
|---|---|---|
| Incoming inspection | The container | Nobody — you throw it in the bin and reach for the next |
| Fill | Container and product | The floor, usually |
| Capping | Container, product and closure | The person capping, who has to clear it |
| Labelling | Everything but the case | Everyone, because the line stops |
| Final check | All of it plus the labour | The margin |
Looking over the empties as they come out of the case is dull and takes seconds, and it is the cheapest inspection available because it catches the failure at the point where it costs the least. It is also the one most often skipped, because the payoff is invisible: nothing happens, which is the point.
Two kinds of label loss, and they are not the same
A unit written off at the labelling stage takes the container, the product, the closure and the label with it. A label ruined on its own — crooked, torn, wasted setting up the applicator — costs a label and the unit carries on. Both are real and they belong in different fields, because at typical costs the first is ten or twenty times the second. Putting all your label trouble into one number will either overstate what a spoiled label costs or hide how expensive the write-offs are.
Where the other numbers come from
Labels to buy, including the roll arithmetic, are on the bottle label wrap calculator. Good units into cases, and the case weight, are on the bottles per case calculator. How long the run takes and which station sets the pace is the bottling line throughput calculator. For a per-unit bill of materials across several inputs bought in packs, without the loss modelling, use the material cost per unit calculator. And for whether a bigger pack of packaging is worth buying at all, the bulk buy optimizer compares pack sizes on true cost per unit.
Questions people ask
Why not just add the loss percentages together?
For the start quantity, adding them is close enough at small rates — five stages of three per cent compound to 14.1 per cent of loss against 15 added. The reason to keep them separate is not precision, it is that the calculator needs to know which stage each loss happens at to work out what it costs. A one per cent loss at the front and a one per cent loss at the end are the same number of units and very different money.
Where do I get the loss rates?
From counting on one real run. Keep a tally by stage — rejected empties in one pile, spoiled at fill in another, and so on — and divide by what reached that stage. It takes one run and you own the figures. Nothing on this page supplies a default that means anything, because the rates depend on your containers, your closures and your equipment.
What counts as product spill?
Everything that leaves the batch without going into a container: the hose, the pump, what is left in the bottom of the tank, drips and the transfer losses. Measure it by comparing the volume you made with the volume that ended up in containers. On a small line it is often larger than any single reject rate and it never shows up as a unit count.
The last stage seems disproportionately expensive.
It is, and that is the useful finding rather than a quirk of the model. By the final check the unit contains the container, the product, the closure, the label and the labour of assembling all of them. The same reject rate at the front of the line costs only the container. That ratio is printed on the page for your own numbers.
Does this say anything about what an acceptable reject rate is?
None at all, and that is deliberate. Labelling is one of the most heavily regulated corners of small manufacturing, the rules differ by product type and by state, and they move. This page has no rule about what goes on a label, how net contents are declared, what counts as an acceptable fill, or how anything may be shipped. It measures containers, labels, cases and station times. The rules come from the agency that regulates your category and from a lawyer.