Capacity Math: Machines x Cycle Time x Yield

Nameplate Capacity Is a Sales Number

Every factory has two capacities. The first is the number in the presentation: machines multiplied by a rated speed, multiplied by twenty-four hours, multiplied by thirty days. The second is what actually leaves the loading dock. The gap between them is usually between thirty and fifty percent, and it is made of changeovers, breakdowns, rework, holidays and the simple fact that machines do not run unattended through the night.

Capacity math is not difficult. What makes it an audit skill is knowing which numbers to distrust and how to test them against history.

The Core Formula

For a single process, monthly output is the product of machine count, available hours, output per hour, and yield. Written out:

• Machines in the process, counted on the floor and not in the asset register.
• Available hours per machine per month, after shifts, breaks, holidays and planned maintenance.
• Cycle time in seconds per shot or per stroke, measured rather than quoted.
• Cavities or parts per cycle, for molding and stamping.
• Yield, expressed as good parts divided by parts started.

A Worked Example

Suppose a molding hall has thirty machines running two shifts of eleven hours, twenty-six days a month. That is five hundred and seventy-two hours per machine per month. At a nine-second cycle with two cavities, one machine produces eight hundred shots per hour and one thousand six hundred parts per hour. Thirty machines at full running time would produce just over twenty-seven million parts a month, which is never the real number.

Apply realistic availability of seventy-five percent and yield of ninety-seven percent, and the figure falls to roughly twenty million. Apply a further allowance for changeover and colour changes, and eighteen million is a defensible planning number. The difference between twenty-seven and eighteen million is not arithmetic error; it is the difference between a rated machine and a factory.

Measure Cycle Time, Do Not Accept It

Stand at a machine with a stopwatch and time ten cycles. Then compare with the quoted cycle.

• Is the quoted cycle the mold-open to mold-close time, or does it include part removal and inspection?
• Does the operator perform any secondary operation inside the cycle, such as degating or visual check?
• Does the cycle slow down when the operator is away, and who covers the machine?
• Is the machine actually running at the quoted parameters, or derated for quality?
• How long does a colour or tool change take, and how often does it happen?

Availability and the Real Calendar

Ask for the production calendar for the last twelve months and for the next three. Then ask for downtime records by machine.

• Shift pattern, including whether night shift is fully staffed or skeleton.
• Public holidays and the factory closure period, which is often longer than the official holiday.
• Planned maintenance hours per machine per month.
• Unplanned downtime hours per machine, by cause, for the last three months.
• Hours lost to material shortage, quality holds and power interruption.

A factory that cannot separate planned from unplanned downtime is telling you that it does not measure availability. In that case, use seventy percent as a planning assumption and state it in the report.

Yield and the Rework Loop

Yield is where capacity claims quietly inflate. A part that is reworked is not a good part on first pass, and the rework consumes capacity that the formula has already allocated to new production.

• First pass yield, by process, for the last three months.
• Rework hours as a percentage of total production hours.
• Scrap rate by process, and whether scrap is counted at the machine or at final inspection.

Ask for scrap weight per month and compare it with purchased material weight. The ratio should roughly match the claimed yield. If it does not, one of the two numbers is wrong.

Find the Bottleneck Before You Multiply

Capacity is set by the slowest process, not by the largest machine count. Map the chain and calculate each step.

• Weaving: looms multiplied by metres per hour multiplied by running hours.
• Dyeing: vessel kilos per cycle multiplied by cycles per day.
• Molding and stamping: machines multiplied by parts per hour.
• Plating: barrel or rack capacity per cycle, which is often the hidden constraint.
• Assembly and inspection: pieces per operator hour, which is usually labour-limited.

Plating is the step most often missed in capacity claims, because it is measured in barrels rather than in machines. Ask for the barrel cycle time and the load per barrel, then calculate independently.

Cross-Check Against History

The best test of a capacity claim is the shipment record. Ask for monthly shipments by product family for the last twelve months and compare the peak month with the claimed capacity.

• If the peak month is well below the claim, ask what constrained it.
• If the peak month exceeds the claim, ask how, because it means the formula is wrong or the records are.
• Check whether the peak month was achieved with overtime or with subcontracting, and how much of each.
• Ask what the factory would have to add to reach the claimed number, and in what time.

The Actionable Audit Checklist

• Machine count taken from the floor, not from the asset register.
• Cycle time measured with a stopwatch for at least ten cycles.
• Quoted cycle time states what it includes and excludes.
• Shift pattern and holiday calendar obtained in writing.
• Planned and unplanned downtime separated by machine and cause.
• First pass yield obtained by process for three months.
• Rework hours are counted against production hours.
• Scrap weight reconciles with purchased material weight.
• Bottleneck identified with arithmetic for every process step.
• Plating capacity calculated from barrel cycle and load.
• Shipment history cross-checked against the capacity claim.
• Subcontracted volume identified and excluded from in-house capacity.

What a Passing Answer Looks Like

Passing sounds like this: "We claim four hundred thousand sliders a month from molding, but plating limits us to three hundred and ten thousand, so three hundred and ten is the number we commit." That answer shows the factory knows its own constraint and is willing to name it. YCC treats that kind of answer as a stronger signal than any capacity chart, because a supplier that names its bottleneck can usually plan around it.