Calculations

How to Calculate Case Forming Yield, Charge Weight Cpk, and Primer Line Capacity

Work the five core calculations in ammunition component manufacturing with real units and worked examples: rolled forming yield, charge weight capability, projectile weight screening, primer assembly capacity, and velocity statistics.

Ammunition component manufacturing runs on five calculations: rolled yield through the case forming line, charge weight process capability on the powder drop, statistical screening limits for projectile weight, primer assembly line capacity, and velocity statistics from the test range. Every one of them uses inputs you already collect, counts at each forming station, scale readings in grains, cycle rates in parts per minute, and chronograph strings in feet per second. This guide works each formula with real numbers so an operator or process engineer can reproduce the math on a clipboard, then check the result against the matching calculator.

Case forming yield is multiplicative, not additive. If cups pass through cup, three draws, trim, head, anneal, and taper, rolled throughput yield equals the product of the station yields: RTY = y1 x y2 x ... x yn. Start 100,000 brass cups with stations at 99.4, 99.1, 98.8, 99.5, 99.0, 99.7, and 99.3 percent and you finish with 100,000 x 0.9493, about 94,900 acceptable cases, even though no single station looks bad. Count rejects at each station per shift, divide by pieces entering that station, and feed the station yields into the Case Forming Yield Calculator to see which draw stage costs the most brass.

Powder fill accuracy is a capability problem. Weigh 50 consecutive charges on a scale with 0.02 grain resolution, compute the mean and standard deviation, then Cpk = min(USL minus mean, mean minus LSL) divided by 3 sigma. Example: target 24.5 grains with limits of 24.2 and 24.8, measured mean 24.54 gr and sigma 0.08 gr. Cpk = (24.8 minus 24.54) / (3 x 0.08) = 0.26 / 0.24 = 1.08, which predicts roughly 600 charges per million outside the high limit. The Powder Fill Accuracy Audit Calculator handles the z score conversion and flags whether the problem is centering, so shift the drop, or spread, so fix the powder bridging.

Projectile weight variation screening uses the same statistics in reverse: given a weight tolerance, predict the reject rate. A 168 grain match bullet with sigma of 0.15 gr and a screening window of plus or minus 0.45 gr sits at z = 3.0, so expect about 2,700 rejects per million, or 0.27 percent. Tighten the window to plus or minus 0.30 gr, which is z = 2.0, and rejects jump to 4.55 percent, seventeen times the fallout for a marginal consistency gain. Weigh a random sample of 100 to 200 bullets per lot to estimate sigma, then use the Projectile Weight Variation Screening Calculator to set a window that balances fallout against downstream velocity spread.

Primer assembly capacity is rated speed multiplied by real availability. Capacity per shift = machine rate in parts per minute x 60 x scheduled hours x uptime fraction x first pass yield. A cup and anvil insertion line rated at 400 parts per minute, scheduled 7.5 hours with 78 percent uptime and 99.2 percent yield, delivers 400 x 60 x 7.5 x 0.78 x 0.992, about 139,300 good primers per shift, not the 180,000 the nameplate implies. Log downtime in minutes by cause code for two weeks to get an honest uptime number, then run scenarios in the Primer Assembly Capacity Calculator before promising delivery dates.

Ballistic consistency math comes off the chronograph. For a test string of n rounds, standard deviation of velocity = sqrt(sum of (vi minus vbar) squared / (n minus 1)), and extreme spread is simply max minus min. A 10 round string averaging 2,700 fps with an SD of 12 fps will typically show an ES of 35 to 40 fps, and because expected ES grows with sample size, a 30 round string from the same lot can read 55 fps with no process change at all. Write acceptance specs on SD with a defined n, never on ES alone, and record string size with every result so lots stay comparable.

Input quality decides output quality. Scale calibration matters: a check weight drift of 0.05 gr biases every Cpk you compute. Station counts must come from piece counters, not operator estimates, which typically understate rejects by 15 to 30 percent. Sample sizes below 30 make sigma estimates unstable; at n = 10 the confidence interval on SD spans roughly 0.7 to 1.8 times the point estimate. Once the core numbers are trusted, the same data feeds planning tools such as the Lot Traceability Workload Calculator for documentation time and the Ballistic Test Lab Workload Cost Calculator for range scheduling, but the forming yield, charge Cpk, and capacity math above is where every analysis starts.

Published 2026-07-02.