Production Cost Curves

References
The Missile Defense Equation: Factors for Decision Making by Peter J. Mantle

CostCurrentUnit = CostFirstUnit * NumberBuiltLCF

Where:

CostCurrentUnit = How much it will cost to build the current unit.

CostFirstUnit = How much it cost to build the first unit.

NumberBuilt = How many units have been built to date.

LCF = Learning Curve Factor (Derived from Learning Curve Slope – See Below)

Example

We want to produce 55,000 missiles for the US Air Force. Initial reports from the engineering department estimate that the first missile off the production line will cost us about $15 million. Assuming a Learning Curve Slope of 80%, how expensive will be the 15,000th and 55,000th missiles built?

15,000,000 * 15,000-0.322 = $678,250 for the 15,000th missile.

15,000,000 * 55,000-0.322 = $446,369 for the 55,000th missile.

Computing Learning Curve Factor

ln(Learning Curve Slope) / ln(2)

If we wanted to compute the LCF for a learning slope of about 80%; our equation would be:

ln(0.80) / ln(2) = -0.322

Some LCFs are:

10% = -4.322
20% = -3.322
30% = -2.322
40% = -1.737
50% = -1.322
60% = -0.737
70% = -0.515
80% = -0.322 (Typical in Aircraft Production)
90% = -0.152 (Typical in Ship Production)
95% = -0.074 (Typical in Ship Production)