103.53
8.63 per delivered partA 10% failure rate is not a 10% cost uplift
If each attempt independently has a 10% chance of failing, a successful plate requires 1 / 0.9 = 1.1111 attempts on average. At 50%, it requires two. At 95%, it requires twenty. The tool supports failure rates up to 95% and warns about high rates rather than presenting them as ordinary production assumptions.
Expected attempts = successful plates / (1 − failure rate)
Expected failed attempts = expected attempts − successful plates
What gets repeated?
Material, electricity, depreciation and maintenance repeat for every attempt. Cleanup and restart labour applies to failed attempts. Initial order setup, finishing of delivered good parts and packaging do not repeat. This distinction prevents a blanket risk multiplier from incorrectly charging packaging again after a failed plate.
Worked example
Suppose one successful plate costs 4.00 in material. Each failed plate adds 2.00 in handling. At a 20% failure rate, expected material cost is 4 / 0.8 = 5.00 and expected retry handling is 0.25 × 2 = 0.50. Expected production cost is 5.50, before other costs or fees. Simply multiplying 4 by 1.2 would give 4.80 and omit part of the modeled risk.
Measure a rate that matches the model
Use failed whole attempts divided by all attempts, including retries, over a relevant sample of similar jobs. A per-part defect percentage is not the same measurement. Failures may also be correlated because a bad profile keeps failing; the independence assumption will then be unreliable. The tool does not estimate statistical confidence from a small sample.
Early failures and reusable output
The current model assumes full material and time are lost. Early aborts, partial plate failures and salvageable parts may make this conservative. Do not add an additional failure allowance elsewhere unless it covers a different risk. The sensitivity table compares assumptions, not probabilities of profit or delivery time.