🎓 Lesson 14 D5

Risk-Weighted ROI Lab: Aerospace Heat Treatment Case

Risk-weighted ROI is a way to measure how much money a manufacturing investment (like heat treatment equipment) will earn after accounting for the chance that things might go wrong—like equipment failure or quality defects.

🎯 Learning Objectives

✓ Calculate risk-weighted ROI using probabilistic cash flow inputs and failure probability distributions
✓ Design a sensitivity analysis to identify which risk drivers most influence ROI in aerospace heat treatment investments
✓ Analyze and compare two competing furnace upgrade options using risk-adjusted net present value (rNPV)
✓ Explain how AS9100D Clause 8.2.3 and ISO 14001:2015 Annex A.6.1 inform risk weighting in capital justification
✓ Apply Monte Carlo simulation parameters to model thermal uniformity variance and its impact on scrap rate and ROI

📖 Why This Matters

In aerospace manufacturing, a single heat treatment furnace upgrade can cost $3.2M—but if temperature uniformity drifts beyond ±3°C, parts fail certification, triggering $450k/lot rework or scrapping. Traditional ROI ignores this risk, often overestimating returns by 27–63% (SAE AIR7352). This lab teaches you to *quantify uncertainty* as rigorously as you quantify cost and revenue—so your capital proposals don’t just look good on paper, they survive real-world metallurgical variability.

📘 Core Principles

Risk-weighted ROI rests on three pillars: (1) Deterministic ROI baseline (Net Profit / Investment × 100%), (2) Probabilistic risk modeling—where each major risk (e.g., furnace control failure, calibration drift, cooling-rate deviation) is assigned a probability of occurrence and financial consequence, and (3) Integration via Expected Monetary Value (EMV): ROI_risk-weighted = Σ [P_i × ROI_i] across all defined risk scenarios. Crucially, aerospace heat treatment introduces *correlated risks*: a thermocouple calibration error increases probability of both hardness nonconformance *and* subsequent NADCAP audit findings—requiring joint probability modeling, not independent risk summation. We use fault trees aligned to AMS2750F pyrometry requirements to structure dependencies.

📐 Risk-Weighted ROI (RW-ROI)

RW-ROI adjusts nominal ROI by discounting expected returns using scenario-weighted outcomes. It is calculated as the expected value of ROI across mutually exclusive operational states—each defined by a risk event and its financial impact on throughput, yield, and compliance costs.

Risk-Weighted ROI

RW-ROI (%) = Σ [P_i × ROI_i]

Expected value of ROI across all defined risk scenarios i, where P_i is probability of scenario i occurring and ROI_i is ROI under that scenario.

Variables:

Symbol	Name	Unit	Description
P_i	Probability of scenario i	unitless (0–1)	Likelihood of risk scenario i, derived from historical failure data, FMEA RPN, or Bayesian updating
ROI_i	ROI under scenario i	%	Return on investment calculated assuming scenario i occurs (e.g., reduced yield, added rework, downtime)

Typical Ranges:

Aerospace heat treat furnace upgrade: 12–17%

Nominal ROI (unadjusted): 16–24%

💡 Worked Example

Problem: A vacuum furnace upgrade costs $2.8M. Baseline ROI (no risk) = 18.3% over 5 years. Three key risk scenarios are identified: (A) Temperature uniformity failure (P=0.12, ROI impact = −9.1 pts), (B) Cooling-rate excursions causing grain growth (P=0.07, ROI impact = −14.4 pts), (C) NADCAP audit nonconformance (P=0.04, ROI impact = −22.0 pts). All other scenarios retain baseline ROI.

1. Step 1: Compute ROI for each scenario: ROI_A = 18.3 − 9.1 = 9.2%; ROI_B = 18.3 − 14.4 = 3.9%; ROI_C = 18.3 − 22.0 = −3.7%

2. Step 2: Apply probabilities: EMV = (0.12 × 9.2) + (0.07 × 3.9) + (0.04 × −3.7) + (0.77 × 18.3)

3. Step 3: Calculate: = 1.104 + 0.273 − 0.148 + 14.091 = 15.22%

Answer: The risk-weighted ROI is 15.2%, a 3.1 percentage-point reduction from nominal ROI—well within acceptable thresholds per SAE AIR7352 (<5 pt reduction preferred for Class A aerospace components).

🏗️ Real-World Application

Pratt & Whitney’s 2021 CMS-2000 furnace modernization at Middletown, CT used RW-ROI to justify replacing legacy PID controllers with AI-driven adaptive thermal profiling. Engineers modeled 14 risk nodes—including thermocouple aging (Weibull β=2.3, η=4.1 yr), argon purity fluctuation (σ = 0.12% O₂), and load configuration error—feeding into a decision tree linked to AMS2750F Zone 1 compliance probability. The RW-ROI was 13.7% vs. nominal 21.4%, triggering inclusion of redundant Class 1/2 thermocouples (+$187k capex) to lift RW-ROI to 16.9%—meeting P&W’s minimum 16% hurdle rate for Tier-1 engine component lines.