Engineering & Technology · Engineering Economics, Projects & Professional Practice
Sensitivity, uncertainty and decisions under incomplete information
A project’s predicted saving is only slightly larger than its extra cost. Listing the prediction to two decimal places does not make it certain. A useful next question is how much an input would need to change before the recommendation changes.
Use design and measurement for comparisons and evidence; systems engineering develops configuration and interfaces. The supplied discount rates are arithmetic inputs, not current official rates or investment guidance. Professional codes and standards are identified by source and scope; actual legal and contractual duties require the applicable context.
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Use sensitivity and break-even reasoning to identify what an uncertain project decision depends on.
Identify the uncertain input and decision rule
An economic model can contain measured quantities, forecasts, negotiated terms, policy choices and simplifying assumptions. Identify each important input’s source, date, range and relation to other inputs. A discount rate chosen for a decision context and an estimated maintenance frequency do not represent the same kind of information.
Sensitivity analysis changes an input and recalculates the outcome while other stated inputs remain fixed. It reveals dependence on that change. A scenario can change several related inputs together. Neither approach supplies probabilities unless a justified probability model is also provided; optimistic and pessimistic labels do not create one.
Use break-even to focus the question
Return to the original three-year cost exercise with initial premium 300 and supplied real 5% rate. Let annual saving S be uncertain but constant across the three end-year payments. The present-value factor is 2.723248. Net present saving is 2.723248 S−300, so break-even occurs near S=110.16 cost units per year.
At a supplied scenario S=80, net present saving is about −82.14; at S=140 it is about 81.25. The plotted line states exactly which assumptions remain fixed. If savings depend on operating hours and energy price, those inputs may move together or differently. Treating their independent extremes as one likely outcome would require additional justification.
Connect further information to the decision
Ask whether an achievable observation could resolve a consequential uncertainty. A representative operating-hours record may matter more than another decimal place in the initial purchase quote. Information has a cost and arrives on a schedule; its value depends on whether it could change a decision that is still available.
An expected value requires probabilities and outcomes, and it does not describe the full range or consequences of outcomes. A robust alternative may remain acceptable across stated scenarios even if it is not best in every one. Keep binding performance, welfare and other obligations explicit. An uncertain cost advantage cannot supply evidence for an unverified requirement or determine the values of affected people.
Compare the margin with a credible question
The supplied central annual saving 120 exceeds the break-even value 110.16 by only 9.84 cost units per year. That gap is about 8.2% of 120. It identifies a sensitivity worth investigating, without stating an 8.2% probability of failure or an acceptable risk.
If the annual-saving estimate includes an uncertain usage assumption, investigate that relationship and the relevant operating conditions. If the uncertainty instead concerns a major replacement in year 2, vary that dated cost explicitly; do not force it into an unexplained annual percentage. Record the revised assumptions and the evidence supporting them so the changed recommendation can be assessed.
Try the reasoning
Do low, central and high scenarios establish probabilities?
Show the answer and reasoning
No. They describe selected assumptions; likelihood needs a separate justified model.
What does the 110.16 break-even value identify?
Show the answer and reasoning
The annual saving that exactly offsets the supplied 300 premium in this fixed three-year, 5% model.
Why investigate an input before seeking greater numerical precision?
Show the answer and reasoning
An uncertain consequential assumption can dominate the decision even when the arithmetic is very precise.
What to carry forward
Expose the threshold and assumptions behind a recommendation, then seek information that can change the actual decision.
References
Teaching resources and research supporting this lesson’s explanations and examples.