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Decision Tree — Overhaul, Monitor or Run to Failure (Risk-Averse)

A maintenance strategy for a critical pump, minimising 12-month cost with a risk tolerance of $400k: condition monitoring has the lowest expected cost ($81.0k) but its tail of unplanned trips gives it a certainty equivalent of $94.7k, so the risk-averse choice is the planned overhaul (CE $87.6k). Illustrative values.

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Boiler feed pump P-101B — overhaul, monitor or run to failure?Boiler feed pump P-101B — overhaul, monitor or run to failure?12-month cost per pump, US$ thousands — parts, labour and lost generation1 decision · 3 chance nodes · 9 outcomes · minimise E[cost] · risk tolerance $400kOPTIMAL STRATEGYPlanned overhaul now·E[cost] $87.4k·CE $87.6kVibration monitoringcost $18k · net $81.0kRun to failureNo degradation0.45Fault caught early0.4Fault caught late0.1Missed: unplanned trip0.05No failure0.45Fails, spare on site0.33Fails, 6-week lead time0.22Condition over 12 monthsE[cost] $63.0k · CE $76.7k$0net $18k$70knet $88k$140knet $158k$420knet $438kFailure in 12 months?E[cost] $187.0k · CE $267.8k$0$160k$610kPlanned overhaul nowcost $85k · net $87.4kRuns clean0.96Infant-mortality failure0.04Maintenance strategyE[cost] $87.4k · CE $87.6kAfter overhaulE[cost] $2.4k · CE $2.6k$0net $85k · P 0.96$60knet $145k · P 0.04DecisionChanceOutcomeOptimal strategyRejected alternativeRisk profile·outcome distribution of the optimal strategy00.51$80k$90k$100k$110k$120k$130k$140k$150kfinal cost0.960.04E[cost]Expected cost$87.4kStandard deviation$11.8kCertainty equivalent$87.6kLowest cost$85kHighest cost$145kP(cost > expected)0.04Distinct outcomes2What the rollback showsBest first choice: “Planned overhaul now”, certainty equivalent $87.6k (E[cost] $87.4k) — $7.1k below the next best, “Vibrationmonitoring” (CE $94.7k).Following it, the cost ranges from $85k to $145k across 2 possible results, standard deviation $11.8k; a 4% chance the cost exceedsits expectation.With risk tolerance $400k the certainty equivalent is $87.6k, a risk premium of $0.2k; a risk-averse decision maker takes “Plannedoverhaul now” instead of the expected-value choice “Vibration monitoring” (E[cost] $81.0k).Note: Risk tolerance of US$400k is the plant's stated appetite for a single unplanned loss.Note: Illustrative failure probabilities for a fictional plant; calibrate them from your maintenance history.

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title "Boiler feed pump P-101B — overhaul, monitor or run to failure?"
subtitle "12-month cost per pump, US$ thousands — parts, labour and lost generation"
currency $
unit k
objective min
measure "E[cost]"
risk-tolerance 400
risk-profile on
branches orthogonal
note "Risk tolerance of US$400k is the plant's stated appetite for a single unplanned loss."
note "Illustrative failure probabilities for a fictional plant; calibrate them from your maintenance history."

decision "Maintenance strategy"
  "Planned overhaul now" cost 85 -> chance "After overhaul"
    "Runs clean" p rest -> 0
    "Infant-mortality failure" p 0.04 -> 60
  "Vibration monitoring" cost 18 -> chance "Condition over 12 months"
    "No degradation" p 0.45 -> 0
    "Fault caught early" p 0.40 -> 70
    "Fault caught late" p 0.10 -> 140
    "Missed: unplanned trip" p rest -> 420
  "Run to failure" -> chance "Failure in 12 months?"
    "No failure" p 0.45 -> 0
    "Fails, spare on site" p 0.33 -> 160
    "Fails, 6-week lead time" p rest -> 610