LEARN. PRACTICE. GROW.Separate branches and decisions
In a fictional project, migration is complex in 20% of cases. Given complexity, delay probability is 60%; given a simple migration, it is 5%. Total delay probability is 0.2×0.6 + 0.8×0.05 = 16%. The 12% component represents complexity and delay together. Among delayed cases in this model, 12/16 = 75% are complex; this does not allow arbitrary reversal of conditional probabilities. Draw branches, check that outcomes at each chance node sum to one, and distinguish what you choose from what you merely observe. Do not assign probabilities to your chosen suppliers as though choices were random events.
Compare distributions and limits
Two options can share an expected cost while having very different consequences. Option A has a 20% chance of losing 80 thousand; B costs 12 thousand and retains a 5% chance of the same loss. Both give expected cost of 16 thousand within this scope. Before choosing, compare maximum losses, constraints, capacity to absorb consequences, and other objectives. An option with a better mean can violate a mandatory case limit. For durations of 40, 60, and 100 minutes with probabilities 50%, 30%, and 20%, the mean is 58 and P80 is 60, using the first value whose cumulative probability reaches 80%. A percentile still allows larger outcomes.
Model common causes and sensitivity
Two rehearsals depending on the same specialist are not automatically independent. In a model where that specialist’s absence, with 10% probability, is the only failure cause and affects both, joint failure is 10%, not 1%. The premise is explicit; a shared supplier in reality does not prove perfect correlation. Represent common causes and seek evidence about relationships. For sensitivity, compare a loss of 50 thousand at probability p against a response costing 6 thousand that eliminates it in the model. Break-even is p=12%. If the plausible estimate crosses this point, more information may change the recommendation; report the decision’s fragility.
Pay for information that can still change the decision
In the second exercise, no response leaves a 30% chance of a loss of 50 thousand. A response costing 8 thousand eliminates that loss in the model and is the best decision without additional information. Perfect information received before choosing would allow paying 8 thousand only in the unfavorable 30% of cases: expected cost of 2.4 thousand and maximum information value of 5.6 thousand. This is a bound for the same problem without other benefits. An imperfect study costing 6 thousand is not justified solely by that gain. Include delay cost and establish whether results arrive before commitment; later information cannot change an irreversible decision already made.
Interpret sensitivity without promising causality
A sensitivity chart can show which inputs most influence outcomes within the model and chosen ranges. That helps direct investigation but does not prove that intervening on an input will produce the predicted reduction. Two variables may share a cause; changing one without changing the cause may not create the assumed effect. Also check the comparison: varying one parameter from 10 to 100 and another from 10 to 11 examines different ranges. Changing a range can change chart ordering. More Monte Carlo iterations can reduce numerical sampling variation but do not correct an omitted dependency, a poorly chosen distribution, or an incorrect calendar. Retain version, assumptions, inputs, and calculation method so differences between runs can be explained.
A sample with no failures
Observing zero failures does not prove zero risk. In an exercise with one hundred independent trials and a 1% failure probability in each, the chance that all succeed is 0.99 to the power 100, approximately 36.6%. Thus no events is compatible with that assumption. This does not automatically estimate actual probability from a sample; it only shows that the outcome does not contradict the supplied model. In a real service, check whether trials are comparable, fully observed, and affected by shared causes. A campaign excluding aborted runs or telemetry failures can look more reliable than it was. Communicate sample size, conditions, and conclusion limits before using results to revise a response or close exposure.
// Original synthetic workshop: thousands of fictional cost units, minutes, probabilities.
const round=x=>Math.round(x*1000000)/1000000;
const delay=.2*.6+.8*.05;
const outcomes=[{minutes:40,p:.5},{minutes:60,p:.3},{minutes:100,p:.2}];
function quantile(rows,p){if(p<=0||p>1||Math.abs(rows.reduce((a,r)=>a+r.p,0)-1)>1e-9)throw Error('Invalid distribution');let sum=0;for(const r of [...rows].sort((a,b)=>a.minutes-b.minutes)){sum+=r.p;if(sum+1e-12>=p)return r.minutes;}}
const noInformation=Math.min(.3*50,8),perfectInformation=.3*8;
console.log(JSON.stringify({delay:round(delay),complexAndDelayed:.12,complexGivenDelayed:round(.12/delay),meanMinutes:outcomes.reduce((a,r)=>a+r.minutes*r.p,0),p80:quantile(outcomes,.8),equalExpectedCosts:[.2*80,12+.05*80],responseBreakEven:6/50,perfectInformationValue:round(noInformation-perfectInformation)}))Workshop: reproduce the delay branches, discrete percentile, and information bound in the local model. Then vary the 50-thousand-loss probability from 5% to 20% and find where the response costing 6 thousand starts minimizing expected cost.
Common pitfalls
Multiplying dependent probabilities, reversing conditionals, choosing solely by the mean, or buying information after the decision can no longer change. Every workshop value is fictional.
Related topics: Priority, expected cost, and confidence · Choose and execute responses · Monitor, close, and hand over to operations
Make the tree, criterion, and information sequence explicit. Check decision robustness and model limits before recommending; the result does not forecast a real migration.
Reference: Decision tree analysis for the risk averse organization · PMI-RMP five-domain ECO, updated-2024 public document