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Residual loss is a mixture of available and unavailable controls; multiplying their marginal effects would incorrectly imply independent operation."],"summary":"The supplied controls reduce annual expected loss from 2,436 to 1,338.76 USDk, at a cost of 450 USDk/year. Net control value is 647.24 USDk/year. The stressed control system produces 3,643.08 USDk/year of expected loss. These sums describe expectations, not a maximum loss or tail confidence level.","methods":["Gross expected loss = probability × event impact.","Controls share one Bernoulli availability state. Residual expected loss = gross expected loss × [(1 − reliability) + reliability × (1 − prevention) × (1 − mitigation)].","Expected avoided loss = gross expected loss × shared availability × (prevention + mitigation − prevention × mitigation). Net control value = avoided expected loss − annual control cost.","Stress changes gross probability and impact and reduces control reliability; probabilities cap at one with an explicit warning.","Residual event probability is a marginal; severity is conditional on an event. Break-even availability = annual control cost / [gross expected loss × (prevention + mitigation − prevention × mitigation)], if attainable.","Event-conditional severity is unavailable when the marginal event probability is zero. A zero monetary severity remains meaningful when the event population exists.","Complements, stress clipping, control-value sums and break-even comparisons use exact rational arithmetic for canonical decimal input numbers. JSON exports retain numerator, denominator and a forty-significant-digit decimal; metrics and charts use numeric approximations.","Equal exact residual losses use literal name order independent of browser language for consistent display; this name order is not a causal risk distinction."],"limitations":["One annual event per risk model, additive expected losses and one shared Bernoulli availability state for prevention and mitigation.","No tail distribution, correlation, causal estimation, insurance recovery or regulatory adequacy is inferred.","Effectiveness and reliability can double count uncertainty unless users define them separately.","Numerical input precision: use zero or absolute values of at least 0.000000001. Smaller nonzero inputs are rejected explicitly.","Canonical decimal evaluation begins after JSON numbers have been parsed. Digits already lost during parsing cannot be recovered. Equal rounded gross and residual means do not establish zero avoided loss; retain the direct avoided-loss and net-value outputs."]}}