Statistical Validation of a Stochastic Nutrient-Risk Model for Variable Fresh-Food Inputs

Conventional quality control for companion-animal formulations certifies a recipe against a single averaged composite: a deterministic point estimate. That method is blind to the variance of fresh agricultural ingredients, to manufacturing tolerance, and to the biological variation of the animal receiving the food. This paper documents a stochastic alternative. Every raw ingredient is treated as a distribution rather than a scalar; five multiplicative lognormal noise sources are applied per simulated feeding day; and a day passes only if every floor nutrient is delivered at or above 90% of its NRC 2006 requirement, with no nutrient reaching 80% of its safe upper limit. The population statistic is the lower limit of a Wilson score interval on the pass proportion. We describe a three-stage verification programme and report its results. A 10,000-draw provisional gate confirms that a formulation change has not broken a floor. An inherited 100,000-draw baseline over a four-fold stress envelope, run as a five-model cascade, returns Wilson-C95 99.996% for both species. A 1,000,000-draw full-population validation on the release-B-2.1.0 engine, accumulated as ten independent 100,000-draw runs with seeds spaced 1,000 apart, returns zero failures for both adult corrections, a pooled Wilson-95 lower bound of 99.9996%, N-limited, and a between-run standard deviation on the worst-nutrient mean of 0.042 (dog) and 0.057 (cat) percentage points of requirement. Past zero observed failures a Wilson bound reduces to n/(n + z²) and is a function of draw count alone; the physical quantity it accompanies converges by roughly 5,000 draws. The 1,000,000-draw run is therefore reported for its replicate dispersion and its audit corpus, not for extra decimal places, and the bound is stated as N-limited every time it appears.