Normaaliraja

Normaaliraja is a term used in Estonian-language statistics and engineering literature to denote a boundary or threshold defined by a normal distribution. The word combines normaali, meaning normal, with raja, meaning boundary or limit. In usage, it identifies a range around a target value that is considered acceptable under typical variation.

Mathematically, if a quantity X is modeled as a normal random variable with mean μ and standard deviation σ, the normaaliraja corresponding to a multiplier k is the interval [μ − kσ, μ + kσ]. The probability that a value falls within this boundary is P(|X − μ| ≤ kσ) = 2Φ(k) − 1, where Φ is the standard normal cdf. Common choices are k = 2 or k = 3, with the three-sigma boundary enclosing about 99.73% of observations.

In practice, normaaliraja is used to define acceptable operating limits in quality control, process monitoring, and risk assessment. Values outside the normaaliraja typically trigger investigation, adjustment, or escalation. The concept is closely related to tolerance limits and control-chart boundaries, though it originates from a probabilistic framing around the normal distribution rather than fixed engineering tolerances alone.

Origin and usage of the term are primarily found in Estonian-language materials, where it is used to describe boundaries derived from the normal model. In English-language contexts, comparable ideas are often referred to as normal-boundary limits or three-sigma limits.

See also: Normal distribution, confidence interval, control chart, process capability, six sigma.