Pmeasured

Pmeasured is a term used in measurement science to denote the probability that a measurement outcome falls within a specified tolerance of the true value. It serves as a concise metric for assessing the practical accuracy of a measurement system under defined conditions, including instrument, method, and environment. Pmeasured can apply across disciplines such as manufacturing, metrology, and laboratory analytics.

In a formal model, if the measured value X is related to the true value X_true by X = X_true + e, where e represents random and systematic error, then Pmeasured is the probability that the absolute error satisfies |X − X_true| ≤ tol, for a chosen tolerance tol. If the measurement error e has a known distribution, this probability can be computed as Pmeasured = P(|e| ≤ tol). For example, with normally distributed error e ~ N(0, sigma^2), Pmeasured equals the cumulative probability within ±tol, expressible via the standard normal distribution or the error function.

Estimation of Pmeasured typically uses calibration data or repeated measurements under specified conditions. It is often reported alongside other performance metrics such as measurement uncertainty, bias, and repeatability. Pmeasured helps compare instruments, methods, or setups by indicating how reliably they meet the required tolerance in practice.

Related concepts include coverage probability, confidence intervals, and agreement statistics. While Pmeasured provides a direct probability of meeting tolerance, it depends on the assumed error model and condition specificity; thus, it should be interpreted within the context of the measurement system and its documented operating conditions. Example applications include quality control acceptance testing and sensor performance evaluation.