1. A method for detecting and estimating leaks in any conserved flow around an industrial boiler wherein said conserved flow and industrial boiler form a process, said method comprising the steps of: (a) measuring mass flow imbalances in the process to uncover any deviation from the mass flow imbalances being zero defined as variability; (b) partitioning the variability in the measured mass flow imbalances into: 1) a process model component; 2) a leak model component; and 3) a noise component; to form a mathematical representation of a leak in the process; (c) utilizing a family of leak shapes for said leak model component and wherein each of said leak shapes represents a leak that is non-decreasing; (d) applying least squares filtering to said mathematical representation by estimating unknown parameters from said measured mass flow imbalances to generate an estimated leak flow model; (e) estimating statistical distributions of said unknown parameters to determine the statistical significance of said unknown parameters; (f) generating a family of statistics from said family of leak shapes and wherein each of said statistics is optimized to detect a variety of leaks; and (g) combining said statistics to form a significance-testing leak statistic.