Distribution Features of Deviation and Determination of a Tolerance Method for Prefabricated Concrete Components

Abstract

According to the current standards for prefabricated buildings, the dimensional tolerances of components are usually determined by experience, lacking a theoretical basis. This work demonstrates the mathematical distribution of the dimensional deviations of precast concrete components by measuring their three-dimensional dimensions. Utilizing the Kolmogorov–Smirnov test, the cumulative distribution function of dimension deviations was evaluated. In response to the fact that the tolerance division principle of equal upper and lower tolerance thresholds for prefabricated components in existing standards does not match the distribution of actual measured deviations of the components, this paper proposed a method for determining the tolerance values of prefabricated components based on the process capability index. The association between the process capability index and the qualification rate was utilized to determine the process capability index at a specified guarantee rate, which, in turn, determines the tolerance threshold values for various components. The results indicate that the range of unqualified random variables for the dimensional geometric parameters of the prefabricated components did not show a significant difference, with all values between 0.99 and 1.02. The coefficients of geometric parameter variation were all less than 0.0061, and the component dimensional deviation adhered to the normal distribution. By linking the process capability index with the pass rate, a process capability index of 0.55 at a guarantee rate of 90% was determined, along with the tolerance for various components.