A double integration method for generating exact tolerance limit factors for normal populations

This article introduces a new method for generating the exact one-sided and two-sided tolerance limit factors for normal populations. This method does not need to handle the noncentral t-distribution at all, but only needs to do a double integration of a joint probability density function with respect to the two independent variables “s” (standard deviation) and “x” (sample mean). The factors generated by this method are investigated through Monte Carlo simulations and compared with the existing factors. As a result, it is identified that the two-sided tolerance limit factors being currently used in practical applications are inaccurate. For the right understanding, some factors generated by this method are presented in Tables along with a guidance for correct use of them. The AQL (Acceptable Quality Level) is a good, common measure about quality of a product lot which was already produced or will be produced. Therefore, when performing sampling inspection on a given lot using a tolerance limit factor, there is a necessity to know the AQL assigned to the factor. This new double integration method even makes it possible to generate the AQLs corresponding to the one-sided and two-sided tolerance limit factors.

Tibial forces are more useful than varus-valgus laxities for identifying and correcting overstuffing in kinematically aligned total knee arthroplasty

Identifying and correcting varus-valgus (V-V) malalignment of the tibial component is important when balancing a kinematically aligned total knee arthroplasty (TKA). Accordingly, the primary objective was to determine whether the tibial forces or V-V laxities are more sensitive to, and thus more useful for identifying and correcting, V-V malalignments of the tibial component that overstuff a compartment. Calipered kinematically aligned TKA was performed on nine human cadaveric knees. Medial and lateral tibial forces and V-V laxities were measured from 0° to 120° flexion with an unmodified reference tibial component and modified tibial components that introduced ±1° and ±2° V-V malalignments from the reference component to overstuff either the medial or lateral compartment. Changes in the tibial forces were most sensitive to V-V malalignments at 0° flexion (medial = 118 ± 34 N/deg valgus malalignment and lateral = 79 ± 20 N/deg varus malalignment). The varus and valgus laxities were most sensitive to V-V malalignments at 30° flexion (-0.6 ± 0.1 deg/deg varus malalignment) and 120° flexion (-0.4 ± 0.2 deg/deg valgus malalignment), respectively. The maximum average signal-to-noise ratios of the sensitivities in tibial forces and V-V laxities (ie, signals) to reported measurement errors using current intraoperative technologies (14 N and 0.7°) (ie, noise) were 8.4 deg^-1 and 0.9 deg^-1 , respectively. Because of the greater signal-to-noise ratios, measuring tibial forces is more useful than measuring V-V laxities for identifying and correcting V-V malalignments of the tibial component that overstuff a compartment. Clinical Significance: The sensitivities of tibial forces provide objective guidance to surgeons performing V-V recuts of the tibia.