LOWER TOLERANCE LIMIT APPROACH TO EQUATION-BASED RATIONAL DESIGN VALUES FOR L-SHAPED MORTISE AND TENON JOINTS

Abstract

Statistical lower tolerance limits (LTLs) were computed for the ratios obtained by dividing the test values for 360 L-shaped rectangular mortise and tenon joints consisting of 72 different configurations of five specimens each by the corresponding values estimated by a nonlinear-regression expression fitted to the test data. LTLs were computed for the resulting ratios at the 75∣75, 90∣75, 75∣90, and 90∣90 confidence∣proportion levels. At these levels, the corresponding LTLs amounted to 88.1%, 87.4%, 75.8%, and 74.9%, respectively, of the estimates. The percentages of values that fell below the above stated LTLs were 24.2%, 23.3%, 8.3%, and 7.5%. On average, 53% of the test values below a given tolerance limit fell in the range of 90-99% of that limit. Differences between 75∣75 and 90∣75 limits as well as between 75∣90 and 90∣90 limits were sufficiently small that the greater confidence level appears desirable. This study is too limited in scope to suggest the appropriate confidence∣proportion level that might be used in determining design values for joints as a percentage of estimated values, but it does raise the question and emphasizes the importance of determining what percentage of failure is acceptable along with what level of confidence is appropriate for furniture design.