Advantages of “Function Domain Sets” Confidence Intervals Over Hypotheses Comparison Tests of One Mean Residual Life (MRL) Function Dominating an Improved Baseline and of Two MRL Functions Comparisons with Applications in Modern Engineered Composite Wood Products: One Sample and Two Sample Cases. Also Exploring General Theory, Insights, and Applications of MRL Functions
Date of Award
Master of Science
Timothy M. Young
Ramon V. Leon, Frank M Guess
In this thesis, we analyze mean residual life (MRL) functions and unique “function domain sets” confidence intervals to identify important opportunities for improving quality of medium density fiberboard (MDF). We stress these tools have tremendous potential for many other forest products (e.g., various composites, natural woods), not just MDF.
These “function domain sets” confidence intervals can assess variation in quality where one MRL function dominates an industrial baseline. Assessments of the internal bond of MDF illuminate opportunities for helpful improvements, plus perform valid statistical comparisons of different types of MDF. For example, these MRL methods detect a new, higher-valued MDF product that represents an opportunity for an MDF producer to increase revenues or reduce costs due to excess MRL for a subgroup. These MRL methods can be used as diagnostics of a MDF manufacture process needing adjustments, etc. We provide MAPLE 10 code to implement these MRL procedures.
Typical traditional confidence intervals for a MRL function are centered about the function. “Function domain sets” intervals, however, produce novel statements like: “we are 95% confident that the MRL function, e(t), is greater than another function for all t in the domain set [0, θˆ ).” We study “function domain sets” intervals on internal bonds (tensile strengths) for various MDF products.
The values of MRL analyses have been demonstrated in a variety of applications beyond MDF production. The usefulness of the MRL function in other areas suggests that it has considerable potential value for the forest products industry. Recent, MRL applications vary from modern accelerated stress testing using proportional MRL modeling, to fuzzy set engineering modeling, to maintenance and replacement of bridges in Europe, to better decision making on materials in nuclear power plants, to general applications in evaluating “degrading” systems. We anticipate that varied analyses of MRL functions and “function domain sets” confidence intervals will furnish practitioners useful tools in many fields. Applications to different areas are highlighted to demonstrate the increasing usefulness and potential of MRL methods in many industries, government agencies, and future academic research.
Steele, Jonathan Cody, "Advantages of “Function Domain Sets” Confidence Intervals Over Hypotheses Comparison Tests of One Mean Residual Life (MRL) Function Dominating an Improved Baseline and of Two MRL Functions Comparisons with Applications in Modern Engineered Composite Wood Products: One Sample and Two Sample Cases. Also Exploring General Theory, Insights, and Applications of MRL Functions. " Master's Thesis, University of Tennessee, 2006.