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Tolerancing began with the notion of limits imposed on the dimensions of realized parts both to maintain functional geometric dimensionality and to enable cost-effective part fabrication and inspection. Increasingly however, component fabrication depends on more than part geometry as many parts are fabricated as a result of a "recipe" rather than dimensional instructions for material addition or removal. Referred to as process tolerancing, this is the case, for example, with IC chips. In the case of tolerance optimization, a typical objective is cost minimization while achieving required functionality or "quality." This paper takes a different look at tolerances, suggesting that rather than ensuring merely that parts achieve a desired functionality at minimum cost, the underlying goal of product design is to make money, more is better and tolerances comprise additional design variables amenable to optimization in a decision theoretic framework. We further recognize that tolerances introduce additional product attributes that relate to product characteristics such as consistency, quality, reliability and durability. These important attributes complicate the computation of the expected utility of candidate designs, requiring additional computational steps for their determination. The resulting theory of tolerancing illuminates the assumptions and limitations inherent to Taguchi's loss function. We illustrate the theory using the example of tolerancing for an apple pie, which conveniently demands consideration of tolerances on both quantities and processes, and the interaction among these tolerances.
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Slicing the pie: Interpreting harmful algal blooms one pie chart at a time
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Abstract Tolerancing began with the notion of limits imposed on the dimensions of realized parts both to maintain functional geometric dimensionality and to enable cost-effective part fabrication and inspection. Increasingly, however, component fabrication depends on more than part geometry as many parts are fabricated as a result of a “recipe” rather than dimensional instructions for material addition or removal. Referred to as process tolerancing, this is the case, for example, with IC chips. In the case of tolerance optimization, a typical objective is cost minimization while achieving required functionality or “quality.” This article takes a different look at tolerances, suggesting that rather than ensuring merely that parts achieve a desired functionality at minimum cost, a typical underlying goal of the product design is to make money, more is better, and tolerances comprise additional design variables amenable to optimization in a decision theoretic framework. We further recognize that tolerances introduce additional product attributes that relate to product characteristics such as consistency, quality, reliability, and durability. These important attributes complicate the computation of the expected utility of candidate designs, requiring additional computational steps for their determination. The resulting theory of tolerancing illuminates the assumptions and limitations inherent to Taguchi’s loss function. We illustrate the theory using the example of tolerancing for an apple pie, which conveniently demands consideration of tolerances on both quantities and processes, and the interaction among these tolerances.more » « less
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Abstract Neutrino events from IceCube have recently been associated with multiple astrophysical sources. Interestingly, these likely detections represent three distinct astrophysical source types: active galactic nuclei (AGNs), blazars, and tidal disruption events (TDEs). Here, we compute the expected contributions of AGNs, blazars, and TDEs to the overall cosmic neutrino flux detected by IceCube based on the associated events, IceCube’s sensitivity, and the source types’ astrophysical properties. We find that, despite being the most commonly identified sources, blazars cannot contribute more than 11% of the total flux (90% credible level), consistent with existing limits from stacked searches. On the other hand, we find that either AGNs or TDEs could contribute more than 50% of the total flux (90% credible level), although stacked searches further limit the TDE contribution to ≲30%. We also find that so-far unknown source types contribute at least 10% of the total cosmic flux with a probability of 80%. We assemble a pie chart that shows the most likely fractional contribution of each source type to IceCube’s total neutrino flux.more » « less
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The Partial Integral Equation (PIE) framework provides a unified algebraic representation for use in analysis, control, and estimation of infinite-dimensional systems. However, the presence of input delays results in a PIE representation with dependence on the derivative of the control input, u˙. This dependence complicates the problem of optimal state-feedback control for systems with input delay – resulting in a bilinear optimization problem. In this paper, we present two strategies for convexification of the H∞-optimal state-feedback control problem for systems with input delay. In the first strategy, we use a generalization of Young's inequality to formulate a convex optimization problem, albeit with some conservatism. In the second strategy, we filter the actuator signal – introducing additional dynamics, but resulting in a convex optimization problem without conservatism. We compare these two optimal control strategies on four example problems, solving the optimization problem using the latest release of the PIETOOLS software package for analysis, control and simulation of PIEs.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1080/00368121.2022.2106172
