Tolerances: Their Analysis and Synthesis

1990 ◽  
Vol 112 (2) ◽  
pp. 113-121 ◽  
Author(s):  
Woo-Jong Lee ◽  
T. C. Woo
Keyword(s):  
Reliability Index ◽  
Cost Minimization ◽  
Probabilistic Approach ◽  
Convex Polytope ◽  
Random Variable ◽  
Structural Safety ◽  
Worst Case Analysis ◽  
Manufacturing Cost ◽  
Worst Case ◽  
Tolerance Synthesis

Tolerance, representing a permissible variation of a dimension in an engineering drawing, is synthesized by considering assembly stack-up conditions based on manufacturing cost minimization. A random variable and its standard deviation are associated with a dimension and its tolerance. This probabilistic approach makes it possible to perform trade-off between performance and tolerance rather than the worst case analysis as it is commonly practiced. Tolerance (stack-up) analysis, as an inner loop in the overall algorithm for tolerance synthesis, is performed by approximating the volume under the multivariate probability density function constrained by nonlinear stack-up conditions with a convex polytope. This approximation makes use of the notion of reliability index [10] in structural safety. Consequently, the probabilistic optimization problem for tolerance synthesis is simplified into a deterministic nonlinear programming problem. An algorithm is then developed and is proven to converge to the global optimum through an investigation of the monotonic relations among tolerance, the reliability index, and cost. Examples from the implementation of the algorithm are given.

scholarly journals Optimum Selection of Discrete Tolerances

1989 ◽  
Vol 111 (2) ◽  
pp. 243-251 ◽  
Author(s):  
W.-J. Lee ◽  
T. C. Woo
Keyword(s):  
Reliability Index ◽  
Probabilistic Approach ◽  
Minimum Cost ◽  
Random Variable ◽  
Manufacturing Cost ◽  
Discrete Optimization Problem ◽  
Integer Programming Problem ◽  
Optimum Selection ◽  
Manufacturing Assembly ◽  
Selection Of

Tolerancing involves considerations from all phases of the life cycle of a product including design, manufacturing, assembly, and inspection. Along with minimum cost and maximum functionality and interchangeability, the practice of tolerancing urges a designer to choose an appropriate manufacturing (or inspection) process as well. This situation is formalized as a discrete optimization problem. For an optimum selection of tolerances from a given discrete model involving various manufacturing processes, minimization of manufacturing cost is achieved under the constraint of tolerance stack-up. A random variable and its standard deviation are associated with a dimension and its tolerance. This probabilistic approach enables a trade-off between performance and tolerance (cost). But it also suggests probabilistic optimization. With the aid of a notion called the reliability index [8], tolerance selection is formulated as an integer programming problem. A branch and bound algorithm for ensuring optimum selection is developed by exploiting the special structure of the constraints. To make the enumeration tree small, monotonic relations among the reliability index, cost, and tolerance are examined. The algorithm is tested with examples.

scholarly journals Reliability Analysis of St. Barbara’s Church in Otovice

2020 ◽  
Vol 868 ◽  
pp. 166-172
Author(s):  
Chandrashekhar Mahato ◽  
Pavel Kuklík
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Probabilistic Approach ◽  
Probability Of Failure ◽  
Structural Safety ◽  
Site Condition ◽  
Baroque Architecture ◽  
Material Parameters ◽  
Safety And Stability ◽  
Present Site

The Churches of the Broumov region are well known for their unique baroque architecture, distinct shapes, sizes, and constitutes an integral part of the Czech cultural heritage. The St. Barbara’s Church that has been studied in this article, is in the Otovice village of Broumov. It was built in the year 1726 by Bavarian architects Christoph Dientzenhofer and Kilian Ignaz and is significant because of its religious, artistic and historic values. The main objective of this study is to evaluate the structural safety and stability of St. Barbara’s Church based on a probabilistic approach. A deterministic assessment of the structure is carried out and the results are assessed concerning the present site condition. Depending upon the observed damages, a condition for failure is defined for the structure. The uncertainties in the material parameters are considered and reliability analysis is performed to determine the reliability index, probability of failure and influence of different material parameters in the structural stability.

scholarly journals FP/FIFO scheduling: coexistence of deterministic and probabilistic QoS guarantees

2007 ◽  
Vol Vol. 9 no. 1 (Distributed Computing and...) ◽  
Author(s):  
Pascale Minet ◽  
Steven Martin ◽  
Leila Azouz Saidane ◽  
Skander Azzaz
Keyword(s):  
Response Time ◽  
Probabilistic Approach ◽  
Worst Case Analysis ◽  
Deterministic Approach ◽  
Worst Case ◽  
Qos Guarantee ◽  
High Resource ◽  
Qos Guarantees ◽  
International Audience

Distributed Computing and Networking International audience In this paper, we focus on applications having quantitative QoS (Quality of Service) requirements on their end-to-end response time (or jitter). We propose a solution allowing the coexistence of two types of quantitative QoS garantees, deterministic and probabilistic, while providing a high resource utilization. Our solution combines the advantages of the deterministic approach and the probabilistic one. The deterministic approach is based on a worst case analysis. The probabilistic approach uses a mathematical model to obtain the probability that the response time exceeds a given value. We assume that flows are scheduled according to non-preemptive FP/FIFO. The packet with the highest fixed priority is scheduled first. If two packets share the same priority, the packet arrived first is scheduled first. We make no particular assumption concerning the flow priority and the nature of the QoS guarantee requested by the flow. An admission control derived from these results is then proposed, allowing each flow to receive a quantitative QoS guarantee adapted to its QoS requirements. An example illustrates the merits of the coexistence of deterministic and probabilistic QoS guarantees.

Robust Tolerance Synthesis With the Design of Experiments Approach

1999 ◽  
Vol 122 (3) ◽  
pp. 520-528 ◽  
Author(s):  
Chang-Xue (Jack) Feng ◽  
Andrew Kusiak
Keyword(s):  
Design Of Experiments ◽  
Heuristic Algorithms ◽  
Exact Algorithms ◽  
Manufacturing Processes ◽  
Manufacturing Cost ◽  
Simulation Approach ◽  
Worst Case ◽  
Quality Cost ◽  
Tolerance Synthesis ◽  
Selection Of

Design of tolerances impacts quality, cost, and cycle time of a product. Most literature on deterministic tolerance design has focused on developing exact and heuristic algorithms to minimize manufacturing cost. Some research has been published on probabilistic tolerance synthesis and optimization. This paper presents the design of experiments (DOE) approach for concurrent selection of component tolerances and the corresponding manufacturing processes. The objective is to minimize the variation of tolerance stackups. Numerical examples illustrate the methodology. The Monte Carlo simulation approach is used to obtain component tolerances and tolerance stackups. Process shift, the worst case and root sum square tolerance stackup constraints, and setup reduction constraints have been incorporated into the proposed methodology. Benefits of the proposed DOE approach over exact algorithms are discussed. [S1087-1357(00)00202-1]

The Comparison of Methods of Assessing the Reliability of the Steel Frame

2015 ◽  
Vol 797 ◽  
pp. 11-18
Author(s):  
Agnieszka Dudzik ◽  
Urszula Radoń
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Random Variable ◽  
Design Parameters ◽  
Variable Sensitivity ◽  
Index Sensitivity ◽  
The Impact ◽  
The Mathematical Model

The study presents a probabilistic approach to the problems of static analysis of a steel building. Structural design parameters were defined as deterministic values and random variables. The latter were not correlated. The criterion of structural failure is expressed by limit functions related to the ultimate and serviceability limit state. The description of limit functions by the Mathematica program was generated. The Hasofer-Lind index was used as a reliability measure. In the description of random variables were used the normal distribution and, for comparison, different types of probability distribution appropriate to the nature of the variable. Sensitivity of reliability index to the random variables was defined. If the reliability index sensitivity due to the random variable Xi is low when compared with other variables, it can be stated that the impact of this variable on failure probability is small. Therefore, in successive computations it can be treated as a deterministic parameter. Sensitivity analysis leads to simplify the description of the mathematical model, determine the new limit functions and values of the Hasofer-Lind reliability index. The primary research method is the FORM method. In order to verify the correctness of the calculation SORM, Monte Carlo and Importance Sampling methods were used. In the examples of reliability analysis the STAND program was used.

Effect of Input Variability on the Performance of Turbine Blade Thermal Design Using Monte Carlo Simulation: An Exploratory Study

2005 ◽  
Vol 127 (4) ◽  
pp. 404-413 ◽  
Author(s):  
Roland S. Muwanga ◽  
Sri Sreekanth ◽  
Daniel Grigore ◽  
Ricardo Trindade ◽  
Terry Lucas
Keyword(s):  
Monte Carlo ◽  
Response Surface ◽  
Field Data ◽  
Turbine Blades ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Thermal Design ◽  
Worst Case Analysis ◽  
Worst Case ◽  
Blade Row

A probabilistic approach to the thermal design and analysis of cooled turbine blades is presented. Various factors that affect the probabilistic performance of the blade thermal design are grouped into categories and a select number of factors known to be significant, for which the variability could be assessed are modeled as random variables. The variability data for these random variables were generated from separate Monte Carlo simulations (MCS) of the combustor and the upstream stator and secondary air system. The oxidation life of the blade is used as a measure to evaluate the thermal design as well as to evaluate validity of the methods. Two approaches have been explored to simulate blade row life variability and compare it with the field data. Field data from several engine removals are used for investigating the approach. Additionally a response surface approximation technique has been explored to expedite the simulation process. The results indicate that the conventional approach of a worst-case analysis is overly conservative and analysis based on nominal values could be very optimistic. The potential of a probabilistic approach in predicting the actual variability of the blade row life is clearly evident in the results. However, the results show that, in order to predict the blade row life variability adequately, it is important to model the operating condition variability. The probabilistic techniques such as MCS could become very practical when approximation techniques such as response surface modeling are used to represent the analytical model.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

Hierarchical Programming for Worst-Case Analysis of Power Grids

2018 ◽  
Author(s):  
Hatim Djelassi ◽  
Stephane Fliscounakis ◽  
Alexander Mitsos ◽  
Patrick Panciatici
Keyword(s):  
Case Analysis ◽  
Power Grids ◽  
Worst Case Analysis ◽  
Worst Case
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