scholarly journals Reliability of Sampling Inspection Schemes Applied to Replacement Steam Generators

2006 ◽  
Vol 129 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Guy Roussel ◽  
Leon Cizelj
Keyword(s):  
Closed Form ◽  
Steam Generator ◽  
The State ◽  
The Other ◽  
Prior Density ◽  
Steam Generators ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Sampling Inspection ◽  
Steam Generator Tubing

The basis for determining the size of the random sample of tubes to be inspected in replacement steam generators is revisited in this paper. A procedure to estimate the maximum number of defective tubes left in the steam generator after no defective tubes have been detected in the randomly selected inspection sample is proposed. A Bayesian estimation is used to obtain closed-form solutions for uniform, triangular, and binomial prior densities describing the number of failed tubes in steam generators. It is shown that the particular way of selecting the random inspection sample (e.g., one sample from both SG, one sample from each SG, etc.) does not affect the results of the inspection and also the information obtained about the state of the uninspected tubing, as long as the inspected steam generators belong to the same population. Numerical examples further demonstrate two possible states of the knowledge existing before the inspection of the tubing. First, virtually no knowledge about the state of the steam generator tubing before the inspection is modeled using uniform and triangular prior densities. It is shown that the knowledge about the uninspected part of the tubing strongly depends on the size of the sample inspected. Further, even small inspection samples may significantly improve our knowledge about the uninspected part. On the other hand, rather strong belief on the state of the tubing prior to the inspection is modeled using binomial prior density. In this case, the knowledge about the uninspected part of the tubing is virtually independent on the size of the sample. Furthermore, it is shown qualitatively and quantitatively that such inspection brings no additional knowledge on the uninspected part of the tubing.

Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains

1997 ◽  
Vol 64 (3) ◽  
pp. 495-502 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Strain Field ◽  
Strain Energy ◽  
Convex Polygon ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Arbitrary Convex ◽  
Shaped Inclusion

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.

scholarly journals Optimal reinsurance: a reinsurer’s perspective

2017 ◽  
Vol 12 (1) ◽  
pp. 147-184 ◽  
Author(s):  
Fei Huang ◽  
Honglin Yu
Keyword(s):  
At Risk ◽  
Closed Form ◽  
Value At Risk ◽  
Optimality Criteria ◽  
Total Loss ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Dependency Structure ◽  
Closed Form Solutions

AbstractIn this paper, the optimal safety loading that the reinsurer should set in the reinsurance pricing is studied, which is novel in the literature. It is first assumed that the insurer will choose the form of the reinsurance contract by following the results derived in Cai et al. Different optimality criteria from the reinsurer’s perspective are then studied, such as maximising the expectation of the profit, maximising the utility of the profit and minimising the value-at-risk of the reinsurer’s total loss. By applying the concept of comonotonicity, the problem in which the reinsurer is facing two risks with unknown dependency structure is also solved. Closed-form solutions are obtained when the underlying losses are zero-modified exponentially distributed. Finally, numerical examples are provided to illustrate the results derived.

Synthesis of Seven-Link Mechanisms

1973 ◽  
Vol 95 (2) ◽  
pp. 533-540 ◽  
Author(s):  
D. Kohli ◽  
A. H. Soni
Keyword(s):  
Closed Form ◽  
Nonlinear Equations ◽  
Degrees Of Freedom ◽  
The Other ◽  
Linear Superposition ◽  
Two Degrees Of Freedom ◽  
Closed Form Solutions ◽  
Highly Nonlinear ◽  
Principle Of Linear Superposition

The mechanisms derived from the seven-link chains with five links in their two loops and having two degrees of freedom are examined for six synthesis problems. Using displacement matrices, closed form synthesis equations are derived. It is shown that three synthesis problems may be solved using the principle of linear superposition, and closed form solutions may be obtained. The other three synthesis problems involve highly nonlinear equations and must be solved numerically.

scholarly journals Solving Nonlinear Differential Algebraic Equations by an Implicit Lie-Group Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chein-Shan Liu
Keyword(s):  
Closed Form ◽  
Lie Group ◽  
Iterative Scheme ◽  
Differential Algebraic Equations ◽  
Group Method ◽  
Computational Results ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Lie Group Method

We derive an implicit Lie-group algorithm together with the Newton iterative scheme to solve nonlinear differential algebraic equations. Four numerical examples are given to evaluate the efficiency and accuracy of the new method when comparing the computational results with the closed-form solutions.

The Effect of Thermal Treatments on Stress Corrosion Cracking of Alloy-800 in a Caustic Environment

CORROSION ◽  
1985 ◽  
Vol 41 (10) ◽  
pp. 575-581 ◽  
Author(s):  
R. S. Pathania ◽  
R. D. Cleland
Keyword(s):  
Stress Corrosion ◽  
Steam Generator ◽  
Stress Corrosion Cracking ◽  
Corrosion Cracking ◽  
Caustic Solution ◽  
Thermal Treatments ◽  
Steam Generators ◽  
Alloy 800 ◽  
Steam Generator Tubing ◽  
Alkaline Environments

Abstract Stress corrosion cracking (SCC) tests under controlled potentials were conducted on plastically stressed C-rings of Alloy-800 to evaluate the effect of thermal treatments (at 500 to 850 C) on SCC of Alloy-800 steam generator tubing. The tests were conducted in a caustic solution at 300 C; such alkaline environments may sometimes form in crevices in nuclear steam generators. The results are presented in the form of a time-temperature-SCC diagram. Thermal treatments generally inhibited the SCC of Alloy-800, and the improvement was substantial in a few cases. Application of anodic potential and increasing stress generally accelerated SCC.

Fitness-for-Service Assessment of Steam Generator Tubing Subject to Dealloying Degradation

2017 ◽  
Author(s):  
Rosita Mousavi ◽  
Xinjian Duan ◽  
Michael Kozluk ◽  
Min Wang ◽  
Yihai Shi
Keyword(s):  
Steam Generator ◽  
Degradation Mechanism ◽  
Life Cycle Management ◽  
Steam Generators ◽  
Nickel Copper ◽  
Steam Generator Tubing ◽  
Management Plans ◽  
Monel 400 ◽  
Technical Basis ◽  
Steam Generator Tubes

A new degradation mechanism has been observed in Monel 400 Steam Generator tubing material, a nickel-copper alloy (63Ni-28Cu-2½Fe) with the ASME material designation SB-163/N04400. The location is above the top preheater support plate of the two re-circulating steam generator in one of the units of the Pickering Nuclear Generating Station. This paper provides a brief description of the regulatory environment, OPG’s steam generator life cycle management plans, the Canadian Industry’s fitness-for-service guidelines for steam generator tubes, and the afflicted steam generators. The paper then goes on to discuss the following activities that were conducted to support the technical basis to justify that the steam generators fit to be returned to service: • Inspection scope expansion, methods, and results. • Examination of removed tubes. • Condition monitoring assessment. • Operational assessment. • Burst-pressure tests of removed tubes and of fabricated test specimens. • Degradation specific flaw model and acceptance standards. • Flaw growth rate predictions. • Plugging limit adopted.

Apparently First Closed-Form Solution for Frequencies of Deterministically and/or Stochastically Inhomogeneous Simply Supported Beams

2000 ◽  
Vol 68 (2) ◽  
pp. 176-185 ◽  
Author(s):  
S. Candan ◽  
I. Elishakoff
Keyword(s):  
Closed Form ◽  
Infinite Number ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Benchmark Solutions

An infinite number of closed-form solutions is reported for a deterministically or stochastically nonhomogeneous beam, for both natural frequencies and reliabilities, for specialized cases. These solutions may prove useful as benchmark solutions. Numerical examples are evaluated.

scholarly journals Multi-bidder First Price Auction with Beliefs

2019 ◽  
Vol 7 (1) ◽  
pp. 140-160
Author(s):  
Hyeon Park
Keyword(s):  
Closed Form ◽  
Arbitrary Number ◽  
Value Of Information ◽  
Jel Classification ◽  
The Other ◽  
Type Space ◽  
Closed Form Solutions ◽  
Price Auction ◽  
Equilibrium Bidding

This paper characterizes the set of equilibria in the first price auction with multiple bidders—specifically three bidders, each of whose type space is multi-dimensional, incorporating a bidder’s beliefs about others’ valuations. In this auction, each bidder independently and privately learns the other two opponents’ valuations with some probability. This paper derives closed form solutions for equilibrium bidding behaviours parameterized by the degree of information when the bidder has homogeneous beliefs regarding each opponent. This paper demonstrates how much the level of information affects the bidding behaviours of the informed bidders. In addition, this paper extends the model into [Formula: see text] bidders when a high value bidder has fixed beliefs that all other bidders are identical types, and show how the value of information changes as the number of participants increases. Finally, this paper speculates on the possible changes in the efficiency of the model from increasing the valuation space to an arbitrary number. JEL Classification: D44, D82, D83

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