A general software availability/reliability model: numerical exploration via the matrix laguerre transform

1986 ◽  
Vol 2 (2) ◽  
pp. 203-236 ◽  
Author(s):  
Yasushi Masuda ◽  
J. George Shanthikumar ◽  
Ushio Sumita‡
Keyword(s):  
Reliability Model ◽  
Laguerre Transform ◽  
Numerical Exploration ◽  
The Matrix

scholarly journals A New Analytic Method of Cold Standby System Reliability Model with Priority

2018 ◽  
Vol 175 ◽  
pp. 03060
Author(s):  
Di Peng ◽  
Ni Zichun ◽  
Hu Bin
Keyword(s):  
System Reliability ◽  
Reliability Function ◽  
Matrix Analysis ◽  
Reliability Model ◽  
Reliability Indicators ◽  
Reliability Modelling ◽  
Maintenance Time ◽  
Cold Standby ◽  
The Matrix ◽  
Standby System

For different importance of components in equipment system, a cold standby system with two different components is studied when important components enjoy the priority in use and maintenance. Considering the application of exponential distribution, Weibull distribution and other typical distributions in resolving the problems subject to complicated calculation and strict constraints in the past reliability modelling, the highly applicable phase-type (PH) distribution is utilized to describe the life and maintenance time of system components in a unified manner. A system reliability model is built for wider applicability. With the matrix analysis method, expressions are obtained for a number of reliability indicators such as system reliability function, steady-state availability, mean up time and mean down time of system. In the end, examples are presented to verify the correctness and applicability of the model.

The bivariate Laguerre transform and its applications: numerical exploration of bivariate processes

1985 ◽  
Vol 17 (4) ◽  
pp. 683-708 ◽  
Author(s):  
Ushio Sumita ◽  
Masaaki Kijima
Keyword(s):  
Numerical Computation ◽  
Orthonormal Basis ◽  
Laguerre Functions ◽  
Bivariate Polynomials ◽  
Laguerre Transform ◽  
Partial Differentiation ◽  
Numerical Exploration ◽  
Shock Models ◽  
Numerical Tool

In the study of bivariate processes, one often encounters expressions involving repeated combinations of bivariate continuum operations such as multiple bivariate convolutions, marginal convolutions, tail integration, partial differentiation and multiplication by bivariate polynomials. In many cases numerical computation of such results is quite tedious and laborious. In this paper, the bivariate Laguerre transform is developed which provides a systematic numerical tool for evaluating such bivariate continuum operations. The formalism is an extension of the univariate Laguerre transform developed by Keilson and Nunn (1979), Keilson et al. (1981) and Keilson and Sumita (1981), using the product orthonormal basis generated from Laguerre functions. The power of the procedure is proven through numerical exploration of bivariate processes arising from correlated cumulative shock models.

The bivariate Laguerre transform and its applications: numerical exploration of bivariate processes

1985 ◽  
Vol 17 (04) ◽  
pp. 683-708 ◽  
Author(s):  
Ushio Sumita ◽  
Masaaki Kijima
Keyword(s):  
Numerical Computation ◽  
Orthonormal Basis ◽  
Laguerre Functions ◽  
Bivariate Polynomials ◽  
Laguerre Transform ◽  
Partial Differentiation ◽  
Numerical Exploration ◽  
Shock Models ◽  
Numerical Tool

In the study of bivariate processes, one often encounters expressions involving repeated combinations of bivariate continuum operations such as multiple bivariate convolutions, marginal convolutions, tail integration, partial differentiation and multiplication by bivariate polynomials. In many cases numerical computation of such results is quite tedious and laborious. In this paper, the bivariate Laguerre transform is developed which provides a systematic numerical tool for evaluating such bivariate continuum operations. The formalism is an extension of the univariate Laguerre transform developed by Keilson and Nunn (1979), Keilson et al. (1981) and Keilson and Sumita (1981), using the product orthonormal basis generated from Laguerre functions. The power of the procedure is proven through numerical exploration of bivariate processes arising from correlated cumulative shock models.

Crystalloid Inclusions in Hepatocyte Mitochondria and Their Similarity to Cytoplasmic Crystalloids

1974 ◽  
Vol 32 ◽  
pp. 198-199
Author(s):  
Odell T. Minick ◽  
Hidejiro Yokoo
Keyword(s):  
Liver Disease ◽  
Alcoholic Liver Disease ◽  
Special Interest ◽  
Structural Variations ◽  
Mitochondrial Alterations ◽  
The Matrix ◽  
Crystalloid Inclusions ◽  
Liver Biopsies

Mitochondrial alterations were studied in 25 liver biopsies from patients with alcoholic liver disease. Of special interest were the morphologic resemblance of certain fine structural variations in mitochondria and crystalloid inclusions. Four types of alterations within mitochondria were found that seemed to relate to cytoplasmic crystalloids.Type 1 alteration consisted of localized groups of cristae, usually oriented in the long direction of the organelle (Fig. 1A). In this plane they appeared serrated at the periphery with blind endings in the matrix. Other sections revealed a system of equally-spaced diagonal lines lengthwise in the mitochondrion with cristae protruding from both ends (Fig. 1B). Profiles of this inclusion were not unlike tangential cuts of a crystalloid structure frequently seen in enlarged mitochondria described below.

Coherency loss in γ' precipitates in nickel-base superalloy

1983 ◽  
Vol 41 ◽  
pp. 244-245
Author(s):  
R. A. Ricks ◽  
Angus J. Porter
Keyword(s):  
Lattice Mismatch ◽  
Lattice Parameter ◽  
Nickel Base Superalloy ◽  
Large Size ◽  
The Matrix ◽  
Nimonic 80A ◽  
Interfacial Dislocations ◽  
Nickel Base ◽  
Coherency Loss ◽  
Nimonic 115

During a recent investigation concerning the growth of γ' precipitates in nickel-base superalloys it was observed that the sign of the lattice mismatch between the coherent particles and the matrix (γ) was important in determining the ease with which matrix dislocations could be incorporated into the interface to relieve coherency strains. Thus alloys with a negative misfit (ie. the γ' lattice parameter was smaller than the matrix) could lose coherency easily and γ/γ' interfaces would exhibit regularly spaced networks of dislocations, as shown in figure 1 for the case of Nimonic 115 (misfit = -0.15%). In contrast, γ' particles in alloys with a positive misfit could grow to a large size and not show any such dislocation arrangements in the interface, thus indicating that coherency had not been lost. Figure 2 depicts a large γ' precipitate in Nimonic 80A (misfit = +0.32%) showing few interfacial dislocations.

Influence of Heat Treatments on Microstructures in an Fe-Co-V Alloy

1974 ◽  
Vol 32 ◽  
pp. 512-513
Author(s):  
S. Mahajan ◽  
M. R. Pinnel ◽  
J. E. Bennett
Keyword(s):  
Single Phase ◽  
Alloy Composition ◽  
Supersaturated Solid Solution ◽  
Cell Formation ◽  
Heat Treatments ◽  
Air Cooling ◽  
Iced Brine ◽  
Transmission Electron ◽  
The Matrix ◽  
Bcc Structure

The microstructural changes in an Fe-Co-V alloy (composition by wt.%: 2.97 V, 48.70 Co, 47.34 Fe and balance impurities, such as C, P and Ni) resulting from different heat treatments have been evaluated by optical metallography and transmission electron microscopy. Results indicate that, on air cooling or quenching into iced-brine from the high temperature single phase ϒ (fcc) field, vanadium can be retained in a supersaturated solid solution (α2) which has bcc structure. For the range of cooling rates employed, a portion of the material appears to undergo the γ-α2 transformation massively and the remainder martensitically. Figure 1 shows dislocation topology in a region that may have transformed martensitically. Dislocations are homogeneously distributed throughout the matrix, and there is no evidence for cell formation. The majority of the dislocations project along the projections of <111> vectors onto the (111) plane, implying that they are predominantly of screw character.

Sign in / Sign up

Export Citation Format

Share Document