scholarly journals Use of exponential distribution in mathematical models of dependability

Dependability ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 20-25
Author(s):  
B. P. Zelentsov
Keyword(s):  
Probability Theory ◽  
Mathematical Models ◽  
Exponential Distribution ◽  
Personal Experience ◽  
Random Distribution ◽  
Time To Event ◽  
Constant Rate ◽  
Mode Of Operation ◽  
Related Process ◽  
Made In

The exponential distribution of time to event or end of state is popular in the dependability theory. This distribution is characterized by the strength that is a convenient parameter used in mathematical models and calculations. The exponential distribution is used as part of dependability-related process simulation. Examples are given to illustrate the applicability of the exponential distribution. Aim. The aim of the paper is to improve the dependability-related simulation methods when using the exponential distribution of periods of states or times to events. Methods. The assumption of the exponential distribution of time between events can be justified or discarded using methods of the probability theory and/or mathematical statistics or on the basis of personal or engineering experience. It has been experimentally established that the failure flow in an established mode of operation is stationary, ordinary and produces no consequences. Such flow is Poisson and is distinct in the fact that the time between two consecutive failures is distributed exponentially with a constant rate. This exponential distribution is reasonably extended to the distribution of an item’s failure-free time. However, in other cases, the use of exponential distribution is often not duly substantiated. The methodological approach and the respective conclusions are case-based. A number of experience-based cases are given to show the non-applicability of exponential distribution. Discussion. Cases are examined, in which the judgement on the applicability or non-applicability of exponential distribution can be made on the basis of personal experience or the probability theory. However, in case of such events as completion of recovery, duration of scheduled inspection, duration of maintenance, etc., a judgement regarding the applicability of exponential distribution cannot be made in the absence of personal experience associated with such events. The distribution of such durations is to be established using statistical methods. The paper refers to the author’s publications that compare the frequency of equipment inspections with regular and exponentially distributed periods. The calculated values of some indicators are retained, while for some others they are different. There is a two-fold difference between the unavailability values for the above ways of defining the inspection frequency. Findings and conclusions. The proposed improvements to the application of exponential distribution as part of dependability simulation come down to the requirement of clear substantiation of the application of exponential distribution of time between events using methods of the probability theory and mathematical statistics. An unknown random distribution cannot be replaced with an exponential distribution without a valid substantiation. Replacing a random time in a subset of states with a random exponentially distributed time with a constant rate should be done with an error calculation.

scholarly journals Mathematical models to describe the drying process of Moringa oleifera leaves in a convective-air dryer

2021 ◽  
Author(s):  
Kivaandra Dayaa Rao Ramarao ◽  
Zuliana Razali ◽  
Chandran Somasundram
Keyword(s):  
Activation Energy ◽  
Mathematical Models ◽  
Moringa Oleifera ◽  
Effective Diffusivity ◽  
Drying Process ◽  
Constant Rate ◽  
Rate Period ◽  
Moringa Oleifera Leaves ◽  
Air Dryer ◽  
Kinetics Of

Drying kinetics of Malaysian Moringa oleifera leaves was investigated using a convective-air dryer. The drying parameters were: temperature (40, 50, 60, 70 °C), air velocity (1.3 m s<sup>–1</sup>, 1.7 m s<sup>–1</sup>). The drying process took place in the falling rate period and there was an absence of a constant rate period in this experiment. Six mathematical models (Lewis, Henderson and Pabis, Wang and Singh, Peleg, Page, and logarithmic) were selected for the description of drying characteristics of the leaves. The Wang and Singh model was determined as the best model based on the highest overall coefficient determinant (R<sup>2</sup>) and the lowest overall root mean square error (RMSE). The effective diffusivity (D<sub>eff</sub><sub> </sub>) was also calculated which was in the range of 3.98 × 10<sup>–11</sup> m<sup>2</sup> s<sup>–1</sup> to 1.74 × 10<sup>–10</sup> m<sup>2</sup> s<sup>–1. </sup>An Arrhenius relation was constructed to determine the activation energy for the samples in the convective air dryer. The activation energy for M. oleifera leaves was 39.82 kJ mol<sup>–1</sup> and 33.13 kJ mol<sup>–1</sup> at drying velocities of 1.3 m s<sup>–1</sup> and 1.7 m s<sup>–1</sup>, respectively.

scholarly journals Ethyl alcohol, a product of high pressure syntheses

1931 ◽  
Vol 131 (818) ◽  
pp. 533-540 ◽  
Keyword(s):  
High Pressure ◽  
Ethyl Alcohol ◽  
Personal Experience ◽  
High Pressures ◽  
Catalytic Reactions ◽  
Chemical Research ◽  
Chemical Research Laboratory ◽  
Pressure Synthesis ◽  
Corroborative Evidence ◽  
Made In

In opening the “discussion on catalytic reactions at high pressures,” one of us (G. T. M.) referred to experiments made in the Chemical Research Laboratory of the Department of Scientific and Industrial Research which had led to the isolation of notable quantities of ethyl alcohol among the condensation products from carbon monoxide and hydrogen interacting at high temperatures and pressures in presence of catalysts. These experiments were first described in March, 1928, and since that date statements have appeared in the scientific press to the effect that ethyl alcohol is a possible exception to the whole sequence of higher alcohols which can be produced by such interactions. Moreover during the above-mentioned discussion Mr. M. P. Appleby, speaking on behalf of the Imperial Chemical Industries, Ltd., Billingham, said “that in our experience we have never succeeded in obtaining, with any catalyst whatsoever, more than a mere trace of ethyl alcohol.” To the latter statement we take no exception whatever. It is a record of personal experience. But we felt that it was desirable to substantiate our earlier experiments by such corroborative evidence as would leave no doubt that ethyl alcohol is a product of high pressure synthesis.

General Solutions to Nurses Travel in Linear and Circular Nursing Units

1974 ◽  
Vol 18 (2) ◽  
pp. 134-134
Author(s):  
Stanley Lippert
Keyword(s):  
Mathematical Models ◽  
Nursing Staff ◽  
General Solutions ◽  
Room Size ◽  
Number Of Patients ◽  
Internal Arrangement ◽  
Objective Determination ◽  
Made In

The hospital literature of the 1960's contains about a dozen reports or articles pertaining to the relative merits of circular vs. conventional (chiefly linear corridors flanked by patient rooms on both sides). The claims included items other than nurses travel, for example, patient visibility to nursing staff, subjective impressions, and building costs. This article is concerned only with general but quantitative comparisons of these two classes of nursing units with respect to nurses travel. Mathematical models have been developed which permit practically instant evaluation of nursing units where all patient rooms are for a single occupant or where all rooms are for two occupants. The model reflects changes in room size and internal arrangement. Examination of the architect's preliminary sketches permits the determination of superior ority of one layout over another in terms of travel. The fact that this is but one of hundreds of determinations to be made in hospital designs does not diminish its importance. The literature contains various claims to “efficiency” based on no objective criteria. The model provides a simple and objective determination of nurses travel, for any number of patients typically visited and for any pattern of randomness or orderliness in their assignments.

Mathematical Modeling of a Biomass Steam Gasifier—A Modified Equilibrium Approach

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Thomas Gröbl ◽  
Heimo Walter
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Present Article ◽  
Equilibrium Model ◽  
Conversion Process ◽  
Thermochemical Conversion ◽  
Equilibrium Models ◽  
Gasification Process ◽  
Equilibrium Approach ◽  
Made In

A large potential is contributed to the energetic utilization of biomass, whereby thermochemical gasification seems to be especially interesting. In order to contribute to a better understanding of the thermochemical conversion process in the gasifier, mathematical models are used. An intensive effort is made in development of mathematical models describing the gasification process and a large number of models, considerably differing in their degree of simplification, and their applications are reported in literature. In the present article, a brief review of models applied, mainly focused on equilibrium models, is provided and a robust and flexible modified stoichiometric equilibrium model, for modeling a novel gasifier, is presented.

scholarly journals Probability of Ruin under Inflationary Conditions or under Experience Rating

1979 ◽  
Vol 10 (2) ◽  
pp. 149-162 ◽  
Author(s):  
G. C. Taylor
Keyword(s):  
Ruin Probability ◽  
Safety Margin ◽  
Simple Modification ◽  
Probability Of Ruin ◽  
Experience Rating ◽  
Constant Rate ◽  
Aggregate Claims ◽  
Premium Income ◽  
Rating Scheme ◽  
Made In

The effect of inflation of premium income and claims size distribution, but not of free reserves, on the probability of ruin of an insurer is studied.An interesting similarity between this problem and the ruin problem in an experience-rated scheme is exhibited. This similarity allows the deduction of parallel results for the two problems in later sections.It is shown that the probability of ruin is always increased when the (constant) inflation rate is increased.The distribution of aggregate claims under inflationary conditions is described and used to calculate an upper bound on the ruin probability. Some numerical examples show that this bound is not always sharp enough to be practically useful. It is also shown, however, that this bound can be used to construct an approximation of the effect of inflation on ruin probability.It is shown that if inflation occurs at a constant rate, then ruin is certain, irrespective of the smallness of that rate and of the largeness of initial free reserves and the safety margin in the premium. The corresponding result for experiencerated schemes is that a practical and “intuitively reasonable” experience-rating scheme leads eventually to certain ruin.Finally, a simple modification of the techniques of the paper is made in order to bring investment income into account.

Evolution of a Cavitating Bubble in a Nonuniform Pressure Field

2007 ◽  
Author(s):  
Vladimir A. Knyazev ◽  
Vladimir A. Soldatov ◽  
Upendra Singh Rohatgi
Keyword(s):  
Volume Content ◽  
Cavitation Erosion ◽  
Flow Characteristics ◽  
Major Effect ◽  
Wall Layer ◽  
Maximum Efficiency ◽  
Mode Of Operation ◽  
Direct Modeling ◽  
Established Fact ◽  
Made In

The cavitation erosion problem is not a new one; however, it is still important and even becomes more pressing. This is associated with requirements to justify and extend service life of power-generating plants while obviously seeking the maximum efficiency. Currently semiempirical correlation relations are typically used in pump designing for prediction of modes of operation that may be hazardous in terms of development of cavitation erosion [1, 2]. It appears, however, that a progress can be made in this field by introducing numerical modeling of flow with direct modeling of the cavitation erosion process. This optimism is based on an established fact that the major effect of erosion damage is observed in the mode of operation between the “NPSH-incipient” mode (mode of activation of vapor-phase formation centers) and the “NPSH-3%” mode (mode where a noticeable vapor volume content is produced in the near-wall layer), i.e. in the mode of operation where the vapor volume content is small and its effect on flow characteristics can be neglected.

Observations of the Earth's magnetic field made in Edinburgh from 1670 to the present day

1994 ◽  
Vol 85 (4) ◽  
pp. 239-252 ◽  
Author(s):  
D. R. Barraclough
Keyword(s):  
Magnetic Field ◽  
Mathematical Models ◽  
Secular Variation ◽  
Geomagnetic Field ◽  
Upper Atmosphere ◽  
The Difference ◽  
Time Changes ◽  
Relative Measurements ◽  
Magnetic North ◽  
Made In

AbstractMagnetic observations made at the same site give valuable information about the time changes (the secular variation) of the geomagnetic field. This paper gives details of all known measurements of the geomagnetic field in and around Edinburgh since the earliest observation of magnetic declination (the difference between true and magnetic north) by George Sinclair in 1670. Early observations of the strength of the field were only relative measurements. Approximate conversion factors are derived to enable these data to be expressed in modern absolute units (nanoteslas). Observed values of declination, inclination and the horizontal intensity of the geomagnetic field are plotted and compared with values computed from mathematical models of the field covering the interval 1690 to 1990, inclusive. The earlier observations were not corrected for the effects of the rapidly varying magnetic fields caused by electric currents in the upper atmosphere. The consequences of this are estimated.

ON A HIERARCHY OF APPROXIMATE MODELS FOR FLOWS OF INCOMPRESSIBLE FLUIDS THROUGH POROUS SOLIDS

2007 ◽  
Vol 17 (02) ◽  
pp. 215-252 ◽  
Author(s):  
K. R. RAJAGOPAL
Keyword(s):  
Mathematical Models ◽  
Mixture Theory ◽  
Incompressible Fluids ◽  
Porous Solids ◽  
Approximate Models ◽  
Made In

The celebrated equations due to Fick and Darcy are approximations that can be obtained systematically on the basis of numerous assumptions within the context of mixture theory; the equations however not having been developed in such a manner by Fick or Darcy. Relaxing the assumptions made in deriving these equations via mixture theory selectively leads to a hierarchy of mathematical models and it can be shown that popular models due to Brinkman, Biot and many others can be obtained via various approximations. It is shown that a variety of other generalizations are possible in addition to those that are currently in favor, and these might be appropriate for describing interesting technological applications.

Research on the Plight of Place-Identity and Reconstructed Strategy

2014 ◽  
Vol 584-586 ◽  
pp. 2411-2414
Author(s):  
Ying Xian Zhang
Keyword(s):  
Personal Experience ◽  
Place Identity ◽  
Local Characteristic ◽  
Specific Population ◽  
Dominant Position ◽  
Cultural Connotation ◽  
Sense Of Direction ◽  
Mode Of Operation ◽  
Local Residents ◽  
Emotional Dependence

The construction of numerous elements make modern city into a meaningless abstract space. Excess material construction and similar spatial pattern increasingly blur residents ' sense of direction and ascription. People cannot based on personal experience to locate itself, and also cannot develop emotional reliance to the space. Extreme mode of operation has not only replaced the traces of history, but also led to the loss of local characteristic. In the context of this reality, the concept of local design show us a new method.It focuses on the behavior of specific population and activity. It also emphasizes the principle to create cultural connotation of the design. The place who based on local element and method of construction is not only establish emotional dependence and recognition to people, but also can shape and strengthen the dominant position for the local residents at the same time.

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