Exponential probability distribution on symmetric matrices

This paper displays the design and application of a model that simulates the queuing system of a fictional post office. Starting point for solving more complicated optimization tasks is to create a system model that consists of elements of reality and the relationships between these elements. The key part of the paper includes the model of a queuing system of a post office created in Anylogic simulation software. The model of the post office displays post office with 5 postal counters, a certain input flow and a certain service time with an exponential probability distribution. The model also includes statistics and cost calculation.

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The Extended Matrix-Variate Beta Probability Distribution on Symmetric Matrices

Methodology And Computing In Applied Probability ◽

10.1007/s11009-019-09725-5 ◽

2019 ◽

Vol 22 (2) ◽

pp. 647-676

Author(s):

Mariem Tounsi

Keyword(s):

Probability Distribution ◽

Symmetric Matrices ◽

Extended Matrix

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Modelling of wear debris in planetary gear drive

Industrial Lubrication and Tribology ◽

10.1108/ilt-03-2018-0121 ◽

2019 ◽

Vol 71 (2) ◽

pp. 199-204

Author(s):

Rakesh Ranjan ◽

Subrata Kumar Ghosh ◽

Manoj Kumar

Keyword(s):

Probability Distribution ◽

Aspect Ratio ◽

Wear Debris ◽

Planetary Gear ◽

Wear Particle ◽

Distribution Model ◽

Wear Particles ◽

Slab Caster ◽

Content Type ◽

Exponential Probability

Purpose The probability distribution of major length and aspect ratio (major length/minor length) of wear debris collected from gear oil used in planetary gear drive were analysed and modelled. The paper aims to find an appropriate probability distribution model to forecast the kind of wear particles at different running hour of the machine. Design/methodology/approach Used gear oil of the planetary gear box of a slab caster was drained out and charged with a fresh oil of grade (EP-460). Six chronological oil samples were collected at different time interval between 480 and 1,992 h of machine running. The oil samples were filtered to separate wear particles, and microscopic study of wear debris was carried out at 100X magnification. Statistical modelling of wear debris distribution was done using Weibull and exponential probability distribution model. A comparison was studied among actual, Weibull and exponential probability distribution of major length and aspect ratio of wear particles. Findings Distribution of major length of wear particle was found to be closer to the exponential probability density function, whereas Weibull probability density function fitted better to distribution of aspect ratio of wear particle. Originality/value The potential of the developed model can be used to analyse the distribution of major length and aspect ratio of wear debris present in planetary gear box of slab caster machine.

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