First Digit Oscillations

The frequency of the first digits of numbers drawn from an exponential probability density oscillate around the Benford frequencies. Analysis, simulations and empirical evidence show that datasets must have at least 10,000 entries for these oscillations to emerge from finite-sample noise. Anecdotal evidence from population data is provided.

NEW EXPONENTIAL PROBABILITY INEQUALITY AND COMPLETE CONVERGENCE FOR F-LNQD RANDOM VARIABLES SEQUENCE WITH APPLICATION TO AR(1)MODEL GENERATED BY F-LNQD ERRORS

The exponential probability inequalities have been important tools in probability and statistics. In this paper, we prove a new tail probability inequality for the distri-butions of sums of conditionally linearly negative quadrant dependent (F-LNQD , in short) random variables, and obtain a result dealing with conditionally complete con-vergence of first-order autoregressive processes with identically distributed (F-LNQD) innovations.

Simulation of a Queuing System of a Post Office in Anylogic Software

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.

An EPQ inventory model considering an imperfect production system with probabilistic demand and collaborative approach

Purpose The purpose of this paper is to propose an economic production quantity (EPQ) inventory model considering imperfect items and probabilistic demand for a two-echelon supply chain. The production process is imperfect and the imperfect quality items are removed from the lot size. The demand rate of the inventory system is random and follows an exponential probability density function and the demand of the retailers is depending on the initiatives of the sales team. Design/methodology/approach Two approaches are examined. In the non-collaborative approach, any member of the supply chain can be the leader and takes decisions to optimize the profits, and in the collaborative system, all members make joint decisions about the production, supply, sales and inventory to optimize the profits of the supply chain members. The calculus approach is applied to find the maximum profit related to the members of the supply chain. Findings A numerical example is presented to illustrate the performance of the EPQ model. The results show that collaborative approach generates greater profits to the supply chain and the market’s demand represents the variable behavior and uncertainty that is generated in the replenishment of a supply chain. Originality/value The new and major contributions of this research are: the inventory model considers demand for products is random variable which follows an exponential probability distribution function and it also depends on the initiatives of sales teams, the imperfect production system generates defective items, different cycle time are considered in manufacturer and retailers and collaborative and non-collaborative approaches are also studied.

Explaining the Effect of Surrounding Pressure on Splashing Phenomena of Liquid Drop using Statistical Mechanics

This paper explains the effect of surrounding gas pressure on splashing phenomena of liquid drop using fixed volume canonical ensemble of gas at high pressure and liquid. The energy state fluctuations in liquid drop energy (𝐸_𝐿) are given by exponential probability distribution at high pressures. High pressure increases the translational components of the kinetic energy which are not normal to the drop surface. This corresponds to higher range of incidence angles, which controls the impact outcome. Furthermore, Surface coverage of liquid molecules (𝜃_𝑙𝑖𝑞) by adsorption process is derived, which is the function of surrounding gas pressure 𝑝. High pressure decreases the surface coverage of liquid molecules making the liquid drop more vulnerable for splashing.

Modelling of wear debris in planetary gear drive

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.