M. Yastrebenetsky, A. Bochkov

IN MEMORY OF PROFESSOR IGOR USHAKOV

Mark P. Kaminskiy

HUMAN LIFESPAN DISTRIBUTION WITH MAXIMUM LIFESPAN PARAMETER

The problem of existence of maximum human lifespan is discussed.  Assuming that the maximum human lifespan exists, a new lifespan distribution is suggested. In opposite to the popular lifespan distributions (Gompertz, Weibull, Extended Weibull, etc.) supported on the semi-infinite interval [0, ∞), the suggested lifespan distribution is supported on the finite interval [0, a), in which a is the non-random maximum lifespan. The suggested lifespan distribution was applied to three death rate datasets (Australia, France, and Switzerland) from the Human Mortality Database, for which the parameters of the suggested lifespan distribution were estimated.  The fitted death rates have the high proportion of variance explained by the models (R2 ≥ 0.96), and the estimated maximum lifespan is about 200 years. A more adequate lifespan distribution might be a distribution having two competing risks – the risk of death from diseases, and the risk of death from “pure” aging.

Mykhailo D. Katsman, Viktor K. Myronenko, Viacheslav I. Matsiuk

MATHEMATICAL MODELS OF ECOLOGICALLY HAZARDOUS RAIL TRAFFIC ACCIDENTS

The paper discusses the queuing system mathematical models simulating the development of processes of rail traffic accidents with hazardous materials as well as elimination of such accidents ecologically dangerous consequences. A new theoretical approach is proposed that enables a more rational dislocation of emergency detachments on railroad network and more successful actions by such detachments aimed at minimization of environmental damage and cargo losses.

Y. Paramonov,  S. Tretyakov,  M. Hauka

FATIGUE-PRONE AIRCRAFT FLEET RELIABILITY BASED ON THE USE OF A P-SET FUNCTION

An inspection interval planning is considered in order to limit a probability of any fatigue failure (FFP) in a fleet of N aircraft (AC). A solution of this problem is based on a processing of the result of the acceptance fatigue test of a new type of an aircraft. During this test an estimate of the parameter of a fatigue crack growth trajectory can be obtained. If the result of this acceptance test is too bad then this new type of aircraft will not be used in service. A redesign of this project should be done. If the result of acceptance test is too good then the reliability of the aircraft fleet will be provided without inspections. For this strategy there is a maximum of FFP as a function of an unknown parameter sigma. This maximum can be limited by the use of the offered here procedure of the choice of an inspection number.

G. Unnikrishnan, Shrihari, Nihal A. Siddiqui

ANALYSIS OF INDEPENDENT PROTECTION LAYERS AND SAFETY INSTRUMENTED SYSTEM FOR OIL GAS SEPARATOR USING BAYESIAN METHODS

Process and Nuclear industries use Independent Protection Layers (IPLs) to prevent initiating abnormal events from becoming accidents. They form layers of protection that acts to prevent an abnormal situation from escalating. IPLs can be hardware (Basic Control System-BPCS) or operator actions, active (Safety Instrumented System-SIS) or passive (Dike walls) or a combination of all these factors. Safety Instrumented System (SIS) is the protection layer that comes in to action in case of failure of BPCS and operator action. Therefore reliability and ability of the SIS to respond should be higher than that of the layer like the BPCS. Reliability of SIS is usually specified in terms of Safety Integrity Level (SIL). The required SIL is calculated by analyzing the Probability of Failure of Demand (PFD) of all the IPLs in the case of an Initiating Event (IE) and comparing the Mitigated Consequence Frequency with a pre-established Tolerable Frequency (TF). The calculations involve probability of failure of each of layers and are usually done through spreadsheet or proprietary software. Bayesian methods are suited to handle these calculations due the nature of conditional probabilities inherent in the system. Further Bayesian methods can analyze the influencing factors affecting the PFD of the IPLs. This paper will present analysis of IPLs and its influencing factors using Bayesian methods including application of Common Cause Failures (CCF) and NoisyAnd distribution to Conditional Probability Tables (CPTs).

M.A.  Dubitsky, A.A.  Rykova

CLASSIFICATION OF POWER RESERVES OF ELECTRIC POWER SYSTEMS 

Single Electric Energy System of Russia (SEES) is one of the largest energy systems in the world. It includes 69 regional power systems that, in turn, form seven interconnected power systems (IPS), namely: IPS of the East, IPS of Siberia, IPS of the Urals, IPS of the Middle Volga, IPS of the South, IPS of the Centre, and IPS of the North-West.      Electric energy complex of SEES of Russia includes more that 700 power plants whose capacity exceeds 5 MW.  As of the end of 2013 the installed capacity of power plants within SEES of Russia totalled 226,470.18 MW. All the IPS are connected by inter-system high-voltage 220-500 kV (and higher) power lines that operate in parallel. Power system of the Crimea is currently referred to technologically independent power systems (PS) of Russia.

V.M.Chacko,  Mariya Jeeja P V, Deepa Paul

p-BIRNBAUM SAUNDERS DISTRIBUTION: APPLICATIONS TO RELIABILITY AND ELECTRONIC BANKING HABITS

Birnbaum and Saunders (1969) introduced a two-parameter lifetime distribution which has been used quite successfully to model a wide variety of univariate positively skewed data. Diaz-Garcia and Leiva-Sanchez proposed a generalized Birnbaum Saunders distribution by using an elliptically symmetric distribution in place of the normal distribution. In this paper, we construct a new distribution, say p-Birnbaum-Saunders distribution, by introducing a new parameter ‘p’, which influences both Skewness and Kurtosis. The deviation from the behaviour of Birnbaum and Saunders distribution can be accommodated in the new p-Birnbaum Saunders (p-BS) distribution. Different properties of this distribution are obtained. Most of the data from Reliability and Banking sector is having skewness and their frequency curve is from among the class of p-BS distribution. A data set from internet banking sector is considered.

Farzaliyev Y.Z.

METHOD AND ALGORITHM OF RANGING OF RELIABILITY OBJECTS OF THE POWER SUPPLY SYSTEM

Ranging of objects is widely applied at the decision of operational problems. However, it is spent mainly intuitively. There are developed method and algorithm of ranging of objects of a power supply system on independent parameters of reliability and profitability of work with the recommendation of the basic directions of improvement of these parameters.

Paolo Rocchi

CAN THE RELIABILITY THEORY BECOME A SCIENCE?

The amount of works in the reliability domain is really huge although this field of research has not yet evolved as a science. It is worth reminding that Gnedenko took the first step to create the reliability science. He adopted the deductive logic – typical of exact sciences such as mechanics, electronics and thermodynamics – and demonstrated the general form of the reliability function. However the hazard rate, which tunes up this function, has not been demonstrated so far. We believe that one should follow and complete the Gnedenko’s seminal work and should demonstrate the various trends of the hazard rate using the deductive approach.  We have conducted a theoretical research using traditional mathematical methods and have even introduced a new tool named Boltzmann-like entropy. The present paper makes a summary of various contributions published in the past decade and means to show the deductive implications developed.