RELIABILITY MEASURES OF SYSTEMS WITH LOCATION-SCALE ACBVE COMPONENTS

Block and Basu (1974) proposed an absolutely continuous bivariate exponential distribution whose marginals are weighted average of exponentials. Chandrasekar and Sajesh (2010) considered location, scale and location-scale families arising out of absolutely continuous bivariate exponential (ACBVE) distribution with equal marginals and derived the minimum risk equivariant estimators of location, scale and location-scale parameters. In this paper we consider a two-component system when failure times follow location-scale ACBVE distribution with equal marginals. We obtain the reliability performance measures of two-component parallel, series and standby systems. Also we provide the UMVUE, the MLE and the MREE of these reliability performance measures.

WIND-HYDRO POWER SYSTEM AS AN EXAMPLE OF DIVERSIFICATION OF DISTRIBUTED GENERATION

The paper considers using renewable wind energy for electricity generating. The system is characterized by high reliability and ecological purity. The authors briefly present the main methodological principles of choosing the parameters of the considered wind-hydro power system.

STEP STRESS ACCELERATED LIFE TESTING PLAN FOR TWO PARAMETER PARETO DISTRIBUTION

In Accelerated life testing if the accelerated test stress level is not high enough then many of the test items will not fail during the available time and one has to be prepared to handle a lot of censured data. To avoid such type of problems, a better way is step-stress ALT. In Step-stress ALT all test items are first tested at a specified constant stress for a specified period of time and then Items which are not failed will be tested at next higher level of stress for another specified time and so on until all items have failed or the test stops for other reasons. In this paper simple step stress pattern of ALT assuming that the lifetime of a product at any constant level of stress follow a two parameter Pareto distribution is considered. The maximum likelihood and asymptotic confidence interval estimate of the parameters are obtained. Optimal step stress ALT plan is proposed by minimizing the asymptotic variance of the MLE of the 100 Pth percentile of the lifetime distribution at normal stress condition.  A simulation study is also performed to analyse the performance of parameter estimates.

OPTIMAL REDUNDANCY IN SYSTEMS WITH MULTI-LEVEL UNITS

Method of Universal Generating Function (UGF) was introduced in many papers. Here we give an example how method of UGF can be implemented to solution problems of optimal redundancy for systems consisting of multi-level units.

MEAN RESIDUAL LIFE CRITERIA OF FIRST PASSAGE TIME OF SEMI-MARKOV PROCESS BASED ON TOTAL TIME ON TEST TRANSFORMS

Mean residual life criteria of first passage time of semi-Markov process is considered. Properties of transition probability functions when using scaled Total Time on Test (TTT) transform for some criteria of mean residual life are discussed. Application to Multistate reliability system is also addressed.

COMPLEX DELTA – FUNCTION

Smagin V.A. the brief review of a history of introduction of delta - function on a complex plane. The proof of the mathematical form of complex delta - function is given. The example of application of complex delta - function for a presence of stationary value alternation casual process of accumulation with the information income and the charge is given.

PROBABILISTIC MODEL OF ECOLOGICAL CONSEQUENCES OF RAILROAD ACCIDENTS

The paper discusses the processes of inertial reacting and self-regulation of the environment impacted by hazards of railway accidents involving dangerous goods and the queuing system Markovian model is proposed to determine the probable consequences of such accidents development.

INLIER PRONESS IN NORMAL DISTRIBUTION

Inliers in a data set are subset of observations not necessarily all zeroes, which appears to be inconsistent with the remaining data set. They are either the resultant of instantaneous or early failures usually encountered in life testing, financial, clinical trial and many other studies. We study the estimation of inliers in Normal distribution. The masking effect problem for correctly identifying the inliers is also discussed. An illustration and a real life example is presented with detailed discussions.

Application of Chebyshev- and MarKov-type inequalities in structural engineering

This paper aims at bringing out the usefulness of Chebyshev- and Markov- type inequalities in structural engineering design decision making.  By examining whether the bounds arising from Chebyshev - type inequality (associated with these are weak upper bound probabilities) enclose the respective experimental values for deflections of six ferrocement I-beams and web shear fatigue life of a steel plate girder it is inferred that the bounds and the associated probabilities estimated are realistic and hence can be used in structural engineering design decision making. The paper also presents some recent developments in application of Markov type inequalities (which are due to Steliga and Szynal (2010)) for estimation of bounds on probability of an event sought.  The importance of such bounds in structural engineering applications is brought out.  It is shown from the results of Monte Carlo simulation that the bounds on probability of an event, estimated using the method presented by Steliga and Szynal, are sharp.  One of the important advantages of the bounds presented by Steliga and Szynal (2010) is that the original (hidden/internal) random variable need not have well defined moments. Possible engineering applications are also pointed out.