Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Concomitants of Order Statistics from Morgenstern Family

The study deals with the distribution theory and applications of concomitants from the Morgenstern family of bivariate distributions.The Morgenstern system of distributions include all cumulative distributions of the form FX,Y(X,Y)=FX(X) FY(Y)[1+α(1-FX(X))(1-FY(Y))], -1≤α≤1.The system provides a very general expression of a bivariate distributions from which members can be derived by substituting expressions of any desired set of marginal distributions.It is a brief description of the basic distribution theory and a quick review of the existing literature.The Morgenstern family considered in the present study provides a very general expression of a bivariate distribution from which several members can be derived by substituting expressions of any desired set of marginal distributions.Order statistics play a very important role in statistical theory and practice and accordingly a remarkably large body of literature has been devoted to its study.It helps to develop special methods of statistical inference,which are valid with respect to a broad class of distributions.The present study deals with the general distribution theory of Mk, [r: m] and Mk, [r: m] from the Morgenstern family of distributions and discuss some applications in inference, estimation of the parameter of the marginal variable Y in the Morgestern type uniform distributions.

Microwave Plasma Assisted ALD Development for the Deposition of Gate Oxides & ALD of High-k Dielectrics

The semiconductor industry's urge towards faster, smaller and cheaper integrated circuits has lead the industry to smaller node devices. The integrated circuits that are now under volume production belong to 22 nm and 14 nm technology nodes. In 2007 the 45 nm technology came with the revolutionary high- /metal gate structure. 22 nm technology utilizes fully depleted tri-gate transistor structure. The 14 nm technology is a continuation of the 22 nm technology. Intel is using second generation tri-gate technology in 14 nm devices. After 14 nm, the semiconductor industry is expected to continue the scaling with 10 nm devices followed by 7 nm. Recently, IBM has announced successful production of 7 nm node test chips. This is the fashion how nanoelectronics industry is proceeding with its scaling trend. For the present node of technologies selective deposition and selective removal of the materials are required. Atomic layer deposition and the atomic layer etching are the respective techniques used for selective deposition and selective removal. Atomic layer deposition still remains as a futuristic manufacturing approach that deposits materials and lms in exact places. In addition to the nano/microelectronics industry, ALD is also widening its application areas and acceptance. The usage of ALD equipments in industry exhibits a diversi cation trend. With this trend, large area, batch processing, particle ALD and plasma enhanced like ALD equipments are becoming prominent in industrial applications. In this work, the development of an atomic layer deposition tool with microwave plasma capability is described, which is a ordable even for lightly funded research labs.

Analysis of Some Queueing Models Related To N-Policy: Operations Research

This study is about the analysis of some queueing models related to N-policy.The optimal value the queue size has to attain in order to turn on a single server, assuming that the policy is to turn on a single server when the queue size reaches a certain number, N, and turn him off when the system is empty.The operating policy is the usual N-policy, but with random N and in model 2, a system similar to the one described here.This study analyses “ Tandem queue with two servers”.Here assume that the first server is a specialized one.In a queueing system,under N-policy ,the server will be on vacation until N units accumulate for the first time after becoming idle.A modified version of the N-policy for an M│M│1 queueing system is considered here.The novel feature of this model is that a busy service unit prevents the access of new customers to servers further down the line.It is deals with a queueing model consisting of two servers connected in series with a finite intermediate waiting room of capacity k.Here assume that server I is a specialized server.For this model ,the steady state probability vector and the stability condition are obtained using matrix – geometric method.

Determination of the nature of the diperiodatocuprate(III) species in aqueous alkaline medium through a kinetic and mechanistic study on the oxidation of iodide ion

The nature of the diperiodatocuprate(III) (DPC) species present in aqueous alkaline medium has been investigated by a kinetic and mechanistic study on the oxidation of iodide by DPC. The reaction kinetics were studied over the 1.0 ´ 10)3±0.1 mol dm)3 alkali range. The reaction order with respect to DPC, as well as iodide, was found to be unity when [DPC] [I)]. In the 1.0 ´ 10)3±1.0 ´ 10)2 mol dm)3 alkali region, the rate decreased with increase in the alkali concentration and a plot of the pseudo-®rst order rate constant, k versus 1/[OH)] was linear. Above 5.0 ´ 10)2 mol dm)3, a plot of k versus [OH)] was also linear with a non-zero intercept. An increase in ionic strength of the reaction mixtures showed no e ect on k at low alkali concentrations, whereas at high concentrations an increase in ionic strength leads to an increase in k. A plot of 1/k versus [periodate] was linear with an intercept in both alkali ranges. Iodine was found to accelerate the reaction at the three di erent alkali concentrations employed. The observed results indicated the following equilibria for DPC.

OPTIMAL UTILIZATION OF SERVICE FACILITY FOR A k-OUT-OF-n SYSTEM WITH REPAIR BY EXTENDING SERVICE TO EXTERNAL CUSTOMERS IN A RETRIAL QUEUE

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability and with probability 1− leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability (< 1) and with probability 1 − leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

Studies on the horizontal and vertical distribution of clouds and their impact on energetics of the Atmosphere over the Indian Region

Motivation for the present study is to improve the scienti c understanding on the prominent gap areas in the average three-dimensional distribution of clouds and their impact on the energetics of the earth-atmosphere system. This study is focused on the Indian subcontinent and the surrounding oceans bound within the latitude-longitude bands of 30 S to 30 N and 30 E to 110 E. Main objectives of this study are to : (i) estimate the monthly and seasonal mean vertical distributions of clouds and their spatial variations (which provide the monthly and seasonal mean 3-dimensional distributions of clouds) using multi-year satellite data and investigate their association with the general circulation of the atmosphere, (ii) investigate the characteristics of the `pool of inhibited cloudiness' that appear over the southwest Bay of Bengal during the Asian summer monsoon season (revealed by the 3-dimensional distribution of clouds) and identify the potential mechanisms for its genesis, (iii) investigate the role of SST and atmospheric thermo-dynamical parameters in regulating the vertical development and distribution of clouds, (iv) investigate the vertical distribution of tropical cirrus clouds and their descending nature using lidar observations at Thiruvananthapuram (8.5 N, 77 E), a tropical coastal station at the southwest Peninsular India, and (v) assessment of the impact of clouds on the energetics of the earth-atmosphere system, by estimating the regional seasonal mean cloud radiative forcing at top-of-the-atmosphere (TOA) and latent heating of the atmosphere by precipitating clouds using satellite data

ToxicMetals Enrichment in the Surficial Sediments of a Eutrophic Tropical Estuary (Cochin Backwaters, Southwest Coast of India)

Concentrations and distributions of trace metals (Cd, Co, Cr, Cu, Fe, Mn, Ni, Pb, and Zn) in surficial sediments of the Cochin backwaters were studied during both monsoon and pre-monsoon periods. Spatial variations were in accordance with textural charaterstics and organic matter content. A principal component analysis distinguished three zones with different metal accumulation capacity: (i) highest levels in north estuary, (ii) moderate levels in central zone, and (iii) lowest levels in southern part. Trace metal enrichments are mainly due to anthropogenic contribution of industrial, domestic, and agricultural effluents, whose effect is enhanced by settling of metals due to organic flocculation and inorganic precipitation associated with salinity changes. Enrichments factors using Fe as a normalizer showed that metal contamination was the product of anthropogenic activities. An assessment of degree of pollution-categorized sediments as moderately polluted with Cu and Pb, moderately-to-heavily polluted with Zn, and heavily-to-extremely polluted with Cd. Concentrations at many sites largely exceed NOAA ERL (e.g., Cu, Cr, and Pb) or ERM (e.g., Cd, Ni, and Zn). This means that adverse effects for benthic organisms are possible or even highly probable.