A. K. Lal

Analysis of reliability and availability of serial processes of plastic‐pipe manufacturing plant

Purpose – The purpose of this paper is to compute reliability, availability, and mean time before failure of the process of a plastic‐pipe manufacturing plant consisting of a (K, N) system for various choices of failure and repair rates of sub‐systems. This plant consists of eight sub‐systems.Design/methodology/approach – In this paper the Chapman‐Kolmogorov differential equations are formed using mnemonic rule from the transition diagram of the plastic‐pipe manufacturing plant. The governing differential equations are solved using matrix method in order to find the reliability of the system with the help of MATLAB software. The same system of differential equations is solved numerically using Runge‐Kutta fourth order method to validate the results obtain by MATLAB.Findings – The findings in the paper are an analysis of reliability, availability and mean time before failure of plastic‐pipe manufacturing plant has been carried out.Practical implications – This paper proposes matrix calculus method using MA...

Reliability analysis of Polytube industry using supplementary variable technique

Abstract The purpose of this paper is to compute reliability of Polytube manufacturing plant having four units using supplementary variable technique. The failure and repair rates of the sub-systems are variable. The mathematical equations are derived using Chapman–Kolmogorov differential equations which are formed using mnemonic rule from the transition diagram of Polytube manufacturing plant. The system of partial differential equations obtained has been solved using Lagrange’s method and reliability of the system for the various choices of constant transition rates is solved numerically using Runge–Kutta fourth order. A sensitive analysis of subsystem is finally carried out to improve overall availability.

Behavioral study of piston manufacturing plant through stochastic models

Piston plays a vital role in almost all types of vehicles. The present study discusses the behavioral study of a piston manufacturing plant. Manufacturing plants are complex repairable systems and therefore, it is difficult to evaluate the performance of a piston manufacturing plant using stochastic models. The stochastic model is an efficient performance evaluator for repairable systems. In this paper, two stochastic models and computation algorithm of the piston manufacturing plant are illustrated using the state-space transition diagram and availability parameter is used for its behavioral study. Finally, the conclusion is discussed based on the resulting computations.

Equilibrium Structures of Differentially Rotating Primary Components of Binary Stars

In this paper a method is proposed for computing the equilibrium structures and various other observable physical parameters of the primary components of stars in binary systems assuming that the primary is more massive than the secondary and is rotating differentially about its axis. Kippenhahn and Thomas averaging approach (1970) is used in a manner earlier used by Mohan, Saxena and Agarwal (1990) to incorporate the rotational and tidal effects in the equations of stellar structure. Explicit expressions for the distortional terms appearing in the stellar structure equations have been obtained by assuming a general law of differential rotation of the typeω2 = b0+b1s2+b2s4, where ω is the angular velocity of rotation of a fluid element in the star at a distance s from the axis of rotation, and b0, b1, b2 are suitably chosen numerical constants. The expressions incorporate the effects of differential rotation and tidal distortions up to second order terms. The use of the proposed method has been illustrated by applying it to obtain the structures and observable parameters of certain differentially rotating primary components of the binary stars assuming the primary components to have polytropic structures.

Equilibrium structure of stars obeying a generalized differential rotation law

In the present paper we have considered the problem of determining the equilibrium structure of differentially rotating stars in which the angular velocity of rotation varies both along the axis of rotation and in directions perpendicular to it. For this purpose, a generalized law of differential rotation of the typeω2 =b0+b1s2+b2s4+b3z2+b4z4+b5z2s2 (here ω is a nondimensional measure of the angular velocity of a fluid element distants from the axis of rotation andz from the plane through the centre of the star perpendicular to the axis of rotation, andbs are suitably chosen parameters) has been used. Whereas Kippenhahn and Thomas averaging approach has been used to incorporate the rotational effects in the stellar structure equations, Kopals results on Roche equipotentials have been used to obtain the explicit form of the stellar structure equations, which incorporate the rotational effects up to second order of smallness in the distortion parameters. The method has been used to compute the equilibrium structure of certain differentially rotating polytropes. Certain differentially rotating polytropes. Certain differentially rotating models of the Sun have also been computed by using this approach.

A Genetic Algorithm Based Technique for Efficient Scheduling of Tasks on Multiprocessor System

Both parallel and distributed network environment systems play a vital role in the improvement of high performance computing. The primary concern when analyzing these systems is multiprocessor task scheduling. This paper addresses the problem of efficient multiprocessor task scheduling. A multiprocessor task scheduling problem is represented as directed acyclic task graph (DAG), for execution on multiprocessors with communication costs. In this paper we have investigated the effectiveness of a proposed paradigm based on genetic algorithms (GAs). GAs is a class of robust stochastic search algorithms for various combinatorial optimization problems. We have designed a GA based encoding mechanism that uses multi-chromosome encoding scheme. The implementation of the technique is simple. The performance of the designed algorithm has been tested on a variety of multiprocessor systems both heterogeneous as well as homogeneous.

An ϵ-uniform hybrid scheme for singularly perturbed delay differential equations

In this paper, a singularly perturbed delay differential equation of first order has been considered. The problem is solved by using a hybrid scheme on a Shishkin mesh. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Truncation errors are obtained. Finally, numerical experiments are carried out on a test problem, confirming the effectiveness of the proposed technique.

Numerical solution of stochastic partial differential difference equation arising in reliability engineering

In this paper, a numerical method is proposed to solve the transient state of Markovian system of equations. Such equations appear in the field of reliability engineering for systems having variable failure and repair rates. Generally, steady state behaviour of the system model is studied due to some constraint on obtaining transient state solution. The proposed method helps to determine the probability values, by utilizing finite difference scheme iteratively in conjunction with the results of integral appearing in stochastic differential difference equation obtained using supplementary variable technique. This method also uses the Lagranges method to interpolate the missing value of repair rates of the system wherever required in computation. Results thus obtained are found to be efficient for studying the transient state behaviour of the system.

Predicting Total Number of Failures in a Software Using NHPP Software Reliability Growth Models

For a software development project, management often faces the dilemma of when to stop testing the software and release it for operation. Estimating the remaining defects (or failures) in software can help test management to make release decisions. Several methods exist to estimate the defect content in software; among them are also a variety of software reliability growth models (SRGMs). SRGMs have underlying assumptions that are often violated in practice, but empirical evidence has shown that a number of models are quite robust despite these assumption violations. However it is often difficult to know which model to apply in practice. In the present study a method for selecting SRGMs to predict total number of defects in a software is proposed. The method is applied to a case study containing 3 datasets of defect reports from system testing of three releases of a large medical record system to see how well it predicts the expected total number of failures in a software.

Effects of differential rotation on the eigenfrequencies of small adiabatic barotropic modes of oscillations of polytropic models of stars

Mohan et al (1992 Astrophys. Space. Sci. 193 69) (1998 Indian J. Pure Appl. Math. 29 199) investigated the problem of equilibrium structures and periods of small adiabatic oscillations of differentially rotating stellar models using a law of differential rotation of the type ω2 = b0 + b1s2 + b2s4 (here ω is a nondimensional measure of the angular velocity of rotation of a fluid element at a distance s from the axis of rotation and bs are suitably chosen constant parameters). This law of differential rotation assumes cylindrical symmetry for the rotating fluid elements. In the present paper, we have extended their study and used a more general law of differential rotation of the type ω2 = b0 + b1s2 + b2s4 + b3z2 + b4z4 + b5z2s2 in which the angular velocity of rotation of a fluid element is assumed to depend both on its distance s from the axis of rotation and on its distance z from the plane through the center of the star perpendicular to the axis of rotation. The main objective of this study has been to investigate whether the dependence of angular velocity of rotation on the parameter z in addition to the parameter s substantially alters the behavior of the eigenfrequencies of small adiabatic barotropic modes of oscillations of differentially rotating stars or not.