American Journal of Mathematical and Management Sciences

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  • ISSN
    0196-6324

Publications in this journal

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    ABSTRACT: Redundancy allocation, being an important and effective way to improve system reliability, has been discussed by many authors. The main idea, which has been advocated in this article, lies in the fact that some components have more significance in the functioning of the system than the others; because of this, it is expected that if allocation of the redundant component is made according to some component-importance measure, optimality can be achieved easily. The novelty of this study is that the problem of redundancy allocation has been solved by allocating redundant components according to some component-importance measures that are not very difficult to obtain and comprehend for an engineered system, even when there is no information about the reliability of the components. The component structural-importance measure and reliability-importance measure have been used in this work for the purpose of allocating redundancy. The results derived can be used to maximize system reliability using redundancy allocation for a general n-component coherent system. Applications of the results have been illustrated with examples of coherent systems.
    American Journal of Mathematical and Management Sciences 01/2014; 33(1).
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    ABSTRACT: The purpose of this work is to study an inventory model for a deteriorating item considering time-quadratic demand and time-dependent partial backlogging, which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle. The model is solved analytically to obtain the optimal solution of the problem. The sufficient condition of the optimal solution is also studied. It is then illustrated with the help of numerical examples.
    American Journal of Mathematical and Management Sciences 01/2014; 33(2).
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    ABSTRACT: The purpose of this paper is to present a linear integer programming approach to construct efficient binary incomplete block designs for any given number of treatments v, number of blocks b, with common block-size k, and with a nearly balanced concurrence matrix. The proposed approach is illustrated by constructing an efficient incomplete block design. A-efficient and D-efficient incomplete block designs have been constructed and catalogued using the proposed algorithm for a restricted range of parameters 3 v 20, b v, and 2 k min(10, v − 1), with vb1, 000. An R package is developed to implement the proposed approach.
    American Journal of Mathematical and Management Sciences 01/2014; 33(2).
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    ABSTRACT: Sousa, Shabbir, Corte-Real, and Gupta (2010) and Gupta, Shabbir, Sousa, and Corte-Real (2012) have presented ratio and regression estimators for the finite population mean of a sensitive study variable utilizing nonsensitive auxiliary information. We improve the results further by using optional scrambling. In the process, we also estimate the sensitivity level of the underlying sensitive question. We compare the proposed method with Sousa et al. (2010) and Gupta et al. (2012) estimators.
    American Journal of Mathematical and Management Sciences 01/2014; 33(2).
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    ABSTRACT: In this article, we propose a double acceptance sampling plan based on the truncated life test for Maxwell distribution. By fixing the consumer’s confidence level, the minimum sample sizes of the first and second samples necessary to ensure the specified mean life are obtained. The operating characteristic values and the minimum ratios of the mean life to the specified life are also analyzed. Several useful tables are provided. We illustrate the double acceptance sampling plan with a numerical example.
    American Journal of Mathematical and Management Sciences 01/2014; 33(2).
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    ABSTRACT: In this study we have considered different methods of estimation of the unknown parameters of a two-parameter Rayleigh distribution from both the frequentists' and the Bayesian view points. First, we briefly describe different frequentists' approaches: maximum likelihood estimators, method of moments estimators, L-moment estimators, percentile-based estimators, and least squares estimators, and we compare them using extensive numerical simulations. We have also considered Bayesian inferences of the unknown parameters. It is observed that the Bayes estimates and the associated credible intervals cannot be obtained in explicit forms, and we have suggested using an importance sampling technique to compute the Bayes estimates and the associated credible intervals. We analyze one dataset for illustrative purposes.
    American Journal of Mathematical and Management Sciences 01/2014; 33(1).
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    ABSTRACT: The product of the independent Bernoulli and exponential random variables (rv's), has received great attention in recent literature, in particular because of its applications in network traffic, computer communications, and health sciences. However, the behavior of the sum of such independent rvs has not been fully explored. In this article, we present the probability density function (PDF) of the product of exponential and Bernoulli sum as a mixture of two types of distribution functions: the Dirac delta and gamma type distributions. The statistical properties of the sum, such as its survival function, moment generating function, and Laplace transform are derived.
    American Journal of Mathematical and Management Sciences 01/2013; 32(1).
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    ABSTRACT: The problem of finding system reliability is difficult in a multicomponent stress-strength model because the strengths of different components may be different, and they may experience the same or different stress levels. In a single-component stress-strength model, reliability of a component is the probability of its strength being greater than the stress imposed on it. In a multicomponent stress-strength model, we must take into account the structure function of the system and respective stress and strength levels of the components while determining the system reliability. In this article we show how the stress-strength reliability of a multicomponent system, at least its lower bound, can be derived. The stress-strength reliability of a system is expressed here as a function of the stress-strength reliabilities of its individual components. This generalized expression helps evaluate the stress-strength reliability of different coherent systems, regardless of the dependent or independent nature of the stress and strength variables.
    American Journal of Mathematical and Management Sciences 01/2013; 32(1).
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    ABSTRACT: Entomological, biological, and epidemiological literature show that two-parameter negative binomial distribution is useful for modeling count data. Here, we consider the problem of selecting the population with the largest (or smallest) mean from at least k(k 2)available negative binomial populations with a known exponent. The selection is to be carried out based on the fixed-sized samples using an indifference approach. It is shown that a single-stage procedure based only on the difference or ratio formulation of the distance measure does not exist for the negative binomial populations.
    American Journal of Mathematical and Management Sciences 01/2013; 32(4).
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    ABSTRACT: In this study we give exact expressions and some recurrence relations for marginal and joint moment generating functions of lower generalized order statistics from Marshall-Olkin extended logistic distribution. The results for order statistics and lower record values are deduced from the relations derived. Further, a characterization of this distribution by considering recurrence relations for marginal moment generating functions of the lower generalized order statistics is presented.
    American Journal of Mathematical and Management Sciences 01/2013; 32(1).
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    ABSTRACT: This study considers a repair-replacement problem for a repairable cold standby system that is composed of two similar components with preventive maintenance. The system may fail because of intrinsic or extrinsic factors such as shocks. The shocks arrive according to a Poisson process. Whenever the magnitude of a shock exceeds a prespecified threshold of the operating component, the operating component fails. We assume that the intrinsic lifetime, the threshold, and the repair time of the operating component are geometric processes. A bivariate repair-replacement policy ( T,N) is adopted for the system, where T is the interval length between preventive maintenances and N is the number of failures of component 1. The explicit expression of the expected long-run cost-per-unit time is derived and the corresponding optimal bivariate policy ( T,N) can be determined analytically or numerically. Finally, three numerical examples are given to validate the theoretical results of the proposed model.
    American Journal of Mathematical and Management Sciences 01/2013; 32(3).
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    ABSTRACT: In this study, we develop a step-down procedure to find the Minimum Effective Dose (MINED) of a new drug when there is more than one control drug. The computation of critical points required to implement the proposed procedure is discussed by taking the normal probability model under equal sample size allocation. Power of the test is computed, and some power comparisons are made under different sample sizes.
    American Journal of Mathematical and Management Sciences 01/2013; 32(4).
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    ABSTRACT: In this study we obtain explicit expressions and some recurrence relations for single and product moments of lower generalized order statistics from the exponentiated Lomax distribution. The results for order statistics and lower record value from the relation are derived. Further, a characterizing result of this distribution on using the conditional moment of lower generalized order statistics is discussed.
    American Journal of Mathematical and Management Sciences 01/2013; 32(4).
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    ABSTRACT: In this paper, we consider approximations to the upper percentiles of the statistic for pairwise comparisons among components of mean vector in elliptical distributions. On the basis of Bonferroni’s inequality, the approximate upper percentiles of the statistic are derived. Also, we investigate the effects of nonnormality on the upper percentiles of this statistic in elliptical distributions. Finally, in order to evaluate the accuracy of the approximations, numerical results are given, and we investigate their robustness for the distribution by Monte Carlo simulations in general distributions.
    American Journal of Mathematical and Management Sciences 01/2013; 32(1).
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    ABSTRACT: Redundancy is an important aspect of system design. The use of redundancy improves system reliability. In the case of systems whose cost of failure is very high, redundancy may be used to make the system fail-safe, and thus, in any safety-critical systems, a proper use of redundancy is essential. Because adding redundancy increases the total cost and complexity of a system design, it should be used wisely, taking the cost and other constraints into account. The question arises with regard to how many redundant components should be added to different components or subsystems of a coherent system in order to maximize the system reliability. The problem becomes more difficult when the maximization is to be done under various constraints. The present study solves a redundancy allocation problem (RAP) in a complex system in an optimal way under various constraints involving cost, weight, volume, and so forth. The rule developed here can be used to maximize the reliability of any simple or complex coherent systems under any number of constraints. A numerical example has been included to illustrate the method.
    American Journal of Mathematical and Management Sciences 01/2013; 32(4).

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