Volume 25, Issue 1

In this paper a cold standby system consisting of two identical components (first component in working state and second one in the cold standby state) and one repairman is studied. A replacement policy is considered which is based on the number of down times in a renewal cycle. The problem is to determine an optimal policy with respect to the the long run reward per unit time. An explicit expression of the long run reward per unit time is derived and illustrated by a numerical example.

We apply the banded matrix inversion theorem given by Kavcic and Moura [IEEE Trans. Inf. Theory 46: 1495–1509, 2000] to symmetric Toeplitz matrices. If the inverse is banded with bandwidth smaller than its size, there is a gain in arithmetic complexity compared to the current methods for Toeplitz matrix inversion. Our algorithm can also be used to find an approximation of the inverse matrix even though it is not exactly banded, but only well localized around its diagonal.

In this paper mixed sampling plans for acceptance sampling of second quality lots are proposed. Mixed sampling plans combine process control and lot control aiming at increasing the reliability and/or the efficiency of acceptance sampling plans. The process control part refers to a measurable process characteristic and is based on the normal approximation with known standard deviation. The lot control part is performed by an attribute sampling plan based on the truncated Poisson distribution. The operating characteristic function and associated measures are derived and tables are constructed and presented for an easy selection of the plans.

Companies in business and industry often make very different demands on statistical software packages, like flexibility concerning customized solutions, possibility of integrating non-standard stochastic approaches, use to validated applications, user-friendly interface, moderate costs, and many more. Usually, it is not possible to find a single software package that satisfies all such demands. Therefore, it would be attractive for entrepreneurs and statistical consultants if a collaboration among statistical software packages (e.g., leading commercial package extended by open source system) could be realized easily. In this article, we show how statistical procedures offered by R are easily integrated into the graphical user interface of STATISTICA, using the R DCOM Server of [Baier and Neuwirth, R/Scilab (D)COM Server V 3.0-1B5, 2008] and STATISTICA Visual Basic (SVB). We present solutions for different versions of STATISTICA, and illustrate all these approaches by an example from time series analysis: Using the tseries package of [Trapletti and Hornik, The tseries Package, Version 0.10-18, 2009], we tune STATISTICA with R by integrating R's ability for fitting GARCH models to given data into the user interface of STATISTICA.

This paper investigates a more general transient shared load k -out-of- n : G system subject to multiple failure modes and repair facilities, with overhauling service (preventive maintenance) of the system. Expressions for the reliability function, the failure density function and availability of time dependent repairable shared load reliability model are attempted. The steady state solution of the system is obtained using a recursive algorithm. The results are depicted for reliability of the system with and without preventive maintenance.

The method to measure the market risk (which stocks are exposed) by the slope coefficient of a linear regression model (that relates the returns of the asset and the returns of a market index) is known as Market Model. When applying this method it is extremely important to check the stability of the parameters (the slope, the intercept and the variance) over the time to neutralize the market risk. Procedures known in statistical quality control as analysis of linear profiles are presented for such purpose. By statistical tests based on the F -statistics, it is possible to identify the sources of variation and also out-of-control samples. Numerical examples illustrate the proposed procedures.

Anis and Pandey [Economic Quality Control 18: 83–90, 2003] have pointed out that the bias and mean squared error expressions of the estimators of the mean μ of a normally distributed random variable envisaged by Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998] for small samples were found to be erroneous. Keeping this in view, Anis and Pandey [Economic Quality Control 18: 83–90, 2003] have derived an alternative expression for the mean squared error (MSE) of one of the estimators proposed in Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998] claiming that the MSE expression obtained by them is correct. Unfortunately the MSE expression of the estimator given by both Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998] and Anis and Pandey [Economic Quality Control 18: 83–90, 2003] are found incorrect for small samples. In this paper we have derived the correct expressions for biases and MSEs of the estimators suggested in Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998] for small samples of a normally distributed random variable. We also propose two new estimators of the mean μ when the coefficient of variation is known and their properties are studied for small samples. Numerical illustration is given in support of the present study. It is shown both theoretically and empirically that the proposed optimum estimators are more efficient than those considered by Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998].

In this paper a Bounded Intensity Process (BIP) reliability growth model is used to analyze the failure data from repairable systems undergoing a Test-Find-Test growth program, in a Bayes-decision framework. Such an analysis is helpful in improving system reliability. Several identical copies of the equipment are put on test at each development stage. At the end of each stage, a decision between two alternative actions, viz., (a) to accept the current design of the system for mass production, or (b) to continue the development program, is made. The mean number of failures in a prefixed time interval is used to measure the system reliability at each testing stage, so that the decision process is based on the posterior distribution of this quantity and on specific loss functions that measure the economical consequences associated with each alternative action. A numerical example is used to illustrate the decision process.

The problem of allocating optimum heterogeneous redundancy in multi-state series-parallel reliability structures is addressed in this paper. The objective is to obtain a configuration that minimizes the total cost of system design satisfying the given reliability constraint and the consumer load demand. The demand distribution is presented as a piecewise cumulative load curve and each subsystem is allowed to consist of parallel redundant components of not more than four types to construct a reliable system. The redundant components are capacitated binary and chosen from a list of products available in the market. The components are characterized by their feeding capacity, reliability and cost. A system that consists of elements with different reliability and productivity parameters has the capacity strongly dependent upon the selection of constituent components. A binomial probability based method to compute exact system reliability index is suggested. To analyze the problem and suggest an optimal system structure an ant colony optimization (ACO) algorithm is presented. The solution approach consists of a series of simple steps as used in basic ACO algorithms and is still capable to yield very good solutions with promising time efficiency. A randomly generated problem of power station coal transportation system with initial structure is solved for illustration.