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The conditional spacings are investigated here based on a series system with n heterogeneous exponential component lifetimes. First, the survival function and the joint distribution of conditional spacings are obtained. Then, the survival function of the first spacing is shown to be Schur-convex in the hazard rates of component lifetimes. Further, some stochastic comparisons of spacings are carried out. Finally, some results for the conditional sample range are discussed. [ABSTRACT FROM AUTHOR]

Often, reliability systems suffer shocks from external stress factors, stressing the system at random. These random shocks may have non ignorable effects on the reliability of the system. In this article, we provide sufficient (and necessary) conditions on components' lifetimes and their survival probabilities from random shocks for comparing the lifetimes of two parallel systems with independent components by means of usual stochastic and reversed hazard rate orders, when the matrix of parameters changes to another matrix in a mathematical sense. We also discuss stochastic comparisons of series systems with independent components under random shocks in the sense of usual stochastic and hazard rate orders, by using the concept of vector majorization and related orders. The results developed in this article generalize some known results in the literature. [ABSTRACT FROM AUTHOR]

This paper examines the problem of stochastic comparisons of series and parallel systems with independent heterogeneous new extended Weibull distributed components. For series systems, we obtain the usual stochastic order via the concepts of weak weighted and unordered majorization orders. Also, we strengthen this result to the hazard rate order under a restriction. For parallel systems, with the help of weak supermajorization and weak submajorization orders, we establish the usual stochastic order. The results of this paper can be used to find some bounds for the important aging characteristics of series and parallel systems consisting of independent heterogeneous new extended Weibull distributed components. [ABSTRACT FROM AUTHOR]

This article deals with stochastic comparisons of series systems comprising a new modified generalized linear failure rate family of distributions. The results are established in three directions. First, we establish based on vector majorization the usual stochastic order and the hazard rate order of series systems. Next, multiple-outlier models are considered. When the number of components is equal, the results are obtained in terms of the likelihood ratio order. For an unequal number of components, we develop comparisons according to the usual stochastic order, and hazard rate order. Then, based on weak majorization and p-larger orders between the vector of parameters, some characterization results for comparing the lifetimes of series systems are also established. Finally, we discuss based on multivariate chain majorization the usual stochastic order of series systems. Numerical examples are considered to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper studies the usual stochastic, star, convex transform, and dispersive orders of both series and parallel systems comprised of dependent log-logistic components. We establish that, without any restriction on the parameters, the lifetime of a parallel or series system with dependent components is smaller than that with dependent homogeneous components in the sense of the dispersive orders. Sufficient conditions are established for the star ordering between the lifetimes of series and parallel systems consisting of multiple outlier dependent log-logistic distributed components. Under certain conditions on the Archimedean copula and the parameter, we also discuss convex transform order of series and parallel systems. [ABSTRACT FROM AUTHOR]

In this paper, we have considered systems with dependent components having a joint distribution modeled by an Archimedean copula and with component lifetimes following accelerated failure time and modified proportional hazards distributions. We have then established characterization results specifically for series, fail-safe, 2-out-of n and parallel systems through comparisons with average systems in terms of mean residual life, hazard rate and reversed hazard rate orders. We have also discussed various stochastic orderings and ageing results for the residual lives of parallel and series systems. The results established here are quite general, and several examples have been used to illustrate all the results and their reliability implications.

The star-shaped ordering between probability distributions is a common way to express aging properties. A well-known criterion was proposed by Saunders and Moran [(1978). On the quantiles of the gamma and F distributions. Journal of Applied Probability 15(2): 426–432], to order families of distributions depending on one real parameter. However, the lifetime of complex systems usually depends on several parameters, especially when considering heterogeneous components. We extend the Saunders and Moran criterion characterizing the star-shaped order when the multidimensional parameter moves along a given direction. A few applications to the lifetime of complex models, namely parallel and series models assuming different individual components behavior, are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with some stochastic comparisons of both series and parallel systems comprising dependent Burr Type XII components under the Archimedean copula. Sufficient conditions are also established for star ordering between the lifetimes of series and parallel systems based on multiple-outlier Burr model. The lifetime of a series system with dependent heterogeneous Burr components is proved to be smaller than that of a system with dependent homogeneous components in the sense of convex transform order. [ABSTRACT FROM AUTHOR]

The ability to accurately determine the temporal safe region in time-variant reliability analysis is seminal for reliability-based design. When stochastic excitations are present and discrete-time approaches are invoked, the errors can be large when one uses only one past safe event (and one new failure event) at each time-step. Furthermore, when all previous safe events are accumulated and used, the calculations can be time consuming and the accuracy not ensured. In this paper, a minimal, or a so-called extreme limit-state, surface is obtained to identify the system temporal safe region in an economical manner. To do this, the limit-state surface motion for each failure mode is recorded as a parametric polar plot that provides both magnitude and relative angle of the vectors from the origin to the most-likely failure points (MLFPs) in standard normal space. The angle differences provide correlation and the magnitude differences provide importance. At the component-level, a few logical policies that compare correlation and the magnitude ensure that the safe region is sufficiently recognized. At the system-level, the temporal average of correlations and the magnitudes at the component-level, along with series or parallel system designations, foretells which failure modes are needed to form the system extreme limit-state surface. The impact of the work includes an immediate recognition of the important failure modes and reduced computation for methods such as multi-normal integration. Case studies of both series-system reliability and parallel-system reliability are presented using structural beams excited by stochastic loads and plagued with degrading material properties and dimensions. The accuracy of the extreme LSS is demonstrated cogently. The use of the polar plots as a design tool becomes evident. [ABSTRACT FROM AUTHOR]

Non-linear finite element analysis (NLFEA) has become a widely used tool in the reliability verification of reinforced concrete (RC) structures. Reliability assessment of RC structures is a challenging task and simplified approaches to reliability verifications are needed to allow for routine applications. Simplified semi-probabilistic methods such as the partial factor method (PFM) or the Method of Estimation of Coefficient of Variation (ECoV) may yield over- or under-conservative approximations. This contribution investigates such errors related to the applications of these two methods to series systems; the design resistances obtained by the probabilistic approach are considered as a reference level. It appears that PFM provides good approximations as the method is focused on critical members in the cases under consideration. ECoV may overestimate up to 20% in situations where NLFEA based on mean and/or characteristic values fails to identify a dominating failure mode. The maximum observed error is attributed mainly to the failure in identifying the type of distribution of the system resistance. The presented limited analysis indicates several directions for further research (analysis of other types of structural systems, cases with non-lognormal resistances, effects of a number of system components, and their mutual correlations, and performance of advanced methods for reliability verification). Recommendations on how to identify situations when a significant error can be expected should be provided for practical applications of simplified semi-probabilistic methods. [ABSTRACT FROM AUTHOR]

The errors of calculation of the availability may bring as a consequence mistakes in the decision making in operational systems management. For this reason, the objective of this paper is to evaluate the efficacy of the current equations for the calculation of the availability of series and parallel systems. For that purpose, the non-manufactured production calculated by these equations was compared with the real non-manufactured production which is a function of the down time of each component. These calculations constituted the deterministic model used in the simulations through Monte Carlo method, for which the statistical software R was used. The results were evaluated by the Kolmogorov Smirnov normality test with the modification of Lilliefors. The comparison of means to evaluate the efficacy of the current equations were performed using the t statistic; for this the data were previously approximated to the normal distribution by the central limit theorem.

Recently, the study of the lifetime of systems in reliability and survival analysis in the presence of several causes of failure (competing risks) has attracted attention in the literature. In this paper, series and parallel systems with exponential lifetime for each item of the system are considered. Several causes of failure independently affect lifetime distributions and observations of failure times of the systems are considered under progressive Type-II censored scheme. For series systems, the maximum likelihood estimates of parameters are computed and confidence intervals for parameters of the model are obtained using Fisher information matrix. For parallel systems, the generalized EM algorithm which uses the Newton-Raphson algorithm inside the EM algorithm is used to compute the maximum likelihood estimates of parameters. Also, the standard errors of the maximum likelihood estimates are computed by using the supplemented EM algorithm. The simulation study confirms the good performance of the introduced approach. [ABSTRACT FROM AUTHOR]

For an optimal system design (OSD), data envelopment analysis (DEA) treats companies as black boxes disregarding their internal processes. Including the effects of these processes into companies, internal mechanisms promote optimal budgeting allocation. The internal processes can be defined as series and parallel networks or a combination of them. In the literature, DEA is utilized as a way for OSD in order to determine the optimal budget for companys activities in a system of series network production; but it is not yet provided a method for the optimal budgeting of dynamic systems. To fill this gap, a new model is presented in this paper to evaluate a company's optimal budgeting having dynamic network system and allocates the optimal budget to each of the internal processes of the Decision Making Units (DMUs), based on the efficiency of internal processes. The advantages of this model (which can be regarded as the first accomplishment) are expounded through the research body. Within the framework of the dynamic network systems, the optimal budgeting, the budget deficit and the budget congestion along with superior features of the proposed model are also investigated for dynamic systems. We have also used some theorems to theoretically examine the feasibility of the model. Two study cases on which the suggested model is implemented are further presented. In one application, the OSD network of a business entity with 5 DMUs is addressed; while in the other, a business venture with 24 DMUs is analyzed. [ABSTRACT FROM AUTHOR]

Statistical process monitoring and maintenance are two major concepts to increase system reliability and conforming products. To simplify mathematical modeling, the most of existing researches in the literature suffer from three significant disadvantages: (1) statistical process monitoring and maintenance often have been implemented on the single unit systems, in spite of the fact that most of real production processes consists of multiple units; (2) they apply control charts with fixed parameters that are slow in detecting small and moderate shifts; and (3) they design control charts by minimizing the quality cost ignoring statistical properties that decreases extremely the power of control chart. To overcome these drawbacks, this research integrates the economic-statistical design of a VP-Shewhart chart with condition-based maintenance for two-unit series systems. The particle swarm optimization algorithm is applied to minimize the expected total cost per time unit subject to specific statistical constraints. Eventually, the cost savings from monitoring the system with the flexible VP-Shewhart chart are compared to the FP-Shewhart chart through several instances based on a case study. Also, a sensitivity analysis is implemented on the decision variables to extend insights into the matter. The attained results demonstrate that applying the VP-Shewhart chart instead of FP-Shewhart chart leads to a significant increase in the cost savings. [ABSTRACT FROM AUTHOR]

Highlights • Maintenance decision interdependencies has been addressed. • Lagrangian relaxation techniques are used. • A numerical application of a pipeline is developed. • Two types of policies were considered. Abstract The extension of maintenance optimization methodologies used for single component to multiple component systems must take into account the interdependencies that may exist between the components. Such dependencies could arise when the maintenance optimization of the system over the time is subject to constraints. In this paper, a methodology using Lagrangian relaxation techniques embedded in dynamic programming is proposed for minimizing the maintenance costs of reliability constrained series systems. The methodology could be applied to deterministic and probabilistic dynamic programming problems, as well as to partially observable Markov Decision process. The computational complexity of the proposed approach is polynomial in the number Q of the system components. Theoretical and practical issues related to the existence, and the computation of the Lagrange multipliers are considered. The proposed methodology is illustrated by a numerical application considering maintenance planning of a pipeline. [ABSTRACT FROM AUTHOR]

This paper investigates sufficient conditions for preservation property of the increasing convex order and the increasing concave order under the taking of maximum and minimum of statistically dependent random variables, respectively. As applications, we develop the preservation of NBUC and NBU(2) aging properties respectively under the parallel and series systems of components with statistically dependent lifetimes. Some copulas are presented as illustrations on statistical dependence structure satisfying the sufficient condition as well. [ABSTRACT FROM AUTHOR]

Stochastic ordering relations between extreme order statistics from exponential, Weibull and gamma distributions have been studied extensively by many researchers in recent years. In this work, we obtain various ordering results for the comparisons of two extreme order statistics from scale models when one set of scale parameters majorizes the other. The new results obtained here are applied when the baseline distributions are exponentiated Weibull or generalized gamma distributions. In this way, we generalize and extend some results established recently in the literature. [ABSTRACT FROM AUTHOR]

LetX1, …,Xnbe independent random variables withXi∼EWG(α, β, λi,pi),i= 1, …,n, andY1, …,Ynbe another set of independent random variables withYi∼EWG(α, β, γi,qi),i= 1, …,n. The results established here are developed in two directions. First, under conditionsp1= ⋅⋅⋅ =pn=q1= ⋅⋅⋅ =qn=p, and based on the majorization andp-larger orders between the vectors of scale parameters, we establish the usual stochastic and reversed hazard rate orders between the series and parallel systems. Next, for the case λ1= ⋅⋅⋅ = λn= γ1= ⋅⋅⋅ = γn= λ, we obtain some results concerning the reversed hazard rate and hazard rate orders between series and parallel systems based on the weak submajorization between the vectors of (p1, …,pn) and (q1, …,qn). The results established here can be used to find various bounds for some important aging characteristics of these systems, and moreover extend some well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we provide several preservation results for Laplace transform ordering of residual lives (Lt-rl) under the reliability operations convolutions, mixtures and series systems. We also show that this order is preserved under completely monotone transformations. [ABSTRACT FROM AUTHOR]

This paper considers the multiple-outlier Weibull model, and derives some sufficient conditions for the comparison of lifetimes of series systems with respect to dispersive order. In these models, order statistic is closed under minima, so convex transform, star and Lorenz orders are not investigated because they are scale variant. The results established here strengthen some of the results presented by Fang and Tang (2014). [ABSTRACT FROM AUTHOR]

In this paper we used the Markov models eigenvectors and eigen values concdpts to propose a methodology for analyzing the transient reliability of system with the identical components and the identical repairmen. The components of the systems under consideration can have two distinct configurations, namely ; they can be arranged in series, or in parallel. We also consider the third case in which the system is up if k –out –of – n components are good. For all three cases we proposed a procedure for calculating the transient probability of the system availability and the duration of the system to reach to the steady state are described.

Purpose – The purpose of this paper is to determine a nearly optimal inspection sequence for a series system consisting of two components subject to gradual deterioration and whose failures are not self-announcing and can be detected only through inspection. Design/methodology/approach – The problem is tackled in the context of condition-based maintenance (CBM) with a maintenance model in the class of the control-limit policies for which the maintenance decision is made following inspection by comparison of the deterioration level to critical thresholds. A mathematical model is developed to express the total expected cost per time unit as a function of the inspection instants. Findings – For any given series system composed of two components with known critical deterioration threshold levels, and for any given set of costs related to inspection, inactivity due to failure, and preventive and corrective replacements of each component, a nearly optimal inspection sequence of the system is derived such as the total expected cost is reduced. Research limitations/implications – Due to the complexity of the cost model with the inspection instants (×1, ×2, ×3, …) being the decision variables, it has not been possible to derive the optimal solution. A quasi-optimal sequence of inspection times is derived along with the corresponding total average cost per time unit. Practical implications – In many practical situations in which CBM is implemented, a tradeoff between inspection costs and inactivity and replacement costs has to be balanced when determining the intervals between successive inspections at which the degradation level of the components should be assessed and compared to predetermined critical threshold levels. Inspecting too often would increase inspection costs but in the same time it would also increase the probability to avoid a failure and end up with a preventive replacement, whereas not inspecting often enough would increase the probability to end up with a failure increasing replacement and inactivity costs. Originality/value – While the inspection problem has been largely treated for single component systems, inspection policies become much more complex when considering multi-component systems. A two-component series system is considered in this paper. [ABSTRACT FROM AUTHOR]

Weibull distribution is a very flexible family of distributions which has been applied in a vast number of disciplines. In this work, we investigate stochastic properties of the smallest order statistics from two independent heterogeneous Weibull random variables with different scale and shape parameters. Furthermore, we study the hazard rate order of the smallest order statistics from lower-truncated Weibull distributions due to, in general, Weibull random variables are not ordered according to this ordering in the shape parameter. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a definition of multi-state coherent systems, the state spaces of which are lattice and not necessarily totally ordered sets. We focus on an examination of series and parallel systems and give an existence theorem of the systems, which shows us conditions on the state spaces making us possible to consider series and parallel systems. We also present an expression of multi-state systems by series systems which is a generalization of well-known max–min formula for the binary-state case. This formula may be used for evaluation of stochastic performance of the systems. [Copyright &y& Elsevier]

Abstract: The Bayesian network (BN) is a convenient tool for probabilistic modeling of system performance, particularly when it is of interest to update the reliability of the system or its components in light of observed information. In this paper, BN structures for modeling the performance of systems that are defined in terms of their minimum link or cut sets are investigated. Standard BN structures that define the system node as a child of its constituent components or its minimum link/cut sets lead to converging structures, which are computationally disadvantageous and could severely hamper application of the BN to real systems. A systematic approach to defining an alternative formulation is developed that creates chain-like BN structures that are orders of magnitude more efficient, particularly in terms of computational memory demand. The formulation uses an integer optimization algorithm to identify the most efficient BN structure. Example applications demonstrate the proposed methodology and quantify the gained computational advantage. [Copyright &y& Elsevier]

Abstract: Weibull mixtures have been considered in many applied problems, and they have also been generalized by allowing negative mixing weights. In this paper, we study the classification of the aging properties of generalized mixtures of two or three Weibull distributions in terms of the mixing weights, scale parameters and a common shape parameter, which extends the cases of exponential or Rayleigh distributions. We apply these general results to classify the aging properties of the minimum and maximum lifetimes of two-component systems whose component lifetimes follow one of the known bivariate Weibull distributions. [Copyright &y& Elsevier]

We discuss suitable conditions such that the lifetime of a series or of a parallel system formed by two components having nonindependent lifetimes may be stochastically improved by replacing the lifetimes of each of the components by an independent mixture of the individual components' lifetimes. We also characterize the classes of bivariate distributions where this phenomenon arises through a new weak dependence notion. [ABSTRACT FROM AUTHOR]

Abstract: Independent random variables are said to belong to the scale family of distributions if , for i=1,…,n, where F is an absolutely continuous distribution function with hazard rate r and reverse hazard rate . We show that the hazard rate (reverse hazard rate) of a series (parallel) system consisting of components with lifetimes is Schur concave (convex) with respect to the vector , if is decreasing (increasing). We also show that if xr(x) is increasing in x, then the survival function of the parallel system is increasing in the vector with respect to p-larger order, an order weaker than majorization. We prove that all these new results hold for the scaled generalized gamma family as well as the power-generalized Weibull family of distributions. We also show that in the case of generalized gamma and power generalized Weibull distribution, under some conditions on the shape parameters, the vector of order statistics corresponding to is stochastically increasing in the vector with respect to majorization thus generalizing the main results in and . [Copyright &y& Elsevier]

The paper is devoted to study stochastic comparisons of series and parallel systems with vectors of component lifetimes sharing the same copula. We show that, under some conditions on the common copula, the series system with heterogeneous components is worse than the series system with homogeneous components having a common reliability function, which is equal to the average of the reliability functions of the heterogeneous components. However, we show that this property is not necessarily true for arbitrary copulas. We obtain similar properties for parallel systems and for general coherent systems. For these purposes, we introduce in our analysis the notion of the mean function of a copula. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper analyzes the optimal distribution of defense resources between protecting the genuine system elements and deploying imperfect false targets (FTs) in simple series and parallel systems. The FTs are not perfect and the attacker can detect a FT with a non-zero probability. Once the attacker has detected certain number of FTs, it ignores them and chooses such number of undetected targets to attack that maximizes the expected damage to the system. The defender decides how many FTs to deploy in order to minimize the expected damage to the system assuming that the attacker uses the most harmful strategy to attack. The expected damage to a series system is proportional to the probability of system destruction. The expected damage to a parallel system can be defined as proportional to the probability that the demand is not met, or as the amount of the unsupplied demand. The paper demonstrates the methodology of analysis of optimal defense strategy as function of different parameters (number of genuine system elements, contest intensity, total attacker''s resource). It presents the decision curves that can be used for the making a decision about efficiency of deploying FTs depending on their cost and detection probability. [Copyright &y& Elsevier]

Abstract: Nowadays, the redundancy allocation problem (RAP) is increasingly becoming an important tool in the initial stages of or prior to planning, designing, and control of systems. The multiple multi-level redundancy allocation problem (MMRAP) is an extension of the traditional RAP such that all available items for redundancy (system, module and component) can be simultaneously chosen. In this paper, a novel particle swarm optimization algorithm (PSO) called the two-stage discrete PSO (2DPSO) is presented to solve MMRAP in series systems such that some subsystems or modules consist of different components in series. To the best of our knowledge, this is the first attempt to use a PSO to MMRAP. The proposed PSO used a totally new, very simple, effective and efficient mechanism to move to the next position without velocity. The result obtained by 2DPSO has been compared with those obtained by genetic algorithm (GA) and binary PSO (BPSO). Computational results show that the proposed 2DPSO is very competitive and performs well in the number of times it finds the best solutions, the average numbers of the earliest finding of the best solutions, and computation times. [Copyright &y& Elsevier]

Parrondo's paradox arises in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may he lost when played individually. We present a suitable version of Parrondo's paradox in reliability theory involving two systems in series, the units of the first system being less reliable than those of the second, If the first system is modified so that the distributions of its new units are mixtures of the previous distributions with equal probabilities, then under suitable conditions the new system is shown to be more reliable than the second in the `usual stochastic order' sense. [ABSTRACT FROM AUTHOR]

Abstract: We apply game theory, optimization, and reliability analysis to identify optimal defenses against intentional threats to system reliability. The goals are to identify optimal strategies for allocating resources among possible defensive investments, and to develop qualitative guidelines that reflect those strategies. The novel feature of the approach is the use of reliability analysis together with game theory and optimization to study optimal management of intentional threats to system reliability. Thus, this work extends and adapts the existing body of game-theoretic work on security to systems with series or parallel structures. The results yield insights into the nature of optimal defensive investments that yield the best tradeoff between investment cost and security. In particular, the results illustrate how the optimal allocation of defensive investments depends on the structure of the system, the cost-effectiveness of infrastructure protection investments, and the adversary''s goals and constraints. [Copyright &y& Elsevier]

We provide the exact expression of the reliability of a system under a Bayesian approach, using beta distributions as both native and induced priors at the system level, and allowing uncertainties in sampling, expressed under the form of misclassifications, or noises, that can affect the final posterior distribution. Exact 100(1-α)% highest posterior density credible intervals, for system reliability, are computed, and comparisons are made with results from approximate methods proposed in the literature. [ABSTRACT FROM AUTHOR]

Many factors should be considered in modeling DWC (discounted warranty cost) of repairable systems or products including system structure, components' failure processes, methods of discounting as well as the warranty policy itself. In this paper, we present DWC models for repairable series systems. In particular, a free repair warranty policy and a pro-rata warranty policy are studied. The impact of repair actions on components' failure times is assumed to be minimal, hence NHPPs are used to describe the failure processes. Two types of discounting methods are considered in this paper: a continuous discount function and a discrete discount function. Expressions for both the expected value and variance of DWC are derived. The applications of our findings can be seen in warranty design, warranty reserve determination and risk analysis. Our approach incorporates the information of system structure, the value of time and the impact of repair actions, which are of great importance to warranty cost prediction and evaluation, but have not been sufficiently studied in the literature of warranty analysis. [ABSTRACT FROM AUTHOR]

Objective functions for discounted cost optimization based on a continuous renewal model for a series of cases are presented. They include failures and subsequent renewals by crossings of loading processes or random disturbances out of safe states of structural components, failures due to aging, non-constant benefit and damage functions, finite renewal times, repeated reconstructions at renewals and inspection and repair. A method for reliability-oriented time-variant structural optimization of separable (independent) series systems using first order reliability methods in standard space is developed generalizing theories proposed earlier for component problems and time-invariant series system problems in a special one-level approach. Certain improvements by taking account of dependencies among failure modes are also given. Numerical Laplace transforms are proposed for the treatment of aging components. A newly developed gradient-based algorithm solves the optimization problem. Some algorithmic details are discussed. The approach is demonstrated at two examples. [Copyright &y& Elsevier]

This article compares two procedures for computing reliability confidence bounds for series systems whose components have independent, exponentially distributed failure times. The Lieberman-Ross method is statistically exact, whereas the Mann-Grubbs method approximates an exact optimum bound. For test plans that involve simultaneous testing of all samples of each component type, it is shown that when the Lieberman-Ross method uses all of the observed failure data in computing the confidence bound, the resulting bound will not be practically lower than that produced by the Mann-Grubbs method. Simulation is used to infer that only when the observed data are ordered so that the observed failure times of a significant fraction of the least reliable samples are not actually used in computing the Lieberman-Ross bound can that method be expected to produce a bound superior to that produced by the Mann-Grubbs procedure, using the full data set. [ABSTRACT FROM AUTHOR]

Shock and stress models are used in reliability analysis to describe different kinds of applications. For instance, shock may refer to damage caused to vital organs by illness or environmental causes. On the other hand, stress can relate, for example, to two components that were maintained working independently, and had joint maintenance scheduled at a fixed time. In this context, the presented paper is aimed to introduce a new class of bivariate Lindley distribution of the Marshall–Olkin type to evaluate a 2-component series system's reliability function. The proposed methodology is based on introducing a latent variable following an Exponential or a Lindley distribution. The obtained results generalize those achieved by using a Marshall–Olkin bivariate Exponential distribution, suggesting a useful way to search for appropriate bivariate lifetime distributions, especially under engineering reliability studies or in other areas of quantitative research. • New approach for system lifetimes using multivariate models. • New class of bivariate Lindley distribution of the Marshall–Olkin type to evaluate a 2-component series system's reliability function. • Estimation of the reliability of series systems under a fully Bayesian approach assuming correlated lifetimes in a series system. • The full system reliability could be predicted using proposed methodology. • Under dependence assumption, the system reliability could be more accurate using the proposed models. [ABSTRACT FROM AUTHOR]