System Failure Time Research Articles

Limiting Behavior of Mixed Coherent Systems With Lévy‐Frailty Marshall–Olkin Failure Times

ABSTRACTIn this article, we show a limit result for the reliability function of a system—that is, the probability that the whole system is still operational after a certain given time—when the number of components of the system grows to infinity. More specifically, we consider a sequence of mixed coherent systems whose components are homogeneous and non‐repairable, with failure‐times governed by a Lévy‐Frailty Marshall–Olkin (LFMO) distribution—a distribution that allows simultaneous component failures. We show that under integrability conditions the reliability function converges to the probability of a first‐passage time of a Lévy subordinator process. To the best of our knowledge, this is the first result to tackle the asymptotic behavior of the reliability function as the number of components of the system grows. To illustrate our approach, we give an example of a parametric family of reliability functions where the system failure time converges in distribution to an exponential random variable, and give computational experiments testing convergence.

Визначення оптимальних норм надійності космічного апарата з урахуванням економічних показників

The goal of this paper is to develop a method for determining the values of system failure rates optimal in terms of net profit maximization with account for spacecraft mass limitations. It is adopted that the spacecraft systems are independent in terms of reliability, each of them can be only in two states (a functioning state or a failure state), and each equipment type of the special complex makes an independent contribution to the overall effect. The paper considers the case where the spacecraft system failure time obeys the exponential law. Use is made of the Lagrange multiplier method and numerical optimization methods. The problem is solved using the mass ? failure rate and cost ? failure rate relationships of the spacecraft systems. For the supporting complex, the dimension of the mathematical simulation problem is reduced to two: a formula is derived to find the optimal failure rates of all the systems of the supporting complex using the optimal failure rates of two systems of it. The variables for the special complex and the supporting complex are separated. Due to the fact that each special complex system makes an independent contribution to the overall effect, the problem for the whole spacecraft is reduced to a system of two equations for the special complex and the supporting complex and ncn equations in one variable for the special complex with two coupling variables between the supporting complex and the special complex where ncn is the number of the special complex systems. The paper presents a numerical-and-analytical method for spacecraft system failure rate optimization where the initial guess is specified indirectly: by specifying the supporting complex mass and probability of no-failure operation. The method may be used in the development of a space hardware design methodology accounting for economic factors. From the optimal values of the spacecraft system failure rates found using the mass ? failure rate and cost ? failure rate relationships, one can find the masses and costs of the spacecraft systems to be used in optimizing the parameters and development cost of the systems. The method is expected to increase the profitability and competitiveness of spacecraft under development.

Predicting failure times of coherent systems

AbstractThe article is focused on studying how to predict the failure times of coherent systems from the early failure times of their components. Both the cases of independent and dependent components are considered by assuming that they are identically distributed (homogeneous components). The heterogeneous components' case can be addressed similarly but more complexly. The present study is for non‐repairable systems, but the information obtained could be used to decide if a maintenance action should be carried out at time . Different cases are considered regarding the information available at time . We use quantile regression techniques to predict the system failure times and to provide prediction intervals. The theoretical results are applied to specific system structures in some illustrative examples.

Security indicators and standards for microprocessor centralization in “2x2” and “1x1” systems

The levels of device failures and performance losses in “2x2” and “1x1” systems are discussed in this article according to safety indicators and system failure time estimations. Ensuring the safety of train operations at the station is the primary objective of both road blocks and electro-centralization. The safe and prompt delivery of people and commodities to their destinations is a key indicator of the quality of the transportation process, and it determines how productive railways are. Railway automation and telemechanics systems depend on each other for their dependability in sustaining high levels of these indicators. Train delays, or worse, mishaps or calamities, can result from malfunctions in the railway automation and telemechanics (RAT) system. Maintaining RAT systems’ reliability and preventing loss of performance.

Frequentist and Bayesian approach for the generalized logistic lifetime model with applications to air-conditioning system failure times under joint progressive censoring data

Frequentist and Bayesian approach for the generalized logistic lifetime model with applications to air-conditioning system failure times under joint progressive censoring data

An In-Depth Review of the Weibull Model with a Focus on Various Parameterizations

The Weibull distribution is a versatile probability distribution widely applied in modeling the failure times of objects or systems. Its behavior is shaped by two essential parameters: the shape parameter and the scale parameter. By manipulating these parameters, the Weibull distribution adeptly captures diverse failure patterns observed in real-world scenarios. This flexibility and broad applicability make it an indispensable tool in reliability analysis and survival modeling. This manuscript explores five parameterizations of the Weibull distribution, each based on different moments, like mean, quantile, and mode. It meticulously characterizes each parameterization, introducing a novel one based on the model’s mode, along with its hazard and survival functions, shedding light on their unique properties. Additionally, it delves into the interpretation of regression coefficients when incorporating regression structures into these parameterizations. It is analytically established that all five parameterizations define the same log-likelihood function, underlining their equivalence. Through Monte Carlo simulation studies, the performances of these parameterizations are evaluated in terms of parameter estimations and residuals. The models are further applied to real-world data, illustrating their effectiveness in analyzing material fatigue life and survival data. In summary, this manuscript provides a comprehensive exploration of the Weibull distribution and its various parameterizations. It offers valuable insights into their applications and implications in modeling failure times, with potential contributions to diverse fields requiring reliability and survival analysis.

Engineering Applications with Stress-Strength for a New Flexible Extension of Inverse Lomax Model: Bayesian and Non-Bayesian Inference

In this paper, we suggest a brand new extension of the inverse Lomax distribution for fitting engineering time data. The newly developed distribution, termed the transmuted Topp–Leone inverse Lomax (TTLILo) distribution, is characterized by an additional shape and transmuted parameters. It is critical to notice that the skewness, kurtosis, and tail weights of the distribution are strongly influenced by these additional characteristics of the extra parameters. The TTLILo model is capable of producing right-skewed, J-shaped, uni-modal, and reversed-J-shaped densities. The proposed model’s statistical characteristics, including the moments, entropy values, stochastic ordering, stress-strength model, incomplete moments, and quantile function, are examined. Moreover, characterization based on two truncated moments is offered. Using Bayesian and non-Bayesian estimating techniques, we estimate the distribution parameters of the suggested distribution. The bootstrap procedure, approximation, and Bayesian credibility are the three forms of confidence intervals that have been created. A simulation study is used to assess the efficiency of the estimated parameters. The TTLILo model is then put to the test by being applied to actual engineering datasets, demonstrating that it offers a good match when compared to alternative models. Two applications based on real engineering datasets are taken into consideration: one on the failure times of airplane air conditioning systems and the other on the active repair times of airborne communication transceivers. Also, we consider the problem of estimating the stress-strength parameter R=P(Z2<Z1) with engineering application.

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

AbstractIn this study, a two‐parameter, upper‐bounded probability distribution called the tau distribution is introduced and its applications in reliability engineering are presented. Each of the parameters of the tau distribution has a clear semantic meaning. Namely, one of them determines the upper bound of the distribution, while the value of the other parameter influences the shape of the cumulative distribution function. A remarkable property of this new probability distribution is that its probability density function, survival function, hazard rate function (HRF), and quantile function can all be expressed in terms of its cumulative distribution function. The HRF of the proposed probability distribution can exhibit an increasing trend and various bathtub shapes with or without a low and long‐flat phase (useful time phase), which makes this new distribution suitable for modeling a wide range of real‐world problems. The constraint maximum likelihood estimation, percentile estimation, approximate Bayesian computation, and approximate quantile estimation computation are proposed to calculate the unknown parameters of the model. The suitability of the estimation methods is verified with the aid of simulation and real‐world data results. The modeling capability of the tau distribution was compared with that of some well‐known two‐ and three‐parameter probability distributions using two data sets known from the literature of reliability engineering: time between failures data of a machining center, and time to failure of data acquisition system cards. Based on empirical results, the new distribution may be viewed as a viable competitor to the Weibull, Gamma, Chen, and modified Weibull distributions.

Interval Type-II Fuzzy Fault-Tolerant Control for Constrained Uncertain 2-DOF Robotic Multi-Agent Systems with Active Fault Detection

This study proposed a novel adaptive interval Type-II fuzzy fault-tolerant control for constrained uncertain 2-DOF robotic multi-agent systems with an active fault-detection algorithm. This control method can realize the predefined-accuracy stability of multi-agent systems under input saturation constraint, complex actuator failure and high-order uncertainties. Firstly, a novel active fault-detection algorithm based on pulse-wave function was proposed to detect the failure time of multi-agent systems. To the best of our knowledge, this was the first time that an active fault-detection strategy had been used in multi-agent systems. Then, a switching strategy based on active fault detection was presented to design the active fault-tolerant control algorithm of the multi-agent system. In the end, based on the interval type-II fuzzy approximated system, a novel adaptive fuzzy fault-tolerant controller was proposed for multi-agent systems to deal with system uncertainties and redundant control inputs. Compared with other relevant fault-detection and fault-tolerant control methods, the proposed method can achieve predefinition of stable accuracy with smoother control input. The theoretical result was verified by simulation.

Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems

This paper develops a model for predicting the failure time of a wide class of weighted k-out-of-n reliability systems. To this aim, we adopt a rational expectation-type approach by artificially creating an information set based on the observation of a collection of systems of the same class–the catalog. Specifically, we state the connection between a synthetic statistical measure of the survived components’ weights and the failure time of the systems. In detail, we follow the evolution of the systems in the catalog from the starting point to their failure–obtained after the failure of some of their components. Then, we store the couples given by the measure of the survived components and the failure time. Finally, we employ such couples for having a prediction of the failure times of a set of new systems–the in-vivo systems–conditioned on the specific values of the considered statistical measure. We test different statistical measures for predicting the failure time of the in-vivo systems. As a result, we give insights on the statistical measure which is more effective in contributing to providing a reliable estimation of the systems’ failure time. A discussion on the initial distribution of the weights is also carried out.

A Predictive Maintenance Strategy Using Deep Learning Quantile Regression and Kernel Density Estimation for Failure Prediction

Failure prediction and maintenance decision-making are two core activities in a prognostics and health management (PHM) system. However, they are often studied independently and hierarchically. The main goal of this article is to combine system failure prediction with maintenance decision-making to develop a predictive maintenance strategy. System failure prediction is achieved by constructing an ensemble model of deep autoencoder (DAE), long short-term memory (LSTM), quantile regression (QR), and kernel density estimation (KDE), namely DAE-LSTMQR-KDE. Then, based on the probability density of system failure time obtained from the ensemble model, a replacement cost function (RCF) and an ordering cost function (OCF) are proposed to support maintenance and inventory decisions. Finally, optimal decisions are determined by minimizing the two cost functions. A score equal to 246.59 and a coverage width-based criterion (CWC) index equal to 0.35 were obtained when the DAE-LSTMQR-KDE ensemble model was applied to the C-MAPSS dataset, while the average maintenance cost rate (MCR) of the proposed maintenance strategy was 0.74. The results demonstrated that the proposed prediction and maintenance method outperforms several state-of-the-art methods. In addition, different cost structure scenarios are also investigated to illustrate the flexibility of maintenance decisions based on failure prediction information.

Copula-based probability for occurrence of the event due to one of dependent NHPPs before the other, past a truncated time

The bivariate Gumbel-Hougaard copula is considered for two dependent non-homogenous Poisson processes, The purpose of this article is to provide a computational tool for estimation of the probability that the next event arrival after a truncated time τ, is due to a specific process. There are many situations in which non-homogenous Poisson processes could be dependent, such as failure times of a two-component repairable system in which the failure of the system at a given time is due to only one of the components. Power Law is used as the intensity function for both non-homogenous Poisson Processes. Maximum likelihood and Bayes estimators for the probability based on gamma priors are derived. It is verified through simulations that Bayes estimator outperforms maximum likelihood estimator with regard to their accuracy. Two examples for illustration of computation via Mathematica code (in the Appendix) are provided.

Optimal redundancy allocation in coherent systems with heterogeneous dependent components

AbstractThis paper is concerned with the optimal number of redundant allocation to n-component coherent systems consisting of heterogeneous dependent components. We assume that the system is built up of L groups of different components, $L\geq 1$ , where there are $n_i$ components in group i, and $\sum_{i=1}^{L}n_i=n$ . The problem of interest is to allocate $v_i$ active redundant components to each component of type i, $i=1,\dots, L$ . To get the optimal values of $v_i$ we propose two cost-based criteria. One of them is introduced based on the costs of renewing the failed components and the costs of refreshing the alive ones at the system failure time. The other criterion is proposed based on the costs of replacing the system at its failure time or at a predetermined time $\tau$ , whichever occurs first. The expressions for the proposed functions are derived using the mixture representation of the system reliability function based on the notion of survival signature. We assume that a given copula function models the dependency structure between the components. In the particular case that the system is a series-parallel structure, we provide the formulas for the proposed cost-based functions. The results are discussed numerically for some specific coherent systems.

System reliability analysis of a lamp problem by simulation

The paper proposes a simulation-based procedure to determine the system reliability of a lamp problem. Suppose we have k lamps to light up a room, and each lamp can light a circular area of radius r. The system reliability is the probability that there is no dark area in the room during time t. We obtain the system reliability function and the expected system lifetime through a simulation when the reliability and the coverage radius of the lamps are given. A Monte Carlo test method and an Intersection test method are used to check the system state (working or failure) for different situations. In numerical examples, Kaplan–Meier and Nelson estimators determine the system reliability function from system failure times generated by the simulation. Additionally, we compare the two methods with numerical examples.

Reliability assessment of repairable systems with series–parallel structure subjected to hierarchical competing risks under minimal repair regime

In this paper, we seek to propose a model that allows us to evaluate the failure times of a single repairable system represented hierarchically, exposed to competing risks and under a minimal repair framework. Our study can be regarded as an extension of the research presented in Louzada et al. (2019), which comprises the representation of complex systems through a hierarchical structure in series and/or in parallel. For this, we deduce the general form of the model, as well as the likelihood function associated with it, to obtain reliable estimates for the parameters that index the model. In addition, we display the mechanism for generating random numbers based on the presented structure, which enables obtaining point and interval estimates (via parametric bootstrap) in a more convenient way for reliability curves at any level of the system hierarchy. We conduct an extensive Monte Carlo simulation study to evaluate the performance of the proposed maximum likelihood estimators and confidence intervals for the model parameters. Finally, we illustrate the applicability of our model and methods with applications that deal with the reliability modeling of a robotic unit still under development, resulting from a project carried out in partnership between Petrobras and other Brazilian research centers.

Reliability Importance Measures considering Performance and Costs of Mechanical Hydraulic System for Hydraulic Excavators

Although some reliability importance measures and maintenance policies for mechanical products exist in literature, they are rarely investigated with reference to weakest component identification in the design stage and preventive maintenance interval during the life cycle. This paper is mainly study reliability importance measures considering performance and costs (RIMPC) of maintenance and downtime of the mechanical hydraulic system (MHS) for hydraulic excavators (HE) with energy regeneration and recovery system (ERRS) and suggests the scheduled maintenance interval for key components and the system itself based on the reliability R i t . In the research, the required failure data for reliability analysis is collected from maintenance crews and users over three years of a certain type of hydraulic excavators. Minitab is used for probable distribution estimation of the mechanical hydraulic system failure times, and the model is verified to obey Weibull distribution. RIMPC is calculated by multiplying the reliability R i t and weighting factor W i and then compared with other classical importance measures. The purpose of this paper is to identify the weakest component for MHS in the design stage and to make appropriate maintenance strategies which help to maintain a high reliability level for MHS. The proposed method also provides the scientific maintenance suggestion for improving the MHS reliability of the HE reasonably, which is efficient, profitable, and organized.

Some Properties and Applications of Topp Leone Kumaraswamy Lomax Distribution

Many Statisticians have developed and proposed new distributions by extending the existing distributions. The distributions are extended by adding one or more parameters to the baseline distributions to make it more flexible in fitting different kinds of data. In this study, a new four-parameter lifetime distribution called the Topp Leone Kumaraswamy Lomax distribution was introduced by using a family of distributions which has been proposed in the literature. Some mathematical properties of the distribution such as the moments, moment generating function, quantile function, survival, hazard, reversed hazard and odds functions were presented. The estimation of the parameters by maximum likelihood method was discussed. Three real life data sets representing the failure times of the air conditioning system of an air plane, the remission times (in months) of a random sample of one hundred and twenty-eight (128) bladder cancer patients and Alumina (Al2O3) data were used to show the fit and flexibility of the new distribution over some lifetime distributions in literature. The results showed that the new distribution fits better in the three datasets considered.

Acceptance Sampling Plans with Truncated Life Tests for the Length-biased Weighted Lomax Distribution

In this paper, we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans (ASPs) where the life test is assumed to be truncated at a pre-assigned time. For the new suggested ASPs, the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained. In addition, the values of the corresponding operating characteristic function and the associated producer’s risks are calculated. Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans; one data set contains the first failure of 20 small electric carts, and the other data set contains the failure times of the air conditioning system of an airplane. Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes. It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study. The suggested acceptance sampling plans are recommended for practitioners in the field.

Extended block replacement policies with mission durations and maintenance triggering approaches

When the missions arrive, it is not feasible to shut down engineering systems for preventive maintenance policies. Otherwise, it would cause major economic losses and even unimaginable accident. Hence, it is interesting and significative to provide appropriate preventive maintenance policies with mission durations to improve the system reliability and maintainability. For the electronic systems consisting of a block or group of units whose ages are not easy observed and only failures are known, we firstly extend the block replacement policy with random arrival time of mission durations. As a required reliability is needed at the mission time and no replacement can be done during the mission durations preventively. From the points of cost and maintainability, two maintenance triggering approaches, i.e., replacement first and replacement last, are discussed in analytical ways, respectively. Furthermore, three replacement policies are compared theoretically and numerically with optimum mission durations and planned replacement time. In addition, a case illustration in maintaining the electronic systems of active phased array radar (APAR) is given when the arrival time of mission durations follows an exponential distribution and the failure time of electronic systems has a gamma distribution.

Определение термодинамических параметров энергосистем, как основа оценки их технического состояния

In the article, the authors present an approach to predicting the failure time of energy systems based on the control of their thermodynamic parameters. Solving this problem can facilitate the transition to an operational strategy based on the actual state. For the forecast has been selected well-proven method of group account of arguments (GMDH), which has found wide application in solving complex scientific and engineering problems. The results of forecasting the failure time of two NK-8-2U gas turbine engines based on the results of measuring the main technical parameters are presented. The calculations were performed in the course of the equivalent-cyclic tests on JSC "Kazan motor building production Association". The results of calculations showed sufficient accuracy of the forecast (no more than 20-25 hours of operation).