Failure Distribution Function Research Articles

Estimation of the Time to Failure Distribution Function in a Highly Reliable N –1-Out-of-N: G Repairable System in the Case of Exponential Distributions of the Uptime Intervals of All Alternating Processes

Estimation of the Time to Failure Distribution Function in a Highly Reliable N –1-Out-of-N: G Repairable System in the Case of Exponential Distributions of the Uptime Intervals of All Alternating Processes

Reliability modeling of systems with random failure threshold subjected to cumulative shocks using machine learning method

AbstractModeling and evaluation of a system reliability is a key issue in shock model analysis. In cumulative shock model, a system fails when the total damages caused by shocks exceeds the system failure threshold level. The reliability of a system with random failure threshold level under cumulative shocks is investigated in this work, considering the general dependency between inter‐arrival times of shocks and their damages magnitudes. Clustering, as one of the unsupervised machine learning methods, is utilized here by applying a genetic algorithm (GA) and particle swarm optimization algorithm (PSO) for its implementation. Phase‐type (PH) distributions and their properties are also applied for finding a system failure distribution functions, determining the convolutions, evaluating the integrals, and ultimately modeling the system reliability. An illustrative example is provided to demonstrate the implementation and effectiveness of the proposed modeling procedure and the suggested approach for computing the system reliability and remaining useful lifetime (RUL). Also, an example case study of X‐ray machine in healthcare industry is provided to demonstrate the application of the proposed model. Applying other machine learning methods for patterns recognition is an area for future research.

Storage reliability prediction of electromechanical components based on virtual manufacturing and testing

Electromechanical components (EMCs) such as relays and contactors have been used extensively in industrial and military areas. The storage reliability of these EMCs has a direct impact on the reliability of the system that contains them. However, during the design phase, it is difficult to predict the storage reliability of EMCs because of few failure rate data of parts, as well as limited testing time and budgets. To address these problems, a virtual Manufacturing and testing method is proposed in this paper, so as to simulate the storage degradation process of batch EMCs. By considering the influence of the quality screening process in the manufacturing process, as well as the unit-to-unit variability of EMCs on the storage degradation paths and the overall life distribution of batch products, the storage failure distribution function is obtained, based on Wiener process. At the same time, the distribution of the diffusion coefficient in the degradation model and the failure distribution model is quantified by introducing testing data of related products as priori information, so as to reflect the uncertainty of the storage degradation process of EMCs. A case study of an electromagnetic relay is carried out to illustrate the effectiveness of the proposed approach.

Reliability analysis for systems subject to dependent and competing failure processes with random failure thresholds

This paper intends to investigate the reliability model for competing failure systems under the influence of random failure thresholds. The random threshold distribution function of hard failure is developed incorporating parameter estimation and goodness-of-fit analysis while the soft failure threshold is assumed to be normally distributed. Specifically, the competing failure result is composed of a degradation process and a shock process, in which the former is simultaneously affected by random shocks and the latter is concurrently influenced by cumulative degradation. For the degradation process, a normal distribution is adopted for soft failure threshold to reflect the randomness of threshold level, and the soft failure survival function is developed subsequently. While for the shock process, the initial random hard failure threshold is regarded as the intensity distribution and a time-varying hard failure threshold function is developed, which describes the dependent strength between the hard failure process and the soft failure process. System reliability function is finally constructed based on the competing and dependent result of these two processes. An illustrative example of a micro-electro-mechanical system (MEMS) is analyzed to examine the developed reliability model, demonstrating that the dependence between degradation and shocks has a greater impact on reliability and overestimation may be caused without considering random characteristics of failure thresholds.

Construction and Simulation of Failure Distribution Model for Cycloidal Gears Grinding Machine

To increase reliability, reduce machine tool failure, and shorten maintenance time, serval failure distribution models are discussed based on the cycloidal gears form grinding. A fault data expansion algorithm model based on the radial basis function (RBF) neural network is proposed to accurately evaluate the reliability of cycloidal gears form grinding machines. The model uses a self-organizing clustering learning algorithm to determine the RBF centers and expansion constants of the neural network. It trains the neural network using the learning algorithm’s output and imports the randomly generated cumulative failure distribution function to obtain simulation data. A numerical example of researching failure distribution is presented which shows that the estimated value of mean time between failures (MTBF) is 909.20h, and the estimated value of reliability is 0.4874. Finally, the fault tree analysis-analytic hierarchy process (FTA-AHP) is used to analyze the fault tree of the cycloidal gear grinding machine. The reliability evaluation indexes are obtained by analyzing the corresponding reliability characteristic function, which proves the failure distribution model is valid. It has important guiding significance in evaluating the reliability and performance of large computer numerical control (CNC) form gear grinding machines.

An Optimization Approach to Minimize the Expected Loss of Demand Considering Drone Failures in Drone Delivery Scheduling

This study proposes a drone-based delivery schedul- ing method considering drone failures to minimize the expected loss of demand (ELOD). An optimization model (DDS-F) is developed to determine the assignment of each drone to a subset of customers and the corresponding delivery sequence. Because solving the optimization model is computationally challenging, a Simulated Annealing (SA) heuristic algorithm is developed to reduce the computational time. The proposed SA features a fast initial solution generation based on the Petal algorithm, a binary integer programming model for path selection, and a local neigh- borhood search algorithm to find better solutions. Numerical results showed that the proposed approach outperformed the well-known Makespan problem in reducing the ELOD by 23.6% on a test case. Several case studies are conducted to illustrate the impact of the failure distribution function on the optimal flight schedules. Furthermore, the proposed approach was able to obtain the exact solutions for the test cases studied in this paper. Numerical results also showed the efficiency of the proposed algorithm in reducing the computational time by 44.35%, on average, compared with the exact algorithm.

The Research of Monte-Carlo Method for Aviation Materials Demand Forecast Based on the Life of the Reliability

With the rapid development of the aviation industry, the increasing number of missions and the impact of other new circumstances, the contradiction between supply and demand in aviation materials has become increasingly prominent. Consequently, more uncertainty and unpredictability in spare parts’ demand, as well as the absence of accurate value of holding, overstocking and backordering costs, result in traditional inventory control policies ineffective. In order to make better use of the existing stock aviation material resources, it is necessary to study the optimization of aviation materials inventory management. In this paper, the reliability analysis of aviation materials maintenance data is conducted to grasp the occurrence rules of aviation materials failures, determine the failure distribution function, and establish a mathematical model of spare parts guarantee and demand based on stochastic process theory. The Monte-Carlo simulation method is used to calculate the aviation materials demand. The calculation results show that the method can achieve the purpose of controlling the inventory level through the demand under varying guarantee degrees, which makes the management of aviation materials more scientific.

Precising the evaluation of radio information system reliability characteristics based on the empirical failure distribution

For highly reliable radio information systems the failures are quite rare phenomena leading to critical decrease in functional characteristics. At the same time, failure distribution may be a subject to rather complex laws, which together with a lack of real data makes it difficult to evaluate the reliability characteristics of the product. Achieving high accuracy of reliability characteristics evaluation is possible due to constant updating the parameters of the radio information system reliability model based on experimental data on the technical condition of the product components starting from the stage of its development. In this case, it is possible to determine the reliability characteristics based on current data on the performance of radio information system components based on the empirical failure distribution function. In this article we propose an algorithm for transferring to an empirical distribution and counting the characteristics (mean time between failures) of radio information system reliability based on it.

Reliability and Risk Assessment of Electric Cable Shovel at Chadormalu Iron Ore Mine in Iran

Nowadays, shovels play an important role in production of open pit mines and their failures result in significant production loss and considerable increase in maintenance costs. Therefore, reliability and risk analysis can help to improve production, productivity and reduce production costs. In this study, reliability of electric cable shovel of Chadormalu iron ore mine in Iran was investigated. Failure distribution function of the subsystems whose failure information is available was provided by statistical analysis using EasyFit 5.5, Minitab 18 and the subsystems with low or unavailable failure information which was generated by experts using normal distribution function. Criticality of subsystems was determined using Birnbaum and Fussell–Vesely importance measures reliability. Results showed that reliability of cable shovel has reached to zero after 40 hours and subsystems of crowd gearbox, swing gearbox, lubrication and bucket door are the most critical subsystems.

Reliability and Risk Assessment of Electric Cable Shovel at Chadormalu Iron Ore Mine in Iran

Nowadays, shovels play an important role in production of open pit mines and their failures result in significant production loss and considerable increase in maintenance costs. Therefore, reliability and risk analysis can help to improve production, productivity and reduce production costs. In this study, reliability of electric cable shovel of Chadormalu iron ore mine in Iran was investigated. Failure distribution function of the subsystems whose failure information is available was provided by statistical analysis using EasyFit 5.5, Minitab 18 and the subsystems with low or unavailable failure information which was generated by experts using normal distribution function. Criticality of subsystems was determined using Birnbaum and Fussell–Vesely importance measures reliability. Results showed that reliability of cable shovel has reached to zero after 40 hours and subsystems of crowd gearbox, swing gearbox, lubrication and bucket door are the most critical subsystems.

Research on Management Strategy of Cost-based Intelligent Manufacturing System

The reliability, efficiency and accuracy of CNC machines as work cells of intelligent manufacturing systems (IMS) are criteria to measure the processing level of the latter. In order to improve the reliability of the IMS and reduce the maintenance cost, very sound preventive maintenance and management strategies concerning the CNC machines should be defined. We realized a parameter estimation of our reliability model for CNC machine units in an IMS environment, carried out a linear correlation test and a distribution fitting test for the model and obtained the failure distribution function and failure rate function. We then built a post-failure maintainability model and realized a maintainability evaluation. Following the above analyses, we built a cost-based preventive maintenance cycle model and obtained its optimal value by using the particle swarm optimization (PSO) algorithm. This research and its result can on the one hand guide the setting-up of preventive maintenance planning and management schemes and on the other hand reduce the production cost and enhance enterprise efficiency.

Fatigue reliability assessment of small sample excavator working devices based on Bootstrap method

To evaluate the fatigue reliability of the excavator working device, the fatigue tests of 2 sets of moving arm and bucket rod of medium-sized excavators with self-weight of 26000 kg were carried out. The virtual augmented sample method (VASM) combined with Bootstrap method was used to analyze the reliability of the excavator working device under extreme small samples, and the interval and point estimations of life parameters were obtained. Based on the lognormal distribution of the excavator working device, the reliability evaluation model of the excavator working device was esTablelished, and reliability indexes, such as reliability function, failure distribution function, inefficiency function, reliable life and so on, were obtained. And the results of fatigue safety life under different confidence and reliability were calculated. The evaluation results show that the average failure time of the excavator working device is 5885 hours under the confidence of 75%, which provides an important reference for the design, the safety inspection and maintenance decision of the excavator working device.

Operational reliability evaluation-based maintenance planning for automotive production line

ABSTRACTReliability evaluation plays a critical role in upgrading the availability and productivity of automotive manufacturing industries by adopting the well-planned maintenance. Due to the lack of operation management studies in automotive industry, this paper addresses an operational reliability evaluation through failure behavior trend in an automotive production line. The main approaches for reliability analysis in this study include statistical structure and Monte Carlo simulation model. The statistical structure consists of three steps: data acquisition and homogenization process, validity of the trend hypothesis and parameters estimation. The reliability evaluation under statistical approach identified the main bottlenecks through the recognized behavior trend of system so that needs to be considered as a priority. Besides, K–R algorithm as Monte Carlo simulation was carried out to simulate reliability regarding failure distribution function. The result of Monte Carlo simulation with different iterations provides a high prediction accuracy of reliability with the lowest error. In addition, regarding the computed reliability through the proposed approaches and total expected cost, a reliability-based maintenance optimization model was conducted. The proposed maintenance intervals could be useful for improving the operational performance of critical components in automotive system.

A novel methodology to update the reliability of the corroding natural gas pipeline by introducing the effects of failure data and corrective maintenance

By introducing the effects of the failure data and corrective maintenance, a novel methodology has been established to update the reliability of the corroding natural gas pipeline. Firstly, the methodology is able to calculate the failure probabilities for the small leak and burst based on the inspection data. The rank regression method is then applied to determine the fittest failure distribution function. Moreover, the failure distribution functions are updated by considering the failure data and the corrective maintenance. The Bayesian method and Markov Chain Monte Carlo (MCMC) simulation techniques are employed in the update process. Furthermore, the actual data from a natural gas pipeline located in China is used to illustrate this methodology, and the assessment indicates that the failure data and the corresponding corrective maintenance exert great impact on failure probability.

Physics of failure‐based failure mode, effects, and criticality analysis for Integrated Circuits

AbstractExisting failure mode, effects, and criticality analysis (FMECA) methods, which still rely mainly on failure data and the empirical information of designers, suffer from subjectivity and inflexibility, which makes the application of these methods on electronic equipment, especially integrated circuit‐based equipment, less credible. Therefore, the idea of physics of failure (PoF)‐based FMECA is presented. First, the relationship between typical failure modes and the failure mechanisms of integrated circuits is analyzed. Based on the results, pseudo‐random samples are generated using a Monte Carlo (MC) simulation. Then, the hybrid hypothesis test method is proposed to determine the failure distribution function, and then a mixed failure rate model based on failure factors is established to calculate the rates of failure modes. This method is applied to a main control module of a control system to correct the original FMECA results. Results show that this method has good applicability to the FMECA of integrated circuits and can obtain more objective and accurate analysis results compared to traditional methods, while being more applicable for testability verification tests.

The Generalised Local Model applied to Fibreglass

In the present research work, the Generalised Local Model (GLM) is employed to characterize the failure of a commercial Fibreglass by determining the Primary Cumulative Distribution Function of Failure (PCDFF) through an experimental campaign and numerical computations. Four criteria used to define the failure condition are based on the following Generalised Parameters (GPs): (i) Maximum Principal Stress; (ii) von Mises Stress; (iii) Tsai-Hill GP; (iv) Hoffman GP. For each GP adopted, the PCDFF is derived in two different ways: (a) by examining data obtained from tension tests only (GLM single application); (b) by collecting data, determined through tension tests and three-point bending tests, into a unique set (GLM joint application). Finally, a comparison between the obtained PCDFFs and the experimental failure results is presented.

ANALYSIS OF EMERGENCY FAILURE OF LONG-TERM OPERATED GAS PIPELINES

At present, the uninterrupted supply of natural gas to consumers is the key to the stability of the Russian economy. The gas transmission system of Gazprom PJSC is at the stage of long-term operation, demanding significant investments to maintain it in an efficient condition. In this connection, the problems of accidents statistical data analysis are impor- tant to maintain the gas transportation system in the conditions of long- term operation. The article analyzes the distribution of accidents on the main gas pipe- lines along the distance from the compressor station. The sample size was 169 accidents occurred on 56 gas pipelines with a nominal diameter of DN 700-1400 for a ten-year period. It is obtained that the nature of the distribution function of the failure distribution obeys the Weibull law. Results analysis made it possible to establish that the probability distribution function of Weibull's failure- free operation describes the experimental data of the probability of fail- ure-free operation quite accurately. The root-mean-square relative error was 2.28 %. The difference between the empirical (obtained from experimental data) and the theoretical functions of the probability of failure-free operation can be traced with considerable run-up of gas pipelines in the period when the risks of sudden failures increase. The paper proposes a three-parameter Gompertz function for character- izing the probability of trouble-free operation of main gas pipelines, which allows to take into account the real aging processes and operating conditions of gas pipelines. A comparative analysis of the theoretical distributions under consideration was made. An analysis of the results obtained showed that the probability distribu- tion function of Gompertz's fail-safe operation describes experimental data with a mean-square relative error of 2.14 %. Thus, the Gompertz distribution is 0.2 % more accurate than the Weibull distribution.

Fault tree analysis in the R programming environment

Aim. Fault tree analysis (FTA) is one of the primary methods of dependability analysis of complex technical systems. This process often employs commercial software tools like Saphire, Risk Spectrum, Arbitr, etc. Each of them has both advantages and drawbacks. It must be noted that the primary purpose of the above software tools consists in performing qualitative fault tree analysis. The software systems additionally feature a number of statistical methods that, among other things, enable uncertainty analysis, interval estimation of indicators, as well as other statistical research. The number of such procedures is not large and is strictly limited by a certain array of proposed distributions and functions. In this paper, let us consider the possibility of solving the task of fault tree analysis by means of the R programming language. R was primarily created and is continuing to evolve as a statistical data processing tool. FTA in this environment is just one of 10 thousand packages. In other words, if compared to commercial packages with the FTA as the main function, the functionality of R is much wider and enables significantly higher quality of analysis. One of R’s undeniable advantages is the freeware open-source environment. This paper aims to present a small number of primary procedures of R’s FaultTree package that enable FTA: construction and display of fault trees, calculation of probability per nodes, determination of minimum cross-sections. Methods. R’s FaultTree scripts were used for the calculations and FTA capabilities demonstration. Conclusions. Three examples are examined in detail. First, a tree is calculated based on known probabilities, then the time to failure distribution function of a technical system is identified. In the last example, FTA is performed for systems with elements that are described by different functional and service models. In conclusion, FTA capabilities of R are described that allow, for instance, taking into consideration common cause failures.

A new direct second-order reliability analysis method

• A new study of the second-order reliability method (SORM) is presented. • All the information from the fitted quadratic polynomial model of the limit state function is used. • The cumulant generating function of the fitted quadratic polynomial surface in normalized standard variables is derived analytically. • The saddlepoint approximation is utilized for reliability analysis. • The proposed method is more accurate than the conventional SORM. In the second-order reliability method, the limit state function in arbitrarily distributed random variables is approximated by a quadratic polynomial of standard normal variables. The fitted quadratic polynomial is then used to calculate the probability of failure of the limit state. However, a closed-form solution for the probability of failure of a general quadratic polynomial surface is not available. As such, in this paper, a new second-order reliability method for reliability analysis is presented using saddlepoint approximation. The second-order approximation of the limit state function is obtained by the second-order Taylor series expansion at the most probable point. The cumulant generating function of the fitted quadratic polynomial of standard normal variables is derived analytically. The saddlepoint approximation is utilized to generate the probability density function, cumulative distribution function and probability of failure of the limit state. Finally, three numerical examples are used to compare the performance of the proposed second-order reliability with that of the first-order reliability method, the conventional second-order reliability method, and Monte Carlo simulation. The comparisons show that the proposed second-order reliability method gives accurate, convergent, and computationally efficient estimates of the probability of failure.

Probabilistic assessment of fatigue data from shape homologous but different scale specimens. Application to an experimental program

With the aim of justifying transferability of fatigue properties of metallic materials from small sized specimens to real components, the influence of specimen shape and size on the fatigue characterization is investigated. Twofold scale effects in the statistical interpretation of fatigue data have been considered in order to allow an equivalent failure distribution function to be achieved indistinctly of the specimen type. The first scale effect, referred to the initiation phase, is related to the specimen surface size and finishing influence. The second one, referred to the propagation phase, is related to the specimen circular cross-section size effect. Assuming LEFM, a non-dimensional crack growth rate curve is derived from the material, allowing the relation between the lifetimes for the different specimens to be found as a function of the crack size and specimen diameter. In this way, the transition crack size between initiation and propagation lifetimes is determined by securing a reasonable correspondence between the modelled and experimental scatter of the experimental results. In order to probe the applicability of the methodology, a fatigue program, developed as a cooperation between the Empa-Dübendorf and the University of Oviedo, is evaluated implying fatigue constant amplitude tests of three samples with homologous specimen shape but markedly different size of 42CrMoS4 steel alloy.