Estimation of the mean cumulative number of failures in a repairable system with mixed exponential component lifetimes

Components in electronic systems are often observed to be likely to fail at an early age, an effect well known as the ‘infant mortality’ effect. Similarly, for systems composed of such components, a decrease in the rate of occurrence of failures, usually called the ‘reliability improvement’ effect, is seen in the early operating period. In this paper we show that such improvement may be considered as a simple consequence of the heterogeneity among the components in the population. We present a simple three-parameter model for the distribution of the component lifetime, which has a simple physical interpretation, and from which we obtain methods for statistical inference, suitable for implementation on even small computers. The methods have been applied successfully to field failure data, collected from an industrial company.     

An investigation of rail bearing reliability under real conditions of use

The objective of the present work is to carry out a performance analysis of roller bearings used in railway ore transportation wagons. Data from 47,000 failed bearings divided in seven groups, were used to determine the failure distribution. Six groups corresponded to operation in the years 1985–1988, 1990, 1991 and one group included all the others. The failure distribution in bearings was described by the three parameter Weibull distribution. To conduct the statistical analysis it was necessary to estimate these parameters by the nonlinear regression method, because it does not require the whole group of failed bearings, and direct inference on the sample. A Monte Carlo technique was used to validate the procedure. Analytically two estimate methodologies were considered. Methodology I is a well established technique while Methodology II is an alternative approach proposed by the authors, which was inspired by a procedure used to design rail shafts. Studying the bearing failure behavior led to the following observations: based on sample inference techniques, an excessive variation was observed in the parameters that characterize the failure distribution. A dispersion of the order of 40 or 25% was found in the minimum and nominal lives when evaluated by the direct inference method or by the nonlinear regression method, respectively, and a dispersion of 17% calculated by nonlinear regression was observed for the shape parameter, . In spite of this dispersion, it was found that the minimum lives estimated by direct inference were conservative by a factor of four, when compared to analytical methods, while estimates of the nominal life were shown to be similar to its smallest value observed in the sample groups.     

Integration of computation and testing for reliability estimation

This paper develops a methodology to integrate reliability testing and computational reliability analysis for product development. The presence of information uncertainty such as statistical uncertainty and modeling error is incorporated. The integration of testing and computation leads to a more cost-efficient estimation of failure probability and life distribution than the tests-only approach currently followed by the industry. A Bayesian procedure is proposed to quantify the modeling uncertainty using random parameters, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. An adaptive method is developed to determine the number of tests needed to achieve a desired confidence level in the reliability estimates, by combining prior computational prediction and test data. Two kinds of tests — failure probability estimation and life estimation — are considered. The prior distribution and confidence interval of failure probability in both cases are estimated using computational reliability methods, and are updated using the results of tests performed during the product development phase.     

Different insights for improving part and system reliability obtained from exactly same DFOM “failure numbers”

Techniques for improving the reliability and maintainability of both nonrepairable and repairable items can be suggested by failure data analysis. It is shown that a given set of failure numbers leads to very different improvement strategies when the numbers are the times-between-successive-failures of one or more repairable items, rather than the times-to-failure of nonrepairable items. Since this should have been obvious more than 50 years ago, at the onset of formal reliability engineering activities, several reasons are proffered for the widespread and protracted misinterpretation of even the most basic—and simple!—conceptual and practical differences between nonrepairable and repairable items.     

Condition-based fault tree analysis (CBFTA): A new method for improved fault tree analysis (FTA), reliability and safety calculations

Condition-based maintenance methods have changed systems reliability in general and individual systems in particular. Yet, this change does not affect system reliability analysis. System fault tree analysis (FTA) is performed during the design phase. It uses components failure rates derived from available sources as handbooks, etc. Condition-based fault tree analysis (CBFTA) starts with the known FTA. Condition monitoring (CM) methods applied to systems (e.g. vibration analysis, oil analysis, electric current analysis, bearing CM, electric motor CM, and so forth) are used to determine updated failure rate values of sensitive components. The CBFTA method accepts updated failure rates and applies them to the FTA. The CBFTA recalculates periodically the top event (TE) failure rate (λ_TE) thus determining the probability of system failure and the probability of successful system operation—i.e. the system's reliability.FTA is a tool for enhancing system reliability during the design stages. But, it has disadvantages, mainly it does not relate to a specific system undergoing maintenance.CBFTA is tool for updating reliability values of a specific system and for calculating the residual life according to the system's monitored conditions. Using CBFTA, the original FTA is ameliorated to a practical tool for use during the system's field life phase, not just during system design phase.This paper describes the CBFTA method and its advantages are demonstrated by an example.     

Analysis of sequential failures for assessment of reliability and safety of manufacturing systems

Assessment of reliability and safety of a manufacturing system with sequential failures is an important issue in industry, since the reliability and safety of the system depend not only on all failed states of system components, but also on the sequence of occurrences of those failures. Methods that are currently available in sequential failure analysis always start with given sequences of the failures in the system, which is not the case in real life situations; therefore, the sequences of the failures should be identified and the probability of their occurrence should be determined. In this paper, we represent a methodology that can be used for identifying the failure sequences and assessing the probability of their occurrence in a manufacturing system. The method employs Petri net modeling and reachability trees constructed based on the Petri nets. The methodology is demonstrated on an example of an automated machining and assembly system.     

Reliability evaluation and optimisation of imperfect inspections for a component with multi-defects

In this paper, a model is developed to evaluate the reliability and optimise the inspection schedule for a multi-defect component. The model uses a non-homogeneous Poisson process (NHPP) method in conjunction with a delay time approach. The inspections are designed to detect any defects in the component, however it can be imperfect. The defect is a definable state before a functional failure happens to the component. Occurrences of defects are assumed to follow an NHPP and a defect will be minimally repaired if it is identified during an inspection. It is shown that the failures occurring in an interval of inspection will also follow an NHPP. The situation of imperfect inspections and non-constant inspection intervals are considered. An algorithm is presented to optimise the intervals of inspections in order to maximise the reliability of the component, and the properties of the algorithm are shown. A numerical example with parametric study is given to show the performance of the model and the algorithm.     

Numerical differences in the survival probabilities obtained by the cumulative-hazard and kaplan–meier estimators of the reliability function

The paper examines two very important non-parametric estimators of the reliability function which are frequently used in reliability practice to estimate survival probabilities. The paper proves that when both of them are calculated for the same data set, the survival probabilities obtained using the cumulative hazard approach are larger in magnitude than the ones given by the method proposed by Kaplan and Meier, and provides the mathematical formula quantifying the magnitude of this difference.     

Estimation of exponential component reliability from uncertain life data in series and parallel systems

Estimating reliability of components in series and parallel systems from masking system testing data has been studied. In this paper we take into account a second type of uncertainty: censored lifetime, when system components have constant failure rates. To efficiently estimate failure rates of system components in presence of combined uncertainty, we propose a useful concept for components: equivalent failure and equivalent lifetime. For a component in a system with known status and lifetime, its equivalent failure is defined as its conditional failure probability and its equivalent lifetime is its expectation of lifetime. For various uncertainty scenarios, we derive equivalent failures and test times for individual components in both series and parallel systems. An efficient EM algorithm is formulated to estimate component failure rates. Two numerical examples are presented to illustrate the application of the algorithm.     

On reliability criteria and the implied cost of failure for a maintained component

This paper considers age-based replacement and block replacement when reliability is also a decision criterion. We describe how specification of the operational reliability of component function determines the replacement policy, and that setting a value for the cost of failure and specifying an operational reliability requirement are equivalent. This duality then implies a simple method for checking the consistency of the cost of failure and operational reliability measures when they are set system operators and maintainers. A simple expression for the median time between operational failures for a socket subject to age-based replacement is also obtained. These ideas are considered briefly in the context of block replacement. Data from an actual case relating to the maintenance and replacement of train traction motors is used for illustration.     

Efficient surrogate models for reliability analysis of systems with multiple failure modes

Despite many advances in the field of computational reliability analysis, the efficient estimation of the reliability of a system with multiple failure modes remains a persistent challenge. Various sampling and analytical methods are available, but they typically require accepting a tradeoff between accuracy and computational efficiency. In this work, a surrogate-based approach is presented that simultaneously addresses the issues of accuracy, efficiency, and unimportant failure modes. The method is based on the creation of Gaussian process surrogate models that are required to be locally accurate only in the regions of the component limit states that contribute to system failure. This approach to constructing surrogate models is demonstrated to be both an efficient and accurate method for system-level reliability analysis.     

A methodology for risk-based inspection planning of oil and gas pipes based on fuzzy logic framework

In an efficient and effective pipe integrity management programme, maintenance engineers often use the risk-based inspection (RBI) and maintenance strategy. Unfortunately, the calculation of risk is a daunting task because in order to calculate the risk of failure, a maintenance engineer needs to predict the rate of growth of a defect, the effect of the defect on the integrity of the structure and the consequence of failure. Unfortunately precise calculation for either of these parts is quite difficult.Fuzzy logic is a mathematical tool suitable for handling imprecise information in the real world. The benefit of this approach lies in its ability to include personal experiences along with acceptable deterministic models in the calculation. The structure of the model also allows easy calibration of the model to suit a particular plant condition. This approach can thus help to reduce the dependence upon the precise data, allow modelling even when a phenomenon is incompletely understood, and reduce the difficulties arising due to the complex computation required by more traditional methods.This paper presents a proposed methodology, based on fuzzy logic framework, for the establishment of an RBI programme for pipes. The paper also presents in detail a section of the methodology that can be used for calculating the estimated rate of CO₂ corrosion in carbon steel pipes. In this technique the plant operating parameters (temperature, gas and liquid flow rates, total pressure, CO₂ partial pressure and pH) are taken as fuzzy variables and used to calculate the Predicted Rate of Corrosion. The inspected rate of corrosion and the efficiency of inspection are also considered as fuzzy variables and are used to calculate Trust in Inspection Results and Trust in Predicted Results. By combining all the modules an estimated rate of corrosion is calculated. This estimated rate of corrosion can then be used for developing the risk-based inspection programme.     

Comparative study of quantitative models for hardware,software and human reliability assessment

Various models which may be used for quantitative assessment of hardware, software and human reliability are compared in this paper. Important comparison criteria are the system life cycle phase in which the model is intended to be used, the failure category and reliability means considered in the model, model purpose, and model characteristic such as model construction approach, model output and model input. The main objective is to present limitations in the use of current models for reliability assessment of computer-based safety shutdown systems in the process industry and to provide recommendations on further model development. Main attention is given to presenting the overall concept of various models from a user's point of view rather than technical details of specific models. A new failure classification scheme is proposed which shows how hardware and software failures may be modelled in a common framework.     

Sensitivity analysis in optimization and reliability problems

The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods.     

Error-based stopping criterion for the combined adaptive Kriging and importance sampling method for reliability analysis

Metamodel-based method is a wise reliability analysis technique because it uses the metamodel to substitute the actual limit state function under the predefined accuracy. Adaptive Kriging (AK) is a famous metamodel in reliability analysis for its flexibility and efficiency. AK combined with the importance sampling (IS) method abbreviate as AK–IS can extremely reduce the size of candidate sampling pool in the updating process of Kriging model, which makes the AK-based reliability method more suitable for estimating the small failure probability. In this paper, an error-based stopping criterion of updating the Kriging model in the AK–IS method is constructed and two considerable maximum relative error estimation methods between the failure probability estimated by the current Kriging model and the limit state function are derived. By controlling the maximum relative error, the accuracy of the estimate can be adjusted flexibly. Results in three case studies show that the error-based stopping criterion based AK–IS method can achieve the predefined accuracy level and simultaneously enhance the efficiency of updating the Kriging model.     

Cost and reliability based strategies for fatigue maintenance planning of floating structures

Floating structures are designed in such way that the appearance of fatigue failures cannot be avoided, implying the need for inspections during their life. Their maintenance has to be planned from an economic point of view so as to minimize maintenance costs but satisfying a minimum reliability level. A method is proposed to quantify the repair costs resulting of different reliability-based maintenance strategies. As an application of this approach a side shell structure typical of a floating production unit is analysed and the influence of different parameter with respect to the repair cost is also studied here.     

Error evaluations for the computation of failure probability in static structural reliability problems

The determination of mathematical reliability in static structures is still a motivating field of research. On one hand, the failure probability values are of greater importance in engineering activities; on the other hand, the determination of this probability remains a time consuming computational task when real problems are examined. To obtain a significant value for the failure probability while preserving a reasonable computation cost is therefore an objective to be considered. One of the necessary conditions to reach this target is to design a method to determine the computational error. Knowing the error will then give the capacity to limit the computation time, in particular by avoiding a too accurate probability evaluation. This paper presents a method allowing one to deal with these factors. The RGMR method, presented at the ICASP'7 meeting (July 1995, Paris) was designed to make such an error evaluation possible. Examples of numerical error computations with the RGMR method, particularly when low significant variables are eliminated, are given. These new developments are a step towards the goal mentioned above.     

A hybrid approach for identification of root causes and reliability improvement of a die bonding process—a case study

This paper presents an industrial case study on reliability improvement of the die bonding machine in the semiconductor industry. A hybrid approach combining dynamic analysis, process decomposition, and a structured fault tree was used to analyze the die bonding process. Firstly, the process was analyzed technically and decomposed into several stages according to different motions. Then, the die movement and force balance at each stage were analyzed according to physical laws, to identify the root causes of die rotation. A structured fault tree was then constructed to trace all possible causes and effects. A qualitative approach was used to identify critical events (root causes) for further analysis. Experiments were conducted to modify the bonding process to reduce the effects of the critical events. Finally, further process modification was proposed for simplification of the fault tree. This case study combined the knowledge in control and reliability engineering and presented a hybrid approach, which is very useful for practising engineers.