A New Method to Determine the Reliability Comparability for Products, Components, and Systems in Reliability Testing

A method is proposed in this paper to determine whether a product, a component, or a system in reliability life testing has a longer lifetime than the other. We propose two indices to compare reliability. The comparison is also distribution-free; i.e., it does not require the assumption on the lifetime distributions. A comparability index that is derived by integrating the weighted difference between the reliability functions of the two groups under comparison is named the "Better or Worse" (BOW) index. The second comparability index that is derived by calculating the overlapping area under the two distributions in comparison is named "Reliability Comparability" (RC) to quantify the degree of similarity between the two distributions. These two new indices are compared with the conventional methods currently used in the IC industries. Practical applications in lifetime-type reliability comparison are also illustrated in this paper     

Optimal allocation of s-identical, multi-functional spares in aseries system

This paper considers the problem of allocating statistically-identical, multi-functional spares to subsystems of a series system. The objective is to maximize the system reliability for mission time T which can be deterministic or stochastic. Several problems which are conceptually similar to this one have been discussed in the literature in different contexts. An algorithm is provided for obtaining standby redundancy allocation, and sufficient conditions are derived for optimality of the resulting allocation for general T. The algorithm is equivalent to a simple allocation rule under the sufficient conditions. The allocation rule gives an optimal allocation for the special cases: the PDF's of component lifetimes are log concave (which implies increasing failure rate), and T is deterministic; the components have exponential failure times, and T follows a gamma distribution; and component lifetime distributions are general, and T follows an exponential or a mixture of exponential distributions. No simpler method is available for latter two cases     

Two Algorithms for Computing Reliability

This paper developes two algorithms for finding the time-dependent reliability of any active-redundant system in terms of component failure probabilities. These algorithms apply to non-loaded, continuously-operating systems in which drift-type failures are neglected. The first algorithm is used when each component can fail in only one mode. A procedure, based on the Quine-McCluskey technique from switching circuit theory, is stated in conjunction with this algorithm which permits rapid simplification of the reliability expression. Two failure modes are permitted in the second algorithm. The relation between the expressions resulting from the algorithms and lifetime random variables is given so that the algorithms do not depend on specific component failure distributions.     

Comparison of Monte Carlo Techniques for Obtaining System-Reliability Confidence Limits

Digital computer techniques are developed using a) asymptotic distributions of maximum likelihood estimators, and b) a Monte Carlo technique, to obtain approximate system reliability s-confidence limits from component test data. 2-Parameter Weibull, gamma, and logistic distributions are used to model the component failures. The components can be arranged in any system configuration: series, parallel, bridge, etc., as long as one can write the equation for system reliability in terms of component reliability. Hypothetical networks of 3, 5, and 25 components are analyzed as examples. Univariate and bivariate asymptotic techniques are compared with a double Monte Carlo method. The bivariate asymptotic technique is shown to be fast and accurate. It can guide decisions during the research and development cycle prior to complete system testing and can be used to supplement system failure data.     

A three-unit standby redundant system with repair and preventive maintenance

This paper deals with the reliability of a renewable three-unit system under preventive maintenance activity. The Laplace transform of the reliability function and the mean lifetime of the system have been obtained under the assumption that the failure times, repair times, inspection times and maintenance times are random variables having different distributions. Some special cases also have been obtained.     

CALYPSO — Critical Area, Lifetime, and Yield Predicting Software

This contribution is divided into three parts. First we introduce a new procedure for the extraction of defect size distributions taken into account the real defect outline. In the second part a definition for reliability metal defects is given. Based on this definition a new lifetime prediction model for metal lines is introduced and theoretical and experimental results are compared. Our new yield and lifetime predicting software system CALYPSO is represented in the third part of the paper. The highlights of CALYPSO are the very high speed of the calculations, the implementation of the above mentioned lifetime prediction algorithms, and a module for the build-in reliability check of layout data.     

Fuzzy states as a basis for a theory of fuzzy reliability

Various engineering backgrounds have shown that the binary state assumption in probist (i.e., conventional) reliability theory, i.e. defining a system as fully failed or functioning, is not extensively acceptable, and thus the fuzzy state assumption should be used to replace the binary state assumption. As a result, the concept of profust reliability is introduced and a conceptual framework of profust reliability theory is developed on the basis of the fuzzy state assumption and the probability assumption. Profust reliability function, profust lifetime function and profust failure rate function and the mathematically rigorous relationships among them, lay a solid foundation for profust reliability theory. On the other hand, the concept of the virtual random lifetime builds a bridge linking profust reliability theory with probist reliability theory. In addition, in this paper, typical systems including the series system, parallel system, Markov model, mixture model and coherent system are briefly discussed within the conceptual framework of profust reliability theory.     

Computational algebra applications in reliability theory

Reliability analysts are typically forced to choose between using an `algorithmic programming language' or a `reliability package' for analyzing their models and lifetime data. This paper shows that computational languages can be used to bridge the gap to combine the flexibility of a programming language with the ease of use of a package. Computational languages facilitate the development of new statistical techniques and are excellent teaching tools. This paper considers three diverse reliability problems that are handled easily with a computational algebra language: system reliability bounds; lifetime data analysis; and model selection     

A probabilistic approach to evaluate the reliability of piezoelectric micro-actuators

In this paper, a probabilistic design approach is presented to evaluate the reliability of piezoelectric micro actuators. Based on the relationship between the lifetime, and degradation mechanism of piezoelectric actuators, and the electric field strength, the concept of "electric strength" is proposed to indicate the electric field strength of the piezoelectric actuators at a specified lifetime. The lifetime (number of cycles to failure) of the piezoelectric actuator, electric strength, and electric load are considered as the random variables; and their probability distributions are discussed. The interference model of electric load, and electric strength is introduced to the reliability design of piezoelectric micro actuators. By this approach, the relationship between the reliability, and the lifetime of the piezoelectric actuator can be given. A case study of the disk drive head positioning system demonstrates the application of the approach.     

Comparative reliability analysis of simplex and redundant systems

This paper presents the comparative reliability analysis of simplex and selective redundant configurations. System configurations such as k-out-of-n units, bridge, series-parallel and parallel-series are compared with the simplex system when the unit failure rate is constant and time dependent. Comparative reliability plots are shown for different reliability networks and failure time distributions. As expected, the detailed investigation shows that the system mean-time-to-failure may be a misleading indicator of performance for mission-oriented systems.     

A Monte Carlo simulation algorithm for finding MTBF

Prediction of mean time between failures (MTBF) is an important aspect of the initial stage of system development. It is often difficult to predict system MTBF during a given time since the component failure processes are extremely complex. The authors present a Monte Carlo simulation algorithm to calculate the MTBF during a given time of a binary coherent system. The algorithm requires the lifetime distributions of the components and the minimal path sets of the system. The MTBF for a specific time interval, e.g. a month or a year, can be estimated. If the component lifetime distributions are unknown, then a lower bound of system MTBF can be estimated by using known constant failure rates for each component     

Big data-enabled multiscale serviceability analysis for aging bridges☆

This work is dedicated to constructing a multi-scale structural health monitoring system to monitor and evaluate the serviceability of bridges based on the Hadoop Ecosystem (MS-SHM-Hadoop). By taking the advantages of the fault-tolerant distributed file system called the Hadoop Distributed File System (HDFS) and high-performance parallel data processing engine called MapReduce programming paradigm, MS-SHM-Hadoop features include high scalability and robustness in data ingestion, fusion, processing, retrieval, and analytics. MS-SHM-Hadoop is a multi-scale reliability analysis framework, which ranges from nationwide bridge-surveys, global structural integrity analysis, and structural component reliability analysis. This Nationwide bridge survey uses deep-learning techniques to evaluate the bridge serviceability according to real-time sensory data or archived bridge-related data such as traffic status, weather conditions and bridge structural configuration. The global structural integrity analysis of a targeted bridge is made by processing and analyzing the measured vibration signals incurred by external loads such as wind and traffic flow. Component-wise reliability analysis is also enabled by the deep learning technique, where the input data is derived from the measured structural load effects, hyper-spectral images, and moisture measurement of the structural components. As one of its major contributions, this work employs a Bayesian network to formulate the integral serviceability of a bridge according to its components serviceability and inter-component correlations. Here the inter-component correlations are jointly specified using a statistics-oriented machine learning method (e.g., association rule learning) or structural mechanics modeling and simulation.     

Mixture models in profust reliability theory

Conventional (i.e. probist) reliability theory is based on the probability assumption and the binary-state assumption, whereas profust reliability theory is based on the probability assumption and the fuzzy-state assumption. The mixture model is an important form of typical systems in profust reliability theory. In this paper we show that a mixture model can be converted into a series system, and study the IFR and DFR preservabilities for mixture models. Various profust reliability bounds are given for the mixture model. In addition, we also show how to construct typical profust lifetime distributions for mixture models.     

Lifetime Distribution of Consecutive-k-out-of-n:F Systems With Exchangeable Lifetimes

Algorithms for computing the lifetime distributions of consecutive-k-out-of-n:F systems with statistically independent, and statistically exchangeable component lifetimes are presented. A load-sharing model for statistically exchangeable component lifetimes and the effects of minimal repair on system lifetime are considered.     

Multi-state homogeneous Markov models in reliability analysis

In the standard Markov technique applied to reliability analysis, components are characterized by two states: an up state and a down state. The present paper explores the possibility of studying system reliability, by modelling each component with a multi-state homogeneous Markov model (MHMM). It is shown that this approach is of value both in approximating non-exponential probability distributions and in helping to build up suitable models for physical processes. Examples are presented which illustrate how the multi-state technique fits many practical situations. Finally some open problems on this topic are suggested.     

Reliability of single strength under n-stresses

In this paper we have considered the reliability of a system when n-stresses acted on a single strength component with probability distributions that were exponential, normal and gamma. We infer that when n-stresses act on a single strength component with an exponential distribution, the component has the same reliability as single stress and strength components which are connected in series, whereas normal and gamma distributions do not follow this rule.     

Modeling and maximizing burn-in effectiveness

System burn-in can get rid of many residual defects left from component and subsystem burn-in since incompatibility exists not only among components but also among different subsystems and at the system level. Even if system, subsystem, and component burn-in are performed, the system reliability often does not achieve the requirement. In this case, redundancy is a good way to increase system reliability when improving component reliability is expensive. This paper proposes a nonlinear model to: estimate the optimal burn-in times for all levels, and determine the optimal amount of redundancy for each subsystem. For illustration, a bridge system configuration is considered; however, the model can be easily applied to other system configurations. Since there are few studies on system, subsystem, and component incompatibility, reasonable values are assigned for the compatibility factors at each level     

Studies in Cascade Reliability?I

An n-Cascade system is defined as a special type of standby system with n components. A component fails if the stress on it is not less than its strength. When a component in cascade fails, the next in standby is activated and will take on the stress. However, the stress on this component will be a multiple k times the stress that acted on its predecessor. The system fails if due to an initial stress, each of the components in succession fails. The stress is random and the component strengths are independent and identically distributed variates, with specified probability functions; k is constant. Expressions for system reliability are obtained when the stress and strength distributions are exponential. Reliability values for a 2-cascade system with Gamma and Normal stress and strength distributions are computed, some of which are presented graphically.     

An algorithmic approach to increased reliability through standbyredundancy

The authors address the issue of optimal redundancy allocation, viz, improving the reliability of a system by adding cold-standby spares, through an algorithmic approach that uses the unique characteristics of an assumed underlying failure distribution. Although the approach applies to systems with mixed parallel and series configurations, the discussion is limited to a series system of components. The lifetime distributions of individual parts are of the phase type. This class of probability distributions is chosen for its ease of numerical implementation. The formulation of the reliability enhancement problem is applied, and several heuristic design algorithms are examined     

Estimation of system reliability for uncooled optical transmittersusing system reliability function

This paper investigates the system reliability for 155 Mb/s optical transmitters by deriving a system reliability function from reliability data of each component for transmitters, laser diode, photodiode, optical assembly, and driver IC. The reliability data for each component reliability function have been obtained from accelerated aging test. The reliability parameters such as failure rate, mean time-to-failure (MTTF), standard deviation are obtained from a probability plotting method. From the system reliability function, the MTTF of the optical transmitter at 65°C was estimated to be 47000 h with 95% confidence. In this estimation, we introduced modified lifetime of laser diodes and reliability function of optical assembly