Showing papers on "Failure rate published in 1996"
Book•
01 Jan 1996
TL;DR: In this paper, the authors present a basic reliability model for failure distribution and a constant failure rate model for time-dependent failure models, as well as a design for maintainability.
Abstract: 1 IntroductionI Basic Reliability Models2 The Failure Distribution3 Constant Failure Rate Model4 Time-Dependent Failure Models5 Reliability of Systems6 State Dependent Systems7 Physical Reliability Models8 Design for Reliability9 Maintainability10 Design for Maintainability11 AvailabilityII The Analysis of Failure Data12 Data Collection and Empirical Methods13 Reliability Testing14 Reliability Growth Testing15 Identifying Failure and Repair Distributions16 Goodness-of-Fit TestsIII Application17 Reliability Estimation and Application18 Implementation
1,469 citations
TL;DR: In this article, a simple model based on adding two Weibull survival functions is proposed to model lifetime distributions for many components with a bathtub-shaped failure rate in practice.
418 citations
TL;DR: In this article, the authors introduced a more flexible model to describe sequential k-out-of-n systems, in which the failure of any component possibly influences the other components such that their underlying failure rate is parametrically adjusted with respect to the number of preceding failures.
Abstract: k-out-of-n systems frequently appear in applications. They consist of n components of the same kind with independent and identically distributed life-lengths. The life-length of such a system is described by the (n−k+1)-th order statistic in a sample of size n when assuming that remaining components are not affected by failures. Sequential order statistics are introduced as a more flexible model to describe ‘sequential k-out-of-n systems’ in which the failure of any component possibly influences the other components such that their underlying failure rate is parametrically adjusted with respect to the number of preceding failures. Useful properties of the maximum likelihood estimators of the model parameters are shown, and several tests are proposed to decide whether the new model is the more appropriate one in a given situation. Moreover, for specific distributions, e.g. Weibull distributions, simultaneous maximum likelihood estimation of the model parameters and distribution parameters is considered.
116 citations
Proceedings Article•
30 Apr 1996
TL;DR: This chapter is mainly aimed at showing that, by using deliberately simple mathematics, the classical reliability theory can be extended in order to be interpreted from both hardware and software viewpoints.
Abstract: This chapter is mainly aimed at showing that, by using deliberately simple mathematics, the classical reliability theory can be extended in order to be interpreted from both hardware and software viewpoints. This is referred to as X-ware [Lapr89, Lapr92b] throughout this chapter. It will be shown that, even though the action mechanisms of the various classes of faults may be different from a physical viewpoint according to their causes, a single formulation can be used from the reliability modeling and statistical estimation viewpoints. A single formulation has several advantages, both theoretical and practical, such as (1) easier and more consistent modeling of hardware-software systems and of hardware-software interactions, (2) adaptability of models for hardware dependability to software systems and vice versa, and (3) mathematical tractability. Section 2.2 gives a general overview of the dependability concepts. Section 2.3 is devoted to the failure behavior of an X-ware system, disregarding the effect of restoration actions (the quantities of interest are thus the time to the next failure or the associated failure rate), considering in turn atomic systems and systems made up of components. In Sec. 2.4, we deal with the behavior of an X-ware system with service restoration, focusing on the characterization of the sequence of the times to failure (i.e., the failure process); the measures of interest are thus the failure intensity, reliability, and availability. Section 2.5 outlines the state of art in dependability evaluation and specification. Finally, Sec. 2.6 summarizes the results obtained.
90 citations
TL;DR: A Bayes model for step-stress accelerated life testing where the failure times at each stress level are exponentially distributed, but strict adherence to a time-transformation function is not required.
Abstract: This paper develops a Bayes model for step-stress accelerated life testing. The failure times at each stress level are exponentially distributed, but strict adherence to a time-transformation function is not required. Rather, prior information is used to define indirectly a multivariate prior distribution for the failure rates at the various stress levels. Our prior distribution preserves the natural ordering of the failure rates in both the prior and posterior estimates. Methods are developed for Bayes point estimates as well as for making probability statements for use-stress life parameters. The approach is illustrated with an example.
88 citations
TL;DR: Various additive cost functions are considered in this paper and it is shown that the optimal burn-in time b* minimizing the cost function is always before t1, i.e., b* > 0.
Abstract: Burn-in procedure is used to improve the quality of products. In field operation only those components which survive the burn-in process will be used. Various additive cost functions are considered in this paper. One part of the cost function is the expense incurred until the first component surviving burn-in is obtained. The other part of cost function is either i the gain proportional to the mean life in field operation or ii the expenditure due to replacement at failure during field operation. We assume that the component before undergoing the burn-in procedure has a bathtub-shaped failure rate function with change points t1 and t2. It is shown that the optimal burn-in time b* minimizing the cost function is always before t1. It is also shown that a large initial failure rate justifies burn-in, i.e., b* > 0.
72 citations
TL;DR: This paper discusses a condition based maintenance model with exponential failures, and fixed inspection intervals, and studies the optimal solution obtained via dynamic programming and compares it to an approximate steady state solution based on renewal theory.
Abstract: This paper discusses a condition based maintenance model with exponential failures, and fixed inspection intervals. A condition of the equipment, such as vibration, is monitored at equidistant time intervals. If the variable indicating the condition is above a threshold an instantaneous maintenance action is performed and the monitored condition takes on its initial value. The equipment can fail only once within an inspection interval. The probability of failure is exponential and the failure rate is dependent on the condition. The cost to be minimized is the long-run average cost of maintenance actions and failures. We study the optimal solution to this problem obtained via dynamic programming and compare it to an approximate steady state solution based on renewal theory.
72 citations
TL;DR: The use of the exponential distribution is frequently preferred over mathematically more complex distributions, such as the Weibull and the lognormal among others, suggests that most engineers favour the application of simpler models to obtain failure rates and reliability figures quickly.
64 citations
01 May 1996
TL;DR: It is shown how fail-awareness can be applied in partitionable systems, i.e. systems in which communication is not certain due to network failures or excessive performance failures, and several fail-aware partitionable services are described to show the applicability of this approach.
Abstract: The guaranteed response paradigm is currently favored by some parts of the research community to design distributed hard real-time systems. It uses peak load and bounded failure rate assumptions to guarantee that the real-time system reacts to events of the controlled object within an a priori known time. Much of the off-the-shelf hardware and software makes it very hard to guarantee the bounded failure rate hypothesis at run-time. If this hypothesis, fundamental to all synchronous service implementations, can be violated at run-time, these implementations can be subject to unpredictable behavior. We address this problem by proposing an approach intended to support the construction of fail-safe or complex real-time systems: fail-awareness. This is a systematic approach to mask all failures whenever the failure rate is within a given bound and if not all failures can be masked, fail-aware services have to provide a well defined exception semantics.
The goal of fail-awareness is as follows: as long as the underlying communication and process services are affected only by a bounded rate of failures, all services have to provide their standard synchronous semantics, i.e. the system reacts within the given time, and each service knows that it provides its synchronous semantics. Each server maintains an (exception) indicator which tells the clients of the server if it currently provides its standard or an exception semantics. When the failure rate rises above some a priori given threshold, a server is allowed to switch to its exception semantics but it has to notify its clients that it has switched to exception semantics. An application can use the indicators to switch to a safe state in case of non-maskable failures.
We show how fail-awareness can be applied in partitionable systems, i.e. systems in which communication is not certain due to network failures or excessive performance failures. Our approach allows the servers in each partition to make progress independent of the servers in other partitions. In case a server provides its standard semantics, its indicator signals its clients to what logical partition they belong. Otherwise, it just signals that the server provides its exception semantics. We describe several fail-aware partitionable services to show the applicability of our approach.
57 citations
30 Oct 1996
TL;DR: The paper describes a different approach to software reliability growth modelling which should enable conservative long term predictions to be made and shows that the predicted bound appears to agree with a wide range of industrial and experimental reliability data.
Abstract: The paper describes a different approach to software reliability growth modelling which should enable conservative long term predictions to be made. Using relatively standard assumptions it is shown that the expected value of the failure rate after a usage time t is bounded by: /spl lambda/~/sub t//spl les/(N/(et)) where N is the initial number of faults and e is the exponential constant. This is conservative since it places a worst case bound on the reliability rather than making a best estimate. We also show that the predictions might be relatively insensitive to assumption violations over the longer term. The theory offers the potential for making long term software reliability growth predictions based solely on prior estimates of the number of residual faults. The predicted bound appears to agree with a wide range of industrial and experimental reliability data. It is shown that less pessimistic results can be obtained if additional assumptions are made about the failure rate distribution of faults.
51 citations
TL;DR: In this article, a general approach is presented to study the mixtures of distributions and show that the failure rates of the unconditional and conditional distributions cross at most at one point, which is not true for increasing failure rate distributions.
Abstract: It is well known that mixtures of decreasing failure rate (DFR) distributions have the DFR property. A similar result is, of course, not true for increasing failure rate (IFR) distributions. In a recent note, Gurland and Sethuraman (1994, Technometrks36(4): 416–418) presented two examples where mixtures of IFR distributions show DFR property. In this paper, we present a general approach to study the mixtures of distributions and show that the failure rates of the unconditional and conditional distributions cross at most at one point. Mixtures of Weibull distribution with a shape parameter greater than 1 are examined in detail. This also enables us to study the monotonic properties of the mean residual life function of the mixture. Some examples are provided to illustrate the results.
TL;DR: In this article, the authors present models for the failure mechanism causing the degraded and critical failures, and estimators for their failure intensities are provided, based on exponentially distributed random variables, but they give non-exponential distributions for the time to failure.
TL;DR: In this paper, the location of critical points (at which the monotonicity changes) for both the failure rate and the mean residual life function (MRLF) were studied.
Abstract: Sometimes it is appropriate to model the survival and failure time data by a non-monotonic failure rate distribution. This may be desirable when the course of disease is such that mortality reaches a peak after some finite period and then slowly declines.In this paper we study Burr, type XII model whose failure rate exhibits the above behavior. The location of the critical points (at which the monotonicity changes) for both the failure rate and the mean residual life function (MRLF) are studied. A procedure is described for estimating these critical points. Necessary and sufficient conditions for the existence and uniqueness of the maximum likelihood estimates are provided and it is shown that the conditions provided by Wingo (1993) are not sufficient. A data set pertaining to fibre failure strengths is analyzed and the maximum likelihood estimates of the critical points are obtained.
TL;DR: In this paper, a Bayesian analysis methodology is proposed to determine appropriate non-periodic inspection intervals of fatigue-sensitive aircraft structures, so that their reliability remains above a prespecified minimum level throughout their service life.
Proceedings Article•
01 Jan 1996TL;DR: This discussion presents practical measurement techniques to accurately determine the Resolving Time Constant and Metastability Window and a comparison is made to a predicted MTBF.
Abstract: Determining metastability characteristics is challenging. Devising reliable and repeatable experiments and procedures requires time, patience, care and knowledge. This discussion presents practical measurement techniques to accurately determine the Resolving Time Constant (/spl tau/) and Metastability Window (W). Also included is a method for observing the metastability failure rate at a designated time following the clock. By converting this failure rate to observed MTBF (Mean Time Between Failure), a comparison is made to a predicted MTBF.
TL;DR: In this paper, the authors present models for analyzing dependent competing risk data, designed to represent interactions of critical failure and maintenance mechanisms responsible for intercepting incipient and degraded failures, and they are fashioned such that the (constant) critical failure rate is identifiable from dependent competitive risk data.
TL;DR: This paper estimates the mean life of the units under usual working conditions, based on censored data obtained from units under stress conditions, considering the very flexible class of failure distributions, piecewise exponential model and a log-linear stress-response relationship.
Abstract: Efficient industrial experiments for the reliability analysis of manufactured products consist of subjecting the units to accelerated life tests where, for each pre-fixed stress level, the experiment ends after the failure of a certain pre-fixed proportion of units or a certain test time is reached. This paper estimates the mean life of the units under usual working conditions, based on censored data obtained from units under stress conditions. This problem is approached through a generalized linear model and related inferential techniques, considering the very flexible class of failure distributions, piecewise exponential model and a log-linear stress-response relationship. The general framework has as particular cases, among others, the power law model, the Arrhenius model and the generalized Eyring model. A numerical example illustrates the methodology.
TL;DR: A nonparametric model of the interval estimation is proposed, based on results of step-stress accelerated life testing, which is proved to be equivalent to the assumptions accepted in numerous papers.
Abstract: A nonparametric model of the interval estimation is proposed. The estimation is based on results of step-stress accelerated life testing. The approach includes: application of a linear model of damage accumulation, which is proved to be equivalent to the assumptions accepted in numerous papers; estimation of the time transformation function, using the test results for all the load levels; and application of a nonparametric approach for interval estimation of reliability measures, based on the assumption that life-time distribution under the constant load has increasing failure rate. A numerical example uses initial data obtained on the basis of statistical simulation thus verifying the proposed approach.
TL;DR: In this article, clear relations have been established between E-sort yield and bum-in, EFR and field failure rates for nearly 50 million high volume products in bipolar, CMOS and BICMOS technologies from different waferfabs.
TL;DR: This paper describes a different approach to software reliability growth modeling which enables long-term predictions based solely on prior estimates of the number of residual faults and the predicted bound appears to agree with a wide range of industrial and experimental reliability data.
Abstract: This paper describes a different approach to software reliability growth modeling which enables long-term predictions. Using relatively common assumptions, it is shown that the average value of the failure rate of the program, after a particular use-time, t, is bounded by N/(e/spl middot/t), where N is the initial number of faults. This is conservative since it places a worst-case bound on the reliability rather than making a best estimate. The predictions might be relatively insensitive to assumption violations over the longer term. The theory offers the potential for making long-term software reliability growth predictions based solely on prior estimates of the number of residual faults. The predicted bound appears to agree with a wide range of industrial and experimental reliability data. Less pessimistic results can be obtained if additional assumptions are made about the failure rate distribution of faults.
TL;DR: The design of the test plan is stated as an optimization problem which minimizes test costs while ensuring that specified consumer and producer risks on system reliability are not exceeded.
Abstract: Acceptance testing is analyzed for a series system of n components, each having an unknown, different, constant failure rate. Components are tested individually, and tests are terminated when a preassigned number of failures is observed for each component. The total time-on-test for each component is noted, and a statistic is constructed using observed test times and the number of failures of the components; the statistic is based on the maximum likelihood estimation of system reliability. This statistic is then used in specifying a decision rule for accepting or rejecting the entire system. The design of the test plan is stated as an optimization problem which minimizes test costs while ensuring that specified consumer and producer risks on system reliability are not exceeded. Numerical examples are provided, and implications of the test plan are discussed.
TL;DR: The Multi-Class Binomial Failure Rate (MCBFR) Model presented here achieves this by assigning observed failures to different classes according to their technical characteristics and applying the BFR formalism to each of these.
TL;DR: This paper uses the common assumptions on the software operational environment to get a stochastic model where the successive times between software failures are exponentially distributed; their failure rates have Markov priors.
Abstract: This paper presents a Bayes nonparametric approach for tracking and predicting software reliability. We use the common assumptions on the software operational environment to get a stochastic model where the successive times between software failures are exponentially distributed; their failure rates have Markov priors. Under these general assumptions we give Bayes estimates of the parameters that assess and predict the software reliability. We give algorithms (based on Monte-Carlo methods) to compute these Bayes estimates. Our approach allows the reliability analyst to construct a personal software reliability model simply by specifying the available prior knowledge; afterwards the results in this paper can be used to get Bayes estimates of the useful reliability parameters. Examples of possible prior physical knowledge concerning the software testing and correction environments are given. The maximum-entropy principle is used to translate this knowledge to prior distributions on the failure-rate process. Our approach is used to study some simulated and real failure data sets.
TL;DR: In this article, a failure rate function for processes describing the dynamics of regenerative models is proposed and various approximations of the failure rate are investigated and their accuracies are investigated.
Abstract: We consider models typical to the area of reliability, and a failure rate function for processes describing the dynamics of these models. Various approximations of the failure rate function are proposed and their accuracies are investigated. The basic case studied in the paper is a regenerative model. Some interesting particular cases (Markov, semi-Markov, etc.) are considered. All proposed estimates are stated in a tractable analytic form.
TL;DR: This research was performed to address the issue of shock robustness in silicon microstructures by considering features to reduce stress concentration and by geometries that have a more uniform stress distribution to be significant factors contributing to the failure rate.
Abstract: This research was performed to address the issue of shock robustness in silicon microstructures. The improvements were incorporated by considering features to reduce stress concentration and by geometries that have a more uniform stress distribution. The design were evaluated by finite element models and by testing with wafer level techniques. The designs were intended to have the same fundamental frequency, inertia properties and damping properties. Six different designs were developed and distributed across 900 die on multiple 4-inch wafers. The wafers were subjected to repeated shocks at magnitudes of 130, 2008, and 3680 gs with a 0.25 msec duration. Automated optical inspection was used to interrogate each die and determine which test structures survived the shock test. Subsequent to testing, analysis of variance was used to identify the significant factors that influence the failure rate. This analysis has shown beam design, wafer orientation, acceleration level, and the interactions of beam design*wafer orientation, wafer orientation*acceleration level to be significant factors contributing to the failure rate. The designs were grouped according to mean failure rate. The `small bow tie' design had the highest failure rate and was a separate population. Its failure rate was two to four times that of other designs. The second grouping of lower failure rates included all designs to address the stress concentration. Of these designs, the `no gusset' design has the highest failure rate (twice that of other designs). The final grouping includes the gusset designs and the `medium' and `large bow tie' designs. The designs to improve stress distribution had the lowest mean failure rates of all designs.
TL;DR: In this paper, a solution to the bandwidth selection problem for this form of hazard estimate and asymptotic properties of the selected bandwidth are given, where the authors restrict their consideration to kernel estimates of density and distribution function, which has the major advantage of being continuous.
Abstract: From among the numerous choices of nonparametric estimate of failure rate, we restrict consideration to that based on kernel estimates of density and distribution function, which has the major advantage of being continuous. We propose a solution to the bandwidth selection problem for this form of hazard estimate and asymptotic properties of the selected bandwidth are given.
TL;DR: A nonparametric approach to estimate the optimal system burn-in time is proposed and the Anderson-Darling statistic is used to check the constant failure rate (CFR), and the pool-adjacent-violator (PAV) algorithm is applied to "unimodalize" the failure rate curve.
Abstract: System burn-in can get rid of more residual defects than component and subsystem burn-ins because incompatibility exists not only among components, but also among different subsystems and at the system level. There are two major disadvantages for performing the system burn-in: the high burn-in cost and the complicated failure rate function. This paper proposes a nonparametric approach to estimate the optimal system burn-in time. The Anderson-Darling statistic is used to check the constant failure rate (CFR), and the pool-adjacent-violator (PAV) algorithm is applied to "unimodalize" the failure rate curve. Given experimental data, the system burn-in time can be determined easily without going through complex parameter estimation and curve fittings.
TL;DR: In this paper, a spline density estimate for the prior density function of the failure rate parameter in the exponential distribution is derived for the failure probability, and the reliability function is also estimated either by using the empirical Bayes estimate of the parameter, or by obtaining the expectation of the reliability functions.
Proceedings Article•
18 Mar 1996
TL;DR: This discussion presents practical measurement techniques to accurately determine the Resolving Time Constant and Metastability Window and a method for observing the metastability failure rate at a designated time following the Clock.
Abstract: Determining metastability characteristics is challenging. Devising reliable and repeatable experiments and procedures requires time, patience, care and knowledge. This discussion presents practical measurement techniques to accurately determine the Resolving Time Constant (tau) and Metastability Window (W). Also included is a method for observing the metastability failure rate at a designated time following the Clock. By converting this failure rate to observed MTBF (Mean Time Between Failure), a comparison is made to a predicted MTBF.
TL;DR: A reliability growth model based on non‐homogeneous Poisson process with intensity function given by the power law, which is realistic, easy to use, and gives a better prediction of reliability of a software.
Abstract: Most of the existing software reliability models assume time between failures to follow an exponential distribution. Develops a reliability growth model based on non‐homogeneous Poisson process with intensity function given by the power law, to predict the reliability of a software. Several authors have suggested the use of the non‐homogeneous Poisson process to assess the reliability growth of software and to predict their failure behaviour. Inference procedures considered by these authors have been Bayesian in nature. Uses an unbiased estimate of the failure rate for prediction. Compares the performance of this model with Bayes empirical‐Bayes models and a time series model. The model developed is realistic, easy to use, and gives a better prediction of reliability of a software.