Data-Based Modeling of the Failure Rate of Repairable Equipment

A databaseof failures of many types of medical equipment was analysed,to study the dependence of failure rate on equipment age andon time since repair. The intention was to use this large datasetto assess the validity of some widely-used models of failurerate, such as the power-law and loglinear Poisson processes,and so to recommend simple and adequate models to those practitionershaving little data to discriminate between rival models. Theaim is also to illustrate a methodology for computing policycosts from failure databases. The power-law process model wasfound to fit slightly better overall than did the loglinear andlinear processes. Some related models were created to fit anobserved peaking of failure rate. The data showed a decreasinghazard of (first) failure after repair for some equipment types.This can be due to imperfect or hazardous repair, and also todiffering failure rates among a population of machines. Two simplemodels of imperfect repair were used to fit the data, and anEmpirical Bayes method was used to fit a model of variable failurerate between machines. Neglect of such variation can lead toan over-estimate of the hazardousness of repair.     

Reliability of Supply Between Production Lines

ABSTRACT

We compare four strategies for ensuring a reliable just-in-time supply from a seat production line, which is prone to machine failure, to a car assembly line, which is assumed to operate at a constant speed over single shifts. The strategies are as follows: holding buffer stock; duplication of the least reliable machine; duplication of the production line as a stand-by; and running two production lines concurrently. Times between machine failures are assumed to have independent exponential distributions. A general distribution of repair times is allowed for by using phase-type representations. We show the stationary distribution for these models, and compare stationary distributions with average times within levels over shifts conditional on all machines working at the start of a shift. We compute moments of sojourn times within an arbitrary subset of states, which are relevant when cost is a non-linear function of downtime. We use first passage time results to obtain probabilities of line failure within a shift, and use these results to compare the four strategies.     

Empowering phase II clinical trials to reduce phase III failures

The large number of failures in phase III clinical trials, which occur at a rate of approximately 45%, is studied herein relative to possible countermeasures. First, the phenomenon of failures is numerically described. Second, the main reasons for failures are reported, together with some generic improvements suggested in the related literature. This study shows how statistics explain, but do not justify, the high failure rate observed. The rate of failures due to a lack of efficacy that are not expected, is considered to be at least 10%. Expanding phase II is the simplest and most intuitive way to reduce phase III failures since it can reduce phase III false negative findings and launches of phase III trials when the treatment is positive but suboptimal. Moreover, phase II enlargement is discussed using an economic profile. As resources for research are often limited, enlarging phase II should be evaluated on a case‐by‐case basis. Alternative strategies, such as biomarker‐based enrichments and adaptive designs, may aid in reducing failures. However, these strategies also have very low application rates with little likelihood of rapid growth.     

Testing of two sample proportional intensity assumption for non-homogeneous Poisson processes

For two independent non-homogeneous Poisson processes with unknown intensities we propose a test for testing the hypothesis that the ratio of the intensities is constant versus it is increasing on (0,t]. The existing test procedures for testing such relative trends are based on conditioning on the number of failures observed in (0,t] from the two processes. Our test is unconditional and is based on the original time truncated data which enables us to have meaningful asymptotics. We obtain the asymptotic null distribution (as t becomes large) of the proposed test statistic and show that the proposed test is consistent against several large classes of alternatives. It was observed by Park and Kim (IEEE. Trans. Rehab. 40 (1), 1992, 107–111) that it is difficult to distinguish between the power-law and log-linear processes for certain parameter values. We show that our test is consistent for such alternatives also.     

Optimal Maintenance Time for Repairable Systems Under Two Types of Failures

Determination of preventive maintenance is an important issue for systems under degradation. A typical maintenance policy calls for complete preventive repair actions at pre-scheduled times and minimal repair actions whenever a failure occurs. Under minimal repair, failures are modeled according to a non homogeneous Poisson process. A perfect preventive maintenance restores the system to the as good as new condition. The motivation for this article was a maintenance data set related to power switch disconnectors. Two different types of failures could be observed for these systems according to their causes. The major difference between these types of failures is their costs. Assuming that the system will be in operation for an infinite time, we find the expected cost per unit of time for each preventive maintenance policy and hence obtain the optimal strategy as a function of the processes intensities. Assuming a parametrical form for the intensity function, large sample estimates for the optimal maintenance check points are obtained and discussed.     

Burn-in for Eliminating Weak Items in Heterogeneous Populations

Burn-in is a method of eliminating early failures in populations of manufactured items. To burn-in a component or a system means to subject it to a ‘‘simulated operation’’ for some time (prior to its actual field use). Various optimal burn-in problems have been intensively studied in the literature under the assumption of decreasing or bathtub-shaped failure rates. However, most of these studies have been conducted for homogeneous populations. In this paper, we discuss burn-in for heterogeneous populations and develop approaches that minimize the risks of selecting items with large levels of individual failure rates. Using simple examples, we consider the optimal burn-in time, which minimizes these risks.     

The Bayesian approach for highly reliable electro-explosive devices using one-shot device testing

Due to the high reliability and high testing cost of electro-explosive devices, even though an accelerated test is performed, one may observe very few failures or even no failures at all due to censoring. In this paper, we consider modelling the reliability of such devices by an exponential lifetime distribution in which the failure rate is assumed to be a function of some covariates and that the observed data are binary. The Bayesian approach, with three different prior settings, is used to develop inference on the failure rate, lifetime and the reliability under some settings. A Monte Carlo simulation study is carried out to show that this approach is quite useful and suitable for analysing data of the considered form, especially when the failure rates are very small. Finally, illustrative data are analysed using this approach.     

On a threshold representation for complex load-sharing systems

Complex load-sharing systems are studied to incorporate dependencies among components through a load-sharing rule. As the load on the system increases, a series of cycles of Phase I/II failures occur where Phase I failure is a single component failure, which then causes a cascade of component failures (Phase II) due to the load transfer as these components fail. A threshold representation for the process of system failure is given. This representation is a gamma-type mixture representation when the component strengths are independent exponentials. In this case, for a given breaking pattern the mixture is over the gamma scale parameter and is based on a convolution of uniforms defined by the load-sharing parameters. Such convolutions can be approximated by normal densities which reduces the dimension of the parameter space. This representation can be generalized to independent component strengths with arbitrary distributions by transforming the strength and load-sharing to pseudo-strength and pseudo-load-sharing rules.     

An Extended Sequential Imperfect Preventive Maintenance Model with Improvement Factors

This article presents a generalization of the imperfect sequential preventive maintenance (PM) policy with minimal repair. As failures occur, the system experiences one of two types of failures: a Type-I failure (minor), rectified by a minimal repair; or a Type-II failure (catastrophic) that calls for an unplanned maintenance. In each maintenance period, the system is maintained following the occurrence of a Type-II failure or at age, whichever takes place first. At the Nth maintenance, the system is replaced rather than maintained. The imperfect PM model adopted in this study incorporates with improvement factors in the hazard-rate function. Taking age-dependent minimal repair costs into consideration, the objective consists of finding the optimal PM and replacement schedule that minimize the expected cost per unit time over an infinite time-horizon.     

Availability of a system subject to hidden failure inspected at constant intervals with non-negligible downtime due to inspection and downtime due to repair/replacement

For systems with hidden or unrevealed failures, a common practice is to inspect the system regularly, since failures can only be detected upon inspection. Recent works in the literature have studied the availability of a system under periodic inspection, assuming perfect repair/replacement with non-negligible downtime due to repair/replacement for a detected failure. In some situations, however, not only downtime due to repair/replacement but also downtime due to inspection is non-negligible regardless whether a failure was detected or not. In this paper, we consider the availability of a system subject to hidden failure inspected at constant interval with both non-negligible downtime due to inspection and non-negligible downtime due to repair/replacement.     

The binomial failure rate mixture model for common cause failure data from the nuclear industry

A model for the lifetime of a system is considered in which the system is susceptible to simultaneous failures of two or more components, the failures having a common external cause. Three sets of discrete failure data from the US nuclear industry are examined to motivate and illustrate the model derivation: they are for motor-operated valves, cooling fans and emergency diesel generators. To achieve target reliabilities, these components must be placed in systems that have built-in redundancy. Consequently, multiple failures due to a common cause are critical in the risk of core meltdown. Vesely has offered a simple methodology for inference, called the binomial failure rate model: external events are assumed to be governed by a Poisson shock model in which resulting shocks kill X out of m system components, X having a binomial distribution with parameters ( m , p ), 0< p <1. In many applications the binomial failure rate model fits failure data poorly, and the model has not typically been applied to probabilistic risk assessments in the nuclear industry. We introduce a realistic generalization of the binomial failure rate model by assigning a mixing distribution to the unknown parameter p . The distribution is generally identifiable, and its unique nonparametric maximum likelihood estimator can be obtained by using a simple iterative scheme.     

A combinatorial estimation approach for storage reliability with initial failures based on periodic testing data

Storage reliability that measures the ability of products in a dormant state to keep their required functions is studied in this paper. Unlike the operational reliability, storage reliability for certain types of products may not be always 100% at the beginning of storage since there are existing possible initial failures that are normally neglected in the models of storage reliability. In this paper, a new combinatorial approach, the nonparametric measure for the estimates of the number of failed products and the current reliability at each testing time in storage, and the parametric measure for the estimates of the initial reliability and the failure rate based on the exponential reliability function, is proposed for estimating and predicting the storage reliability with possible initial failures. The proposed method has taken into consideration that the initial failure and the reliability testing data, before and during the storage process, are available for providing more accurate estimates of both initial failure probability and the probability of storage failures. When storage reliability prediction that is the main concern in this field should be made, the nonparametric estimates of failure numbers can be used into the parametric models for the failure process in storage. In the case of exponential models, the assessment and prediction method for storage reliability is provided in this paper. Finally, numerical examples are given to illustrate the method. Furthermore, a detailed comparison between the proposed method and the traditional method, for examining the rationality of assessment and prediction on the storage reliability, is presented. The results should be useful for planning a storage environment, decision-making concerning the maximum length of storage, and identifying the production quality.     

A sequential scheme to estimate the optimal age replacement policy

Consider a system which is subject to failure and must be replaced when this occurs. If it costs less to replace the system in advance before failure, it may be advantageous to use an age replacement policy. However, the optimal age to replace the system is unknown if the underlying failure distribution is unknown. This paper develops a scheme to update the current estimate of the optimal age replacement policy in an on-line fashion and simultaneously controlling costs by reducing system failures.     

Analyzing space-time sensor network data under suppression and failure in transmission

In this paper we present a fully model-based analysis of the effects of suppression and failure in data transmission with sensor networks. Sensor networks are becoming an increasingly common data collection mechanism in a variety of fields. Sensors can be created to collect data at very high temporal resolution. However, during periods when the process is following a stable path, transmission of such high resolution data would carry little additional information with regard to the process model, i.e., all of the data that is collected need not be transmitted. In particular, when there is cost to transmission, we find ourselves moving to consideration of suppression in transmission. Additionally, for many sensor networks, in practice, we will experience failures in transmission—messages sent by a sensor but not received at the gateway, messages sent but arriving corrupted. Evidently, both suppression and failure lead to information loss which will be reflected in inference associated with our process model. Our effort here is to assess the impact of such information loss under varying extents of suppression and varying incidence of failure. We consider two illustrative process models, presenting fully model-based analyses of suppression and failure using hierarchical models. Such models naturally facilitate borrowing strength across nodes, leveraging all available data to learn about local process behavior.     

ON THE PREDICTION OF FUTURE FAILURES FOR A REPAIRABLE EQUIPMENT SUBJECT TO OVERHAULS

This paper deals with the prediction, from a Bayes viewpoint, of future failures for a repairable equipment subjected both to minimal repairs and periodic overhauls. The effect of major overhauls on the reliability of the equipment is modeled by a proportional age reduction model, while the failure process between two successive overhaul epochs is modeled by the power law process. Prediction both of the future failure times and of the number of failures in a future time interval are provided on the basis of the observed data and of a number of suitable prior densities, which reflect different degrees of belief on the failure mechanism and overhaul effectiveness. Finally, a numerical application illustrates the proposed prediction procedures and their use in assessing the adequacy of the model to describe the observed data set.     

Successive sampling and software reliability

The connection between successive sampling and exponential order statistics (EOS) models of software failures is highlighted. Maximum likelihood and unbiased estimators designed for successive sampling inference can be applied to software failure data generated by EOS models. They lead naturally to predictive estimators of waiting times to future failures based on an observed software failure history.     

An extension of the Freund's bivariate distribution to model cascading failures

The notion of cascading failures is a common phenomenon we observe around us. Here the initial failure alters the structure function of the system, which leads to subsequent failures within a short period of time referred to as threshold time. The concept of cascading failures within the framework of reliability theory and the Freund bivariate exponential distribution to model cascading failures has been studied by few authors. The Freund bivariate exponential distribution allows modelling a parallel redundant system with two components. In this system, the lifetimes of the two components behave as if they are independent, until one of the components fail, after which the remaining component suffers an increased/decreased stress. In this article, we further generalize this model to accommodate cascading failures. Various properties of the model are investigated and statistical inference procedures are developed using L-moments and method of moments. A practical application of this model is illustrated using data from www.espncricinfo.com. Also well analysed Diabetic Retinopathy Study (DRS) data is further analysed using this model and our findings are presented.     

Analysis op failure time data by burr distribution

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.     

Estimation of Weibull distribution parameters for irregular interval group failure data with unknown failure times

SUMMARY This paper presents three methods for estimating Weibull distribution parameters for the case of irregular interval group failure data with unknown failure times. The methods are based on the concepts of the piecewise linear distribution function (PLDF), an average interval failure rate (AIFR) and sequential updating of the distribution function (SUDF), and use an analytical approach similar to that of Ackoff and Sasieni for regular interval group data. Results from a large number of simulated case problems generated with specified values of Weibull distribution parameters have been presented, which clearly indicate that the SUDF method produces near-perfect parameter estimates for all types of failure pattern. The performances of the PLDF and AIFR methods have been evaluated by goodness-of-fit testing and statistical confidence limits on the shape parameter. It has been found that, while the PLDF method produces acceptable parameter estimates, the AIFR method may fail for low and high shape parameter values that represent the cases of random and wear-out types of failure. A real-life application of the proposed methods is also presented, by analyzing failures of hydrogen make-up compressor valves in a petroleum refinery.     

Exact distributions of constrained (k, ℓ) strings of failures between subsequent successes

Consider a sequence of binary (success–failure) random variables (RVs) ordered on a line. The number of strings with a constrained number of consecutive failures between two subsequent successes is studied under an overlapping enumeration scheme. The respective waiting time is examined as well. The study is first developed on sequences of independent and identically distributed RVs. It is extended then on sequences of dependent, exchangeability and Markovian dependency is considered, and independent, not necessarily identically distributed, RVs. Exact probabilities and moments are obtained by means of combinatorial analysis and via recursive schemes. An explicit expression of the mean value of the number of strings for both independent and dependent sequences is derived. An application in system reliability is provided.