Failure and maintenance data extraction from power plant maintenance management databases

Reliability analysis is plagued by a lack of accurate data, leading to suboptimal parameter estimates and inaccurate decisions about replacement intervals and preventive maintenance activities. This paper discusses some of the problems associated with failure and maintenance data extraction from coal-fired power plant maintenance databases. Data from four generating units were observed for over 5 years and a reasonable number of equipment classes reviewed. The coal mills are identified as significant equipment that affects the availability of the generating units. This paper describes the interplay of events which includes failure modes, failure, repair and operating time. We investigate a database showing operation of coal mills, and give an exploratory data analysis in which we investigate engineering hypotheses related to mill operation. A competing risk probability model is proposed which captures some of the observed features of the systems under study.     

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.     

Optimal scheduling replacement policies for a system with multiple random works

From the economical viewpoint in reliability theory, this paper addresses a scheduling replacement problem for a single operating system which works at random times for multiple jobs. The system is subject to stochastic failure which results the imperfect maintenance activity based on some random failure mechanism: minimal repair due to type-I (repairable) failure, or corrective replacement due to type-II (non-repairable) failure. Three scheduling models for the system with multiple jobs are considered: a single work, N tandem works, and N parallel works. To control the deterioration process, the preventive replacement is planned to undergo at a scheduling time T or the job's completion time of for each model. The objective is to determine the optimal scheduling parameters (T^* or N^*) that minimizes the mean cost rate function in a finite time horizon for each model. A numerical example is provided to illustrate the proposed analytical model. Because the framework and analysis are general, the proposed models extend several existing results.     

Bayesian estimation of a proportional hazards model for double-censored durations

Double-censored data consist of uncensored, left- and right-censored observations and occur in survival time analysis. In this paper, parametric Bayes estimation is investigated for a proportional hazards model with durations subject to double-censoring. We prove consistency and asymptotic normality of the posterior mean with the Bernstein–von Mises theorem. In addition, we estimate asymptotic standard errors. A simulation study shows that the finite-sample performance is similar to that of the maximum likelihood estimator. Finally, the proposed model is applied to rating transition data. The analysis suggests that an upgrade of a rating increases the duration in that class by about 10 days on average.     

The repair alert models with fixed and random effects

This article extends a random preventive maintenance scheme, called repair alert model, when there exist environmental variables that effect on system lifetimes. It can be used for implementing age-dependent maintenance policies on engineering devices. In other words, consider a device that works for a job and is subject to failure at a random time X, and the maintenance crew can avoid the failure by a possible replacement at some random time Z. The new model is flexible to including covariates with both fixed and random effects. The problem of estimating parameters is also investigated in details. Here, the observations are in the form of random signs censoring data (RSCD) with covariates. Therefore, this article generalizes derived statistical inferences on the basis of RSCD albeit without covariates in past literature. To do this, it is assumed that the system lifetime distribution belongs to the log-location-scale family of distributions. A real dataset is also analyzed on basis of the results obtained.     

How Long Is a Spell of Unemployment? Illusions and Biases in the Use of CPS Data

Most data used to study the durations of unemployment spells come from the Current Population Survey (CPS), which is a point-in-time survey and gives an incomplete picture of the underlying duration distribution. We introduce a new sample of completed unemployment spells obtained from panel data and apply CPS sampling and reporting techniques to replicate the type of data used by other researchers. Predicted duration distributions derived from this CPS-like data are then compared to the actual distribution. We conclude that the best inferences that can be made about unemployment durations by using CPS-like data are seriously biased.     

Using quantile regression for duration analysis

Summary Quantile regression methods are emerging as a popular technique in econometrics and biometrics for exploring the distribution of duration data. This paper discusses quantile regression for duration analysis allowing for a flexible specification of the functional relationship and of the error distribution. Censored quantile regression addresses the issue of right censoring of the response variable which is common in duration analysis. We compare quantile regression to standard duration models. Quantile regression does not impose a proportional effect of the covariates on the hazard over the duration time. However, the method cannot take account of time-varying covariates and it has not been extended so far to allow for unobserved heterogeneity and competing risks. We also discuss how hazard rates can be estimated using quantile regression methods. This paper benefitted from the helpful comments by an anonymous referee. Due to space constraints, we had to omit the details of the empirical application. These can be found in the long version of this paper, Fitzenberger and Wilke (2005). We gratefully acknowledge financial support by the German Research Foundation (DFG) through the research project ‘Microeconometric modelling of unemployment durations under consideration of the macroeconomic situation’. Thanks are due to Xuan Zhang for excellent research assistance. All errors are our sole responsibility.     

Business cycle asymmetry and duration dependence: an international perspective

The business cycle behaviour of macroeconomic variables has long been of interest to economists, and attention has recently focused on two aspects of this behaviour - the 'stylized facts' of cyclical asymmetry and duration dependence. Cyclical asymmetry is where the economy behaves differently over the expansion and recession phases of the business cycle. Duration dependence, on the other hand, concerns the question of whether, for example, the probability of a cyclical expansion is dependent on how long the expansion has been running, or whether business cycle lengths tend to cluster around a particular duration. Using an international data set containing annual output per capita for 22 countries, we focus attention on non-parametric techniques for extracting cyclical components and for modelling and testing asymmetry and duration dependence. Once outliers, primarily associated with wars, are omitted, there is little international evidence of asymmetry. There is considerably more evidence of duration dependence, which is detected in the majority of countries using a variety of non-parametric tests. There is thus widespread evidence against the constant hazard hypothesis that cyclical patterns occur simply by chance. Business cycle durations do appear to cluster around certain values, with the average duration being about 3.6 years.     

Inverse Gaussian Distribution for Modeling Conditional Durations in Finance

The durations between market activities such as trades and quotes provide useful information on the underlying assets while analyzing financial time series. In this article, we propose a stochastic conditional duration model based on the inverse Gaussian distribution. The non-monotonic nature of the failure rate of the inverse Gaussian distribution makes it suitable for modeling the durations in financial time series. The parameters of the proposed model are estimated by an efficient importance sampling method. A simulation experiment is conducted to check the performance of the estimators. These estimates are used to compute estimated hazard functions and to compare with the empirical hazard functions. Finally, a real data analysis is provided to illustrate the practical utility of the models.     

BATHTUB-TYPE CURVES IN RELIABILITY AND BEYOND

Finding optimal, or at least good, maintenance and repair policies is crucial in reliability engineering. Likewise, describing life phases of human mortality is important when determining social policy or insurance premiums. In these tasks, one searches for distributions to fit data and then makes inferences about the population(s). In the present paper, we focus on bathtub‐type distributions and provide a view of certain problems, methods and solutions, and a few challenges, that can be encountered in reliability engineering, survival analysis, demography and actuarial science.     

Survey non-response and the duration of unemployment

Summary.  Social surveys are often used to estimate unemployment duration distributions. Survey non-response may then cause a bias. We study this by using a data set that combines survey information of individual workers with administrative records of the same workers. The latter provide information on durations of unemployment and personal characteristics of all survey respondents and non-respondents. We develop a method to distinguish empirically between two explanations for a bias in results based on only survey data: selectivity due to related unobserved determinants of durations of unemployment and non-response and a causal effect of a job exit on non-response. The latter may occur even in fully homogeneous populations. The methodology exploits variation in the timing of the duration outcome relative to the survey moment. The results show evidence for both explanations. We discuss implications for standard methods to deal with non-response bias.     

Long memory in intertrade durations,counts and realized volatility of NYSE stocks

We study the persistence of intertrade durations, counts (number of transactions in equally spaced intervals of clock time), squared returns and realized volatility in 10 stocks trading on the New York Stock Exchange. A semiparametric analysis reveals the presence of long memory in all of these series, with potentially the same memory parameter. We introduce a parametric latent-variable long-memory stochastic duration (LMSD) model which is shown to better fit the data than the autoregressive conditional duration model (ACD) in a variety of ways. The empirical evidence we present here is in agreement with theoretical results on the propagation of memory from durations to counts and realized volatility presented in Deo et al. (2009).     

Mixture inverse Gaussian for unobserved heterogeneity in the autoregressive conditional duration model

In this paper, we assume that the duration of a process has two different intrinsic components or phases which are independent. The first is the time it takes for a trade to be initiated in the market (for example, the time during which agents obtain knowledge about the market in which they are operating and accumulate information, which is coherent with Brownian motion) and the second is the subsequent time required for the trade to develop into a complete duration. Of course, if the first time is zero then the trade is initiated immediately and no initial knowledge is required. If we assume a specific compound Bernoulli distribution for the first time and an inverse Gaussian distribution for the second, the resulting convolution model has a mixture of an inverse Gaussian distribution with its reciprocal, which allows us to specify and test the unobserved heterogeneity in the autoregressive conditional duration (ACD) model.

Our proposals make it possible not only to capture various density shapes of the durations but also easily to accommodate the behaviour of the tail of the distribution and the non monotonic hazard function. The proposed model is easy to fit and characterizes the behaviour of the conditional durations reasonably well in terms of statistical criteria based on point and density forecasts.     

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.     

非参数随机条件持续期模型及其迭代算法

 随机条件持续期（SCD）模型能有效刻画超高频时间序列中持续期的变化,但该模型假定期望持续期生成机制固定,且模型参数估计存在一定的困难。文章在不假定条件均值形式和冲击项分布的基础上结合核估计方法提出了非参数SCD模型及其迭代求解方法。然后,基于TEACD(1,1)模型生成的模拟数据,将非参数SCD模型与用卡尔漫滤波进行伪似然估计的参数SCD模型和用Gibbs抽样进行马尔科夫蒙特卡罗估计的参数SCD模型的拟合效果进行比较,实证表明在大样本条件下非参数SCD模型的拟合效果与用MCMC估计的参数SCD模型的拟合结果相差不大,但明显优于用QML估计的参数SCD模型的拟合结果,且非参数SCD模型能为参数SCD模型的参数设定提供参考。     

The effect of classification errors in survival data analysis

Survival data analysis aims at collecting data on durations spent in a state by a sample of units, in order to analyse the process of transition to a different state. Survival analysis applied to social and economic phenomena typically relies upon data on transitions collected, for a sample of units, in one or more follow-up surveys. We explore the effect of misclassification of the transition indicator on parameter estimates in an appropriate statistical model for the duration spent in an origin state. Some empirical investigations about the bias induced when ignoring misclassification are reported, extending the model to include the possibility that the rate of misclassification can vary across units according to the value of some covariates. Finally it is shown how a Bayesian approach can lead to parameter estimates.     

Semi parametric estimation of employment duration models

Semi parametric methods provide estimates of finite parameter vectors without requiring that the complete data generation process be assumed in a finite-dimensional family. By avoiding bias from incorrect specification, such estimators gain robustness, although usually at the cost of decreased precision. The most familiar semi parametric method in econometrics is ordi¬nary least squares, which estimates the parameters of a linear regression model without requiring that the distribution of the disturbances be in a finite-parameter family. The recent literature in econometric theory has extended semi parametric methods to a variety of non-linear models, including models appropriate for analysis of censored duration data. Horowitz and Newman make perhaps the first empirical application of these methods, to data on employment duration. Their analysis provides insights into the practical problems of implementing these methods, and limited information on performance. Their data set, containing 226 male controls from the Denver income maintenance experiment in 1971-74, does not show any significant covariates (except race), even when a fully parametric model is assumed. Consequently, the authors are unable to reject the fully parametric model in a test against the alternative semi parametric estimators. This provides some negative, but tenuous, evidence that in practical applications the reduction in bias using semi parametric estimators is insufficient to offset loss in precision. Larger samples, and data sets with strongly significant covariates, will need to be interval, and if the observation period is long enough will eventually be more loyal on average for those starting employment spells near the end of the observation period.     

A model of preventive maintenance for parallel,series, and single-item replacement systems based on statistical analysis

Preventive maintenance (PM) scheduling of units is addressed as a crucial issue that effects on both economy and reliability of power systems. In this paper, we describe an application of statistical analysis for determining the best PM strategy in the case of parallel, series, and single-item replacement systems. A key aspect of industrial maintenance is the trade-off between cost and time of performing PM operations. The goals of this study is to determine the best time for performing PM operations in each system and also finding the number of spare parts and facilities in single-item replacement and parallel systems respectively so that the average cost per unit time is minimized. In this proposed maintenance strategy, PM operations are regularly performed on the production unit in equal time intervals. Finally, three examples are presented to demonstrate the effectiveness of the proposed models.     

Reliability of semi-Markov missions

We consider a device that is designed to perform missions consisting of a random sequence of phases or stages with random durations. The mission process is described by a Markov renewal process and the system is a complex one consisting of a number of components whose lifetimes depend on the phases of the mission. We discuss models and tools to compute system, mission, and phase reliabilities using Markov renewal theory. A simplified model involving a mission-based system with maximal repair is analyzed first, and the results are then extended to the case where there is no repair using intrinsic aging concepts. Our objective is to focus on computation of system reliability for these two possible extreme cases.     

Determining the minimum duration of treatment in tuberculosis: An order restricted non-inferiority trial design

Tuberculosis (TB) is one of the biggest killers among infectious diseases worldwide. Together with the identification of drugs that can provide benefits to patients, the challenge in TB is also the optimisation of the duration of these treatments. While conventional duration of treatment in TB is 6 months, there is evidence that shorter durations might be as effective but could be associated with fewer side effects and may be associated with better adherence. Based on a recent proposal of an adaptive order-restricted superiority design that employs the ordering assumptions within various duration of the same drug, we propose a non-inferiority (typically used in TB trials) adaptive design that effectively uses the order assumption. Together with the general construction of the hypothesis testing and expression for type I and type II errors, we focus on how the novel design was proposed for a TB trial concept. We consider a number of practical aspects such as choice of the design parameters, randomisation ratios, and timings of the interim analyses, and how these were discussed with the clinical team.