Marta Afonso Freitas

Using degradation data to assess reliability: a case study on train wheel degradation

Degradation experiments are usually used to assess the lifetime distribution of highly reliable products, which are not likely to fail under the traditional life tests or accelerated life tests. In such cases, if there exist product characteristics whose degradation over time can be related to reliability, then collecting ‘degradation data’ can provide information about product reliability. In general, the degradation data are modeled by a nonlinear regression model with random coefficients. If we can obtain the estimates of parameters under the model, then the failure-time distribution can be estimated. In order to estimate those parameters, three basic methods are available, namely, the analytical, numerical and the approximate. They are chosen according to the complexity of the degradation path model used in the analysis. In this paper, the numerical and the approximate methods are compared in a simulation study, assuming a simple linear degradation path model. A comparison with traditional failure-time analysis is also performed. The mean-squared error of the estimated 100pth percentile of the lifetime distribution is evaluated for each one of the approaches. The approaches are applied to a real degradation data set. Copyright

ARA and ARI imperfect repair models: Estimation, goodness-of-fit and reliability prediction

An appropriate maintenance policy is essential to reduce expenses and risks related to equipment failures. A fundamental aspect to be considered when specifying such policies is to be able to predict the reliability of the systems under study, based on a well fitted model. In this paper, the classes of models Arithmetic Reduction of Age and Arithmetic Reduction of Intensity are explored. Likelihood functions for such models are derived, and a graphical method is proposed for model selection. A real data set involving failures in trucks used by a Brazilian mining is analyzed considering models with different memories. Parameters, namely, shape and scale for Power Law Process, and the efficiency of repair were estimated for the best fitted model. Estimation of model parameters allowed us to derive reliability estimators to predict the behavior of the failure process. These results are a valuable information for the mining company and can be used to support decision making regarding preventive maintenance policy.

Degradation data analysis for samples under unequal operating conditions: a case study on train wheels

Traditionally, reliability assessment of devices has been based on life tests (LTs) or accelerated life tests (ALTs). However, these approaches are not practical for high-reliability devices which are not likely to fail in experiments of reasonable length. For these devices, LTs or ALTs will end up with a high censoring rate compromising the traditional estimation methods. An alternative approach is to monitor the devices for a period of time and assess their reliability from the changes in performance (degradation) observed during the experiment. In this paper, we present a model to evaluate the problem of train wheel degradation, which is related to the failure modes of train derailments. We first identify the most significant working conditions affecting the wheel wear using a nonlinear mixed-effects (NLME) model where the log-rate of wear is a linear function of some working conditions such as side, truck and axle positions. Next, we estimate the failure time distribution by working condition analytically. Point and interval estimates of reliability figures by working condition are also obtained. We compare the results of the analysis via an NLME to the ones obtained by an approximate degradation analysis.

A Statistical Model for Shelf Life Estimation Using Sensory Evaluations Scores

Abstract This article focuses on the problem of estimating the shelf life of food products by modeling the results coming from sensory evaluations. In such studies, trained panelists are asked to judge food attributes by reference to a scale of numbers (scores varying often from 0 to 6). The usual statistical approach for data analysis is to fit a regression line relating the scores and the time of evaluation. The estimate of the shelf life is obtained by solving the regression equation and replacing the score by a cut-off point (which indicates product “failure”) previously chosen by the food company. The procedure used in these sensory evaluations is such that one never knows the exact “time to failure”. Consequently, data arising from these studies are either right or left censored. We propose a model which incorporates these informations and assumes a Weibull for the underlying distribution of the failure time. Simulation studies were implemented. The approach was used in a real data set coming from sensory evaluations of a dehydrated food product.

Optimal periodic maintenance policy under imperfect repair: A case study on the engines of off-road vehicles

ABSTRACT In the repairable systems literature one can find a great number of papers that propose maintenance policies under the assumption of minimal repair after each failure (such a repair leaves the system in the same condition as it was just before the failure—as bad as old). This article derives a statistical procedure to estimate the optimal Preventive Maintenance (PM) periodic policy, under the following two assumptions: (i) perfect repair at each PM action (i.e., the system returns to the as-good-as-new state) and (ii) imperfect system repair after each failure (the system returns to an intermediate state between as bad as old and as good as new). Models for imperfect repair have already been presented in the literature. However, an inference procedure for the quantities of interest has not yet been fully studied. In the present article, statistical methods, including the likelihood function, Monte Carlo simulation, and bootstrap resampling methods, are used in order to (i) estimate the degree of efficiency of a repair and (ii) obtain the optimal PM check points that minimize the expected total cost. This study was motivated by a real situation involving the maintenance of engines in off-road vehicles.

Dynamics of an optimal maintenance policy for imperfect repair models

A preventive maintenance policy that considers information provided by observing the failure history of a repairable system is proposed. For a system that is to be operated for a long time, it is shown that the proposed policy will have a lower expected cost than a periodical one which does not take into account the failure history. Statistical inference using both maximum likelihood point estimates and bootstrap confidence intervals is discussed. The proposed policy is applied to a real situation involving maintenance of off-road engines owned by a Brazilian mining company. A simulation study compares the performance between the maintenance policy proposed and the periodical one.

Sample plans comparisons for shelf life estimation using sensory evaluation scores

Sensory evaluations to determine the shelf life of food products are routinely conducted in food experimentation as a part of each product development program, whether it includes a new product, product improvement or a change in type or specification of an ingredient. In such experiments, trained panelists are asked to judge food attributes by reference to a scale of numbers. The “failure time” associated with a product unit under test is usually defined as the time required to reach a cut‐off point previously defined by the food company. Important issues associated with the planning and execution of this kind of testing are total sampling size, frequency of sample withdrawals, panel design, and statistical analysis of the panel data, to list a few. Different approaches have been proposed for the analysis of this kind of data. In particular, Freitas et al. proposed an alternative model based on a dichotomization of the score data and a Weibull as the underlying distribution for the time to failure. Also, through a simulation study, the bias and mean square error of the estimates obtained for percentiles and fraction defectives were evaluated. These quantities were used to estimate the shelf life. The simulation study used only the same sample plan implemented in the real situation. This paper focuses on the planning issues associated with these experiments. Sample plans are contrasted and compared in a simulation study, through the use of the approach proposed by Freitas et al.. The simulation results showed that, in general, one can get results much more precise and with smaller bias with a shorter follow‐up time, allocating more panelists to each evaluation time.

A Closer Look at Degradation Models: Classical and Bayesian Approaches

Traditionally, reliability assessment of devices has been based on (accelerated) life tests. However, for highly reliable products, little information about reliability is provided by life tests in which few or no failures are typically observed. Since most failures arise from a degradation mechanism at work for which there are characteristics that degrade over time, one alternative is to monitor the device for a period of time and assess its reliability from the changes in performance (degradation) observed during that period. The goal of this chapter is to illustrate how degradation data can be modeled and analyzed by using “classical” and Bayesian approaches. Four methods of data analysis based on classical inference are presented. Next we show how Bayesian methods can also be used to provide a natural approach to analyzing degradation data. The approaches are applied to a real data set regarding train wheels degradation.

Practical modeling strategies for unbalanced longitudinal data analysis

In practice, data are often measured repeatedly on the same individual at several points in time. Main interest often relies in characterizing the way the response changes in time, and the predictors of that change. Marginal, mixed and transition are frequently considered to be the main models for continuous longitudinal data analysis. These approaches are proposed primarily for balanced longitudinal design. However, in clinic studies, data are usually not balanced and some restrictions are necessary in order to use these models. This paper was motivated by a data set related to longitudinal height measurements in children of HIV-infected mothers that was recorded at the university hospital of the Federal University in Minas Gerais, Brazil. This data set is severely unbalanced. The goal of this paper is to assess the application of continuous longitudinal models for the analysis of unbalanced data set.

Projeto robusto de parâmetros em sistemas sinal-resposta: comparação de métodos de modelagem e análise

Most of the literature concerning robust parameter design (RPD), a methodology introduced by Taguchi (1986), involves situations where the quality characteristic of interest (response) is a single quantity which has a specified optimal value. A recent trend in the industrial applications of RPD consists in consider complex systems which are called “systems with dynamic characteristics” or “dynamic systems”, in Taguchi ́s terminology, or “signal-response systems”, in this paper. Recently, modeling and analysis methods for the dynamic system have been developed. In this paper, three modeling approaches are compared by use of a real example: Performance Measure Modeling (PMM), Response Modeling (RM) and Response Function Modeling (RFM). It is shown that the RFM approach allows greater flexibility to investigate factor effects for the RPD experiment.