Multiple Censored Data Research Articles

Analysis of Production and Failure Data in Automotive: From Raw Data to Predictive Modeling and Spare Parts

The present analysis examines extensive and consistent data from automotive production and service to assess reliability and predict failures in the case of an engine control device. It is based on statistical evaluation of production and lead times to determine vehicle sales. Mileages are integrated to establish the age of the vehicle fleet over time and to predict the censored data. Failure and censored times are merged in a multiple censored data and combined by the Kaplan-Meier estimator for survivals. The Weibull distribution is used as parametric reliability model and its parameters identified to assure precision in predictions (>95%). An average time to failure >80 years and a slightly increasing failure rate ensure a low risk. The study is based on real-world data from various sources, acknowledging that the data are not homogeneous, and it offers a comprehensive roadmap for processing this diverse raw data and evolving it into sophisticated predictive models. Furthermore, it provides insights from various perspectives, including those of the Original Equipment Manufacturer, Car Manufacturer, and Users.

Statistical inferences under step stress partially accelerated life testing based on multiple censoring approaches using simulated and real-life engineering data

Evaluating the lifespan distribution of highly reliable commodities under regular use is exceedingly difficult, time consuming, and extremely expensive. As a result of its ability to provide more failure data faster and at a lower experimental cost, accelerated life testing has become increasingly important in life testing studies. In this article, we concentrate on parametric inference for step stress partially life testing utilizing multiple censored data based on the Tampered Random Variable model. Under normal stress circumstances, the lifespan of the experimental units is assumed to follow the Nadarajah–Haghighi distribution, with and being the shape and scale parameters, respectively. Maximum likelihood estimates for model parameters and acceleration factor are developed using multiple censored data. We build asymptotic confidence intervals for the unknown parameters using the observed Fisher information matrix. To demonstrate the applicability of the different methodologies, an actual data set based on the timings of subsequent failures of consecutive air conditioning system failures for each member of a Boeing 720 jet aircraft fleet is investigated. Finally, thorough simulation studies utilizing various censoring strategies are performed to evaluate the estimate procedure performance. Several sample sizes were studied in order to investigate the finite sample features of the considered estimators. According to our numerical findings, the values of mean squared errors and average asymptotic confidence intervals lengths drop as sample size increases. Furthermore, when the censoring level is reduced, the considered estimates of the parameters approach their genuine values.

Estimation of Entropy for Inverse Lomax Distribution under Multiple Censored Data.

The inverse Lomax distribution has been widely used in many applied fields such as reliability, geophysics, economics and engineering sciences. In this paper, an unexplored practical problem involving the inverse Lomax distribution is investigated: the estimation of its entropy when multiple censored data are observed. To reach this goal, the entropy is defined through the Rényi and q-entropies, and we estimate them by combining the maximum likelihood and plugin methods. Then, numerical results are provided to show the behavior of the estimates at various sample sizes, with the determination of the mean squared errors, two-sided approximate confidence intervals and the corresponding average lengths. Our numerical investigations show that, when the sample size increases, the values of the mean squared errors and average lengths decrease. Also, when the censoring level decreases, the considered of Rényi and q-entropies estimates approach the true value. The obtained results validate the usefulness and efficiency of the method. An application to two real life data sets is given.

Estimation of entropy for inverse Weibull distribution under multiple censored data

ABSTRACTEntropy is a measure of uncertainty in a random variable which quantifies the expected value of the information contained in that random variable. This article estimates the Shannon entropy of the inverse Weibull distribution in case of multiple censored data. The maximum likelihood estimator and the approximate confidence interval are derived. Simulation studies are performed to investigate the performance of the estimates at different sample sizes. Real data are analysed for illustration purposes. In general, based on the outcomes of study we reveal that the mean square errors values decrease as the sample size increases. The maximum likelihood of entropy estimates approaches the true value as the censoring level decreases. The intervals of the entropy estimates appear to be narrow as the sample size increases with high probability.

Constant-stress partially accelerated life tests for inverted Weibull distribution with multiple censored data

Testing the lifetime of items under normal use condition often requires a long period of time, especially for products having high reliability. To minimize the costs involved in testing without reducing the quality of the data obtained, the items run at higher than usual level of stresses to induce early failures in a short time. This article concerns with constant–stress partially accelerated life test with multiple censored data. The life time of test item is assumed to follow inverted Weibull distribution. Maximum likelihood estimates are obtained for the model parameters and acceleration factor. In addition, asymptotic variance and covariance matrix of the estimators is given. The confidence intervals of the unknown parameters and acceleration factor are constructed for large sample sizes. Simulation studies are performed to investigate the performance of the estimators.

Multiple censored data in dentistry: A new statistical model for analyzing lesion size in randomized controlled trials.

Caries infiltration is a novel treatment option for proximal caries lesions. The idea is to build a diffusion barrier inside the lesion to slow down or stop the caries progression. If a lesion still reaches a critical size, restorative treatment is required. Clinical trials investigating caries infiltration thus produce multiple censored ordinal data. Standard statistical models do not take into account this censoring, and we therefore propose the Multiple Ordered Tobit (MOT) model. The model is implemented in R and compared with standard approaches. Simulation studies demonstrate that for all sample sizes and scenarios the MOT model has the largest statistical power among all methods compared, and it is robust against heteroscedasticity to some extent. Finally, a comparison with dichotomous and ordinal scaled models shows that the use of metric data for the lesion size reduces the required sample size considerably.

Implementing particle swarm optimization algorithm to estimate the mixture of two Weibull parameters with censored data

We present the maximum likelihood estimation (MLE) via particle swarm optimization (PSO) algorithm to estimate the mixture of two Weibull parameters with complete and multiple censored data. A simulation study is conducted to assess the performance of the MLE via PSO algorithm, quasi-Newton method and expectation-maximization (EM) algorithm for different parameter settings and sample sizes in both uncensored and censored cases. The simulation results showed that the PSO algorithm outperforms the quasi-Newton method and the EM algorithm in most cases regarding bias and root mean square errors. Two numerical examples are used to demonstrate the performance of our proposed method.

Estimating the Burr XII Parameters in Constant-Stress Partially Accelerated Life Tests Under Multiple Censored Data

In this article, we present the performance of the maximum likelihood estimates of the Burr XII parameters for constant-stress partially accelerated life tests under multiple censored data. Two maximum likelihood estimation methods are considered. One method is based on observed-data likelihood function and the maximum likelihood estimates are obtained by using the quasi-Newton algorithm. The other method is based on complete-data likelihood function and the maximum likelihood estimates are derived by using the expectation-maximization (EM) algorithm. The variance–covariance matrices are derived to construct the confidence intervals of the parameters. The performance of these two algorithms is compared with each other by a simulation study. The simulation results show that the maximum likelihood estimation via the EM algorithm outperforms the quasi-Newton algorithm in terms of the absolute relative bias, the bias, the root mean square error and the coverage rate. Finally, a numerical example is given to illustrate the performance of the proposed methods.

EM algorithm for estimating the Burr XII parameters with multiple censored data

AbstractThe two‐parameter Burr XII distribution has been widely used in various practical applications such as business, chemical engineering, quality control, medical research and reliability engineering. In this paper, we present maximum likelihood estimation (MLE) via the expectation–maximization (EM) algorithm to estimate the Burr XII parameters with multiple censored data. We also provide a method that can be used to construct the confidence intervals of the parameters, a method that computes the asymptotic variance and the covariance of the MLE from the complete and missing information matrices. A simulation study is conducted to compare the performance of the MLE via the EM algorithm and the Netwon–Raphson (NR) algorithm. The simulation results show that the EM algorithm outperforms the NR algorithm in most cases in terms of bias and errors in the root mean square. A numerical example is also used to demonstrate the performance of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.

Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data

Estimation of the Weibull shape parameter is important in reliability engineering. However, commonly used methods such as the maximum likelihood estimation (MLE) and the least squares estimation (LSE) are known to be biased. Bias correction methods for MLE have been studied in the literature. This paper investigates the methods for bias correction when model parameters are estimated with LSE based on probability plot. Weibull probability plot is very simple and commonly used by practitioners and hence such a study is useful. The bias of the LS shape parameter estimator for multiple censored data is also examined. It is found that the bias can be modeled as the function of the sample size and the censoring level, and is mainly dependent on the latter. A simple bias function is introduced and bias correcting formulas are proposed for both complete and censored data. Simulation results are also presented. The bias correction methods proposed are very easy to use and they can typically reduce the bias of the LSE of the shape parameter to less than half percent.

Locally most powerful rank tests for multiple-censored data

A locally most powerful rank test is derived for multiple censored data in the context of a two-sample problem where the alternatives involve a single parameter. With independent random samples , from F and G respectively, let the combined sample order statistics be denoted by where N = m+n, We present results for the triple censoring scheme where two blocks of order statistics are observed in addition to recording the number of X's and Y’s among the censored values. These extend the derivation of optimal rank tests for single censored data to the multiple censored situation.