Component Reliability Estimation From Partially Masked and Censored System Life Data Under Competing Risks.

This research presents new approaches to the estimation of component reliability distribution parameters from partially masked and/or censored system life data. Such data are common in continuous production environments. The methods were tested on Monte Carlo simulated data and compared to the only alternative suggested in literature. This alternative did not converge on many masked datasets. The new methods produce accurate parameter estimates, particularly at low masking levels. They show little bias. One method ignores masked data and treats them as censored observations. It works well if at least 2 known-cause failures of each component type have been observed and is particularly useful for analysis of any size datasets with a small fraction of masked observations. It provides quick and accurate estimates. A second method performs well when the number of masked observations is small but forms a significant portion of the dataset and/or when the assumption of independent masking does not hold. The third method provides accurate estimates when the dataset is small but contains a large fraction of masked observations and when independent masking is assumed. The latter two methods provide an indication which component most likely caused each masked system failure, albeit at the price of much computation time. The methods were implemented in user-friendly software that can be used to apply the method on simulated or real-life data. An application of the methods to real-life industrial data is presented. This research shows that masked system life data can be used effectively to estimate component life distribution parameters in a situation where such data form a large portion of the dataset and few known failures exist. It also demonstrates that a small fraction of masked data in a dataset can safely be treated as censored observations without much effect on the accuracy of the resulting estimates. These results are important as masked system life data are becoming more prevalent in industrial production environments. The research results are gauged to be useful in continuous manufacturing environments, e.g. in the petrochemical industry. They will also likely interest the electronics and automotive industry where masked observations are common

Contributions to Reliability and Lifetime Data Analysis.

This dissertation deals with problems in reliability and lifetime data analysis. The first part focuses on the study of graphical estimators from probability plots with right censored data. The second part deals with reliability inference for repairable systems. Probability plots are popular graphical tools for assessing parametric distributional assumptions among reliability engineers and other practitioners. They are particularly well suited for location-scale families or those that can be transformed to such families. When the plot indicates a reasonable conformity to the assumed family, it is common to estimate the underlying location and scale parameters by fitting a line through the plot. This quick-and-easy method is especially useful with censored data. Indeed, the current version of a popular statistical software package uses this as the default estimation method. Part I of the dissertation investigates the properties of graphical estimators with multiply right-censored data and compares their performance to maximum likelihood estimators. Large-sample results on consistency, asymptotic normality, and asymptotic variance expressions are obtained. Small-sample properties are studied through simulation for selected distributions and censoring patterns. The results presented in this study extend the work of Nair (1984) to right-censored data. Analysis of failure data arising from repairable systems has received considerable attention in the statistical, engineering, computer software, and medical literature. Data pertaining to a repairable system is viewed as some type of `recurrent event'. Part II of the dissertation investigates some models and methodologies for analyzing failures from repairable systems with multiple failure modes. We consider the case where the cause-specific failures (from each failure mode) follow some counting processes with an emphasis on nonhomogeneous Poisson processes (NHPPs). Some properties of the data are characterized and estimation methods are studied, both from a single system and multiple systems assuming independence of the failure modes. Some results are also developed when there is partial masking of the failure modes. The NHPP case with a power law intensity function is studied in detail.Ph.D.StatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57718/2/asomboon_1.pd

Non-ignorable missing covariate data in parametric survival analysis

Within any epidemiological study missing data is almost inevitable. This missing data is often ignored; however, unless we can assume quite restrictive mechanisms, this will lead to biased estimates. Our motivation are data collected to study the long-term effect of severity of disability upon survival in children with cerebral palsy (henceforth CP). The analysis of such an old data set brings to light statistical difficulties. The main issue in this data is the amount of missing covariate data. We raise concerns about the mechanism causing data to be missing. We present a flexible class of joint models for the survival times and the missing data mechanism which allows us to vary the mechanism causing the missing data. Simulation studies prove this model to be both precise and reliable in estimating survival with missing data. We show that long term survival in the moderately disabled is high and, therefore, a large proportion will be surviving to times when they require care specifically for elderly CP sufferers. In particular, our models suggest that survival from diagnosis is considerably higher than has been previously estimated from this data. This thesis contributes to the discussion of possible methods for dealing with NMAR data

Modified weibull distributions in reliability engineering

Ph.DDOCTOR OF PHILOSOPH

Reliability Analysis of Discrete Lifetime Distributions

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Assessment of semi-parametric proportional intensity models applied to recurrent failure data with multiple failure types for repairable-system reliability.

Certain systems experience a substantial period of downtime due to performing maintenance following a major failure. This discontinuity in observation time has been a concern in the accuracy of estimating the covariate effect. Therneau and Hamilton (1997) proposed a discontinuous risk-free-intervals method for biomedical applications that could also apply to this engineering problem. This study has recommended the more favorable engineering applications range. Major and minor failure events are commonly seen in industry, but most researchers have pooled them as though they are identical. Lin (1993, 1994) proposed a covariate PI modeling approach to handle multiple failure types. This study has examined covariate PI modeling as an approach for explicit treatment of two recurrent failure types (major and minor).The class of semi-parametric proportional intensity (PI) models applies to recurrent failure event modeling for a repairable system with covariates. Abundant federal funding received in biostatistics/medical research has advanced the PI models to become well developed and widely referenced. PI models for medical applications could also apply to recurring failure/repair data in engineering problems. Wider engineering use of these models requires better understanding of applications, performance, and methods to accommodate important situations such as censoring, maintenance intervals, and multiple failure types.Landers and Soroudi (1991), Qureshi et al. (1994), and Landers et al. (2001) have examined robustness of the Prentice-Williams-Peteson-gap time (PWP-GT) model for the case of an underlying Non-homogeneous Poisson Process (NHPP) with power-law and log-linear intensity functions and complete (uncensored) data. However, the phenomenon of censoring is generally present in field data. This research has extended their work to the important case of right-censorship and has examined other semi-parametric PI models (PWP-total time (PWP-TT), Andersen-Gill (AG), and Wei-Lin-Weissfeld (WLW)).The PWP-GT and AG models prove to outperform the PWP-TT and WLW models in the robustness studies on right-censoring severity and multiple failure types. The results of examining the PI models in the discontinuous risk-free-intervals modeling indicate that the PWP-GT model performs better in the short overhaul duration. The AG model performs consistently well in the small sample size (20) regardless of the overhaul duration in a HPP case

Non-ignorable missing covariate data in parametric survival analysis

Within any epidemiological study missing data is almost inevitable. This missing data is often ignored; however, unless we can assume quite restrictive mechanisms, this will lead to biased estimates. Our motivation are data collected to study the long-term effect of severity of disability upon survival in children with cerebral palsy (henceforth CP). The analysis of such an old data set brings to light statistical difficulties. The main issue in this data is the amount of missing covariate data. We raise concerns about the mechanism causing data to be missing. We present a flexible class of joint models for the survival times and the missing data mechanism which allows us to vary the mechanism causing the missing data. Simulation studies prove this model to be both precise and reliable in estimating survival with missing data. We show that long term survival in the moderately disabled is high and, therefore, a large proportion will be surviving to times when they require care specifically for elderly CP sufferers. In particular, our models suggest that survival from diagnosis is considerably higher than has been previously estimated from this data. This thesis contributes to the discussion of possible methods for dealing with NMAR data.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (EPSRC)GBUnited Kingdo