Parametric inference for multiple repairable systems under dependent competing risks

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115899/1/asmb2079.pd

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

Statistical Inference for Power-Law Process With Competing Risks

<p>The focus of this article is on failure history of a repairable system for which the relevant data comprise successive event times for a recurrent phenomenon along with an event-count indicator. We undertake an investigation for analyzing failures from repairable systems that are subject to multiple failure modes. Failure data representing a cluster of recurrent events from a single system are studied under the parametric framework of a <i>power-law process</i>, a model that has found considerable attention in industrial applications. Some interesting and nonstandard asymptotic results ensue in this context that are discussed in detail. Extensive simulation has been carried out that supplements the theoretical findings. An extension to the case where the specific cause of failure may be missing is investigated in detail. The methodology has been implemented on recurrent failure data obtained from a warranty claim database for a fleet of automobiles. Supplementary material for this article is available online.</p

Effects of public health interventions on the epidemiological spread during the first wave of the COVID-19 outbreak in Thailand.

A novel infectious respiratory disease was recognized in Wuhan (Hubei Province, China) in December 2019. In February 2020, the disease was named "coronavirus disease 2019" (COVID-19). COVID-19 became a pandemic in March 2020, and, since then, different countries have implemented a broad spectrum of policies. Thailand is considered to be among the top countries in handling its first wave of the outbreak-12 January to 31 July 2020. Here, we illustrate how Thailand tackled the COVID-19 outbreak, particularly the effects of public health interventions on the epidemiological spread. This study shows how the available data from the outbreak can be analyzed and visualized to quantify the severity of the outbreak, the effectiveness of the interventions, and the level of risk of allowed activities during an easing of a "lockdown." This study shows how a well-organized governmental apparatus can overcome the havoc caused by a pandemic