Re-Establishing the Theoretical Foundations of a Truncated Normal Distribution: Standardization Statistical Inference, and Convolution

There are special situations where specification limits on a process are implemented externally, and the product is typically reworked or scrapped if its performance does not fall in the range. As such, the actual distribution after inspection is truncated. Despite the practical importance of the role of a truncated distribution, there has been little work on the theoretical foundation of standardization, inference theory, and convolution. The objective of this research is three-fold. First, we derive a standard truncated normal distribution and develop its cumulative probability table by standardizing a truncated normal distribution as a set of guidelines for engineers and scientists. We believe that the proposed standard truncated normal distribution by standardizing a truncated normal distribution makes more sense than the traditionally-known truncated standard normal distribution by truncating a standard normal distribution. Second, we develop the new one-sided and two-sided z-test and t-test procedures under such special situations, including their associated test statistics, confidence intervals, and P-values, using appropriate truncated statistics. We then provide the mathematical justifications that the Central Limit Theorem works quite well for a large sample size, given samples taken from a truncated normal distribution. The proposed hypothesis testing procedures have a wide range of application areas such as statistical process control, process capability analysis, design of experiments, life testing, and reliability engineering. Finally, the convolutions of the combinations of truncated normal and truncated skew normal random variables on double and triple truncations are developed. The proposed convolution framework has not been fully explored in the literature despite practical importance in engineering areas. It is believed that the particular research task on convolution will help obtain a better understanding of integrated effects of multistage production processes, statistical tolerance analysis and gap analysis in engineering design, ultimately leading to process and quality improvement. We also believe that overall the results from this entire research work may have the potential to impact a wide range of many other engineering and science problems

Optimal infrastructure maintenance scheduling problem under budget uncertainty

textThis research addresses the infrastructure maintenance scheduling problems under budget uncertainty. Infrastructure agencies usually face budget uncertainties that will eventually lead to suboptimal planning if maintenance decisions are made without taking the uncertainty into consideration. It is important for decision makers to adopt maintenance scheduling policies that take future budget uncertainty into consideration. The author proposes a multistage, stochastic linear programming model to address this problem. The author also develops solution procedures using the augmented Lagrangian decomposition algorithm and scenario reduction method. A case study exploring the computational characteristics of the proposed methods is conducted and the benefit of using the stochastic programming approach is discussed. In the case study, the road network in Dallas District is used with data taken from the Texas Department of Transportation’s Pavement Management Information System. The case study results reveal that the stochastic programming solutions tend to allocate more resources to preventive maintenance than deterministic solutions that ignore the uncertainty information. The proposed methodology can help decision makers effectively obtain optimal maintenance plan under budget uncertainty.Civil, Architectural, and Environmental Engineerin

Novel methods based on regression techniques to analyze multistate models and high-dimensional omics data.

The dissertation is based on four distinct research projects that are loosely interconnected by the common link of a regression framework. Chapter 1 provides an introductory outline of the problems addressed in the projects along with a detailed review of the previous works that have been done on them and a brief discussion on our newly developed methodologies. Chapter 2 describes the first project that is concerned with the identification of hidden subject-specific sources of heterogeneity in gene expression profiling analyses and adjusting for them by a technique based on Partial Least Squares (PLS) regression, in order to ensure a more accurate inference on the expression pattern of the genes over two different varieties of samples. Chapter 3 focuses on the development of an R package based on Project 1 and its performance evaluation with respect to other popular software dealing with differential gene expression analyses. Chapter 4 covers the third project that proposes a non-parametric regression method for the estimation of stage occupation probabilities at different time points in a right-censored multistate model data, using an Inverse Probability of Censoring (IPCW) (Datta and Satten, 2001) based version of the backfitting principle (Hastie and Tibshirani, 1992). Chapter 5 describes the fourth project which deals with the testing for the equality of the residual distributions after adjusting for available covariate information from the right censored waiting times of two groups of subjects, by using an Inverse Probability of Censoring weighted (IPCW) version of the Mann-Whitney U test

Studies in condition based maintenance using proportional hazards models with imperfect observations

Introduction and literature review -- Preliminary notations -- problem statement -- Optimal inspection period and replacement policy for CBM with imperfect information using PHM -- Problem formulation -- Formulation of the POMDP -- Long-run average cost and total long-run average cost -- Optimal inspection period -- Numerical example -- Evaluating the remaining life for equipment with unobservable states -- Practical implications -- Model assumptions -- Development of parameter estimation methods for a condition based maintenance with indirect observations -- Proposed model -- Parameters' estimation -- Optimal inspection interval and optimal replacement policy -- Reliability function and mean residual life -- Estimation of the model's parameter

An information economics perspective on main bank relationships and firm R&D

Information economics has emerged as the primary theoretical lens for framing financing decisions in firm R&D investment. Successful outcomes of R&D projects are either ex-ante impossible to predict or the information is asymmetrically distributed between inventors and investors. As a result, bank lending for firm R&D has been rare. However, firms can signal the value of their R&D activities and as a result reduce the information deficits that block the availability of external funding. In this study we focus on three types of signals: Firm's existing patent stock, the presences of a joint venture investor and whether the firm has received a government R&D subsidy. We argue theoretically that all of these signals have the potential to alter the risk assessment of the firm's main bank. Additionally, we explore heterogeneities in these risk assessments arising from the industry level and the main bank's portfolio. We test our theoretical predictions for a sample of more than 7,000 firm observations in Germany over a multi-year period. Our theoretical predictions are only supported for firms' past patent activity while other signals fail to alter the risk assessment of a firm's main bank. Besides, we confirm that the risk evaluation is not randomly distributed across bank-firm dyads but depends on industry and bank characteristics. --Innovation,banking,information asymmetry