A Quantile Variant of the EM Algorithm and Its Applications to Parameter Estimation with Interval Data

The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the expectation in each E-step and the maximization in each M-step are straightforward. A difficulty with the implementation of the EM algorithm is that each E-step requires the integration of the log-likelihood function in closed form. The explicit integration can be avoided by using what is known as the Monte Carlo EM (MCEM) algorithm. The MCEM uses a random sample to estimate the integral at each E-step. However, the problem with the MCEM is that it often converges to the integral quite slowly and the convergence behavior can also be unstable, which causes a computational burden. In this paper, we propose what we refer to as the quantile variant of the EM (QEM) algorithm. We prove that the proposed QEM method has an accuracy of $O(1/K^2)$ while the MCEM method has an accuracy of $O_p(1/\sqrt{K})$. Thus, the proposed QEM method possesses faster and more stable convergence properties when compared with the MCEM algorithm. The improved performance is illustrated through the numerical studies. Several practical examples illustrating its use in interval-censored data problems are also provided

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program

Life expectancy inequalities in the elderly by socioeconomic status. Evidence from Italy

Background: life expectancy considerably increased in most developed countries during the twentieth century. However, the increase in longevity is neither uniform nor random across individuals belonging to various socioeconomic groups. From an economic policy perspective, the difference in mortality by socioeconomic conditions challenges the fairness of the social security systems. We focus on the case of Italy and aim at measuring differences in longevity at older ages by individuals belonging to different socioeconomic groups, also in order to assess the effective fairness of the Italian public pension system, which is based on a notional defined contribution (NDC) benefit computation formula, whose rules do not take into account individual heterogeneity in expected longevity. Methods: We use a longitudinal dataset that matches survey data on individual features recorded in the Italian module of the EU-SILC, with information on the whole working life and until death collected in the administrative archives managed by the Italian National Social Security Institute. In more detail, we follow until 2009 a sample of 11,281 individuals aged at least 60 in 2005. We use survival analysis and measure the influence of a number of events experienced in the labor market and individual characteristics on mortality. Furthermore, through Kaplan- Meier simulations of hypothetical social groups, adjusted by a Brass relational model, we estimate and compare differences in life expectancy of individuals belonging to different socioeconomic groups. Results: Our findings confirm that socioeconomic status strongly predicts life expectancy even in old age. All Estimated models show that the prevalent type of working activity before retirement is significantly associated with the risk of death, even when controlling for dozens of variables as proxies of individual demographic and socioeconomic characteristics. The risk of death for self-employed individuals is 26% lower than that of employees, and life expectancy at 60 differs by five years between individuals with opposite socioeconomic statuses. Conclusions: our study is the first that links results based on a micro survival analysis on subgroups of the elderly population with results related to the entire Italian population. The extreme differences in mortality risks by socioeconomic status found in our study confirm the existence of large health inequalities and strongly question the fairness of the Italian public pension system

Prediction of remaining life of power transformers based on left truncated and right censored lifetime data

Prediction of the remaining life of high-voltage power transformers is an important issue for energy companies because of the need for planning maintenance and capital expenditures. Lifetime data for such transformers are complicated because transformer lifetimes can extend over many decades and transformer designs and manufacturing practices have evolved. We were asked to develop statistically-based predictions for the lifetimes of an energy company's fleet of high-voltage transmission and distribution transformers. The company's data records begin in 1980, providing information on installation and failure dates of transformers. Although the dataset contains many units that were installed before 1980, there is no information about units that were installed and failed before 1980. Thus, the data are left truncated and right censored. We use a parametric lifetime model to describe the lifetime distribution of individual transformers. We develop a statistical procedure, based on age-adjusted life distributions, for computing a prediction interval for remaining life for individual transformers now in service. We then extend these ideas to provide predictions and prediction intervals for the cumulative number of failures, over a range of time, for the overall fleet of transformers.Comment: Published in at http://dx.doi.org/10.1214/00-AOAS231 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Data Analysis and Experimental Design for Accelerated Life Testing with Heterogeneous Group Effects

abstract: In accelerated life tests (ALTs), complete randomization is hardly achievable because of economic and engineering constraints. Typical experimental protocols such as subsampling or random blocks in ALTs result in a grouped structure, which leads to correlated lifetime observations. In this dissertation, generalized linear mixed model (GLMM) approach is proposed to analyze ALT data and find the optimal ALT design with the consideration of heterogeneous group effects. Two types of ALTs are demonstrated for data analysis. First, constant-stress ALT (CSALT) data with Weibull failure time distribution is modeled by GLMM. The marginal likelihood of observations is approximated by the quadrature rule; and the maximum likelihood (ML) estimation method is applied in iterative fashion to estimate unknown parameters including the variance component of random effect. Secondly, step-stress ALT (SSALT) data with random group effects is analyzed in similar manner but with an assumption of exponentially distributed failure time in each stress step. Two parameter estimation methods, from the frequentist’s and Bayesian points of view, are applied; and they are compared with other traditional models through simulation study and real example of the heterogeneous SSALT data. The proposed random effect model shows superiority in terms of reducing bias and variance in the estimation of life-stress relationship. The GLMM approach is particularly useful for the optimal experimental design of ALT while taking the random group effects into account. In specific, planning ALTs under nested design structure with random test chamber effects are studied. A greedy two-phased approach shows that different test chamber assignments to stress conditions substantially impact on the estimation of unknown parameters. Then, the D-optimal test plan with two test chambers is constructed by applying the quasi-likelihood approach. Lastly, the optimal ALT planning is expanded for the case of multiple sources of random effects so that the crossed design structure is also considered, along with the nested structure.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

Planning progressive type-I interval censoring life tests with competing risks

[[abstract]]In this article, we investigate some reliability and quality problems when the competing risks data are progressive type-I interval censored with binomial removals. The failure times of the individual causes are assumed to be statistically independent and exponentially distributed with different parameters. We obtain the estimates of the unknown parameters through a maximum likelihood method, and also derive the Fisher's information matrix. The optimal lengths of the inspection intervals are determined under two different criteria. The reliability sampling plans are established under given producer's and customer's risks. A Monte Carlo simulation is conducted to evaluate the performance of the estimators, and also some numerical results are presented.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]電子

Thinking outside the box: recent advances in the analysis and presentation of uncertainty in cost-effectiveness studies

As many more clinical trials collect economic information within their study design, so health economics analysts are increasingly working with patient-level data on both costs and effects. In this paper, we review recent advances in the use of statistical methods for economic analysis of information collected alongside clinical trials. In particular, we focus on the handling and presentation of uncertainty, including the importance of estimation rather than hypothesis testing, the use of the net-benefit statistic, and the presentation of cost-effectiveness acceptability curves. We also discuss the appropriate sample size calculations for cost-effectiveness analysis at the design stage of a study. Finally, we outline some of the challenges for future research in this area—particularly in relation to the appropriate use of Bayesian methods and methods for analyzing costs that are typically skewed and often incomplete

Drilling Induced Fatigue Damage in Ti-6Al-4V

The objective of this work is to develop an understanding of the relationship between hole drilling processes and the fatigue performance of the resulting part in Ti-6Al-4V. This problem is significant, as on the order of one-hundred thousand to a million holes are created in a typical large aircraft, and the limiting performance criterion is usually the fatigue lifetime. The path between the drilling process parameters and the fatigue performance has two main steps: characterization of the thermo-mechanical drill process and assessment of the relationship between the hole integrity left by the drill process and the fatigue performance. Development has been limited by the robustness of previously available thermal characterization systems, poor correlation between drill processes and physical observations of metallic effects, and limited success identifying the key hole integrity characteristics. This work develops robust novel thermal methods which enable integration into current drill process development techniques. The key integrity drivers in the hole wall are identified, characterized, and a system to assess is presented. The thermal and hole integrity trends are presented as guidance for drill process development providing significant opportunities to optimize processes. Thus, this work advances knowledge of the process to fatigue lifetime relationship by correlating the thermo-mechanical drill process to fatigue life in Ti-6Al-4V

Optimal Progressive Group-Censoring Plans for Chen Distribution under Cost Constraint

[[abstract]]In this paper, the optimal design of a progressively group-censored life test with the restriction of experimental budget is developed for the Chen distribution is considered. The maximum likelihood estimates, approximate confidence intervals for the parameters based on progressively group-censored sample are obtained. Wu et al.’s (2008a) approach is used to determine the number of test units, the number of inspections and the length of inspection interval of a life test under a pre-determined budget of experiment such that the determinant of the asymptotic variances-covariance matrix of estimators of parameters is minimum. A numerical example is presented and the sensitivity analysis is also studied.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

Real Effort, Real Leisure and Real-time Supervision: Incentives and Peer Pressure in Virtual Organizations.

We propose a novel approach to the analysis of organizations by developing a computerized platform that reproduces relevant features of existing organizations such as real-effort tasks and real-leisure alternative activities (Internet). In this environment, we find strong incentives effects as organizations using individual incentives significantly outperform those relying on team incentives. Combining real-time peer monitoring with team incentives, we report striking evidence of positive peer effects as production increases by 50% and Internet usage decreases by 54% compared with organizations using team incentives alone. Peer monitoring allows virtual organizations using team incentives to perform as well as those using individual incentives. However, the positive effect of peer monitoring does not apply to low performers.team incentives, free-riding, monitoring, peer pressure, virtual organization