Accelerated life tests for log-normal series system with dependent masked data under Type-I progressive hybrid censoring

This article considers the constant stress accelerated life test for series system products, where independent log-normal distributed lifetimes are assumed for the components. Based on Type-I progressive hybrid censored and masked data, the expectation-maximization algorithm is applied to obtain the estimation for the unknown parameters, and the parametric bootstrap method is used for the standard deviation estimation. In addition, Bayesian approach combining latent variable with Gibbs sampling is developed. Further, the reliability functions of the system and components are estimated at use stress level. The proposed method is illustrated through a numerical example under different masking probabilities and censoring schemes.     

An Enhanced Data Perturbation Approach for Small Data Sets

As modern organizations gather, analyze, and share large quantities of data, issues of privacy, and confidentiality are becoming increasingly important. Perturbation methods are used to protect confidentiality when confidential, numerical data are shared or disseminated for analysis. Unfortunately, existing perturbation methods are not suitable for protecting small data sets. With small data sets, existing perturbation methods result in reduced protection against disclosure risk due to sampling error. Sampling error may also produce different results from the analysis of perturbed data compared to the original data, reducing data utility. In this study, we develop an enhancement of an existing perturbation technique, General Additive Data Perturbation, that can be used to effectively mask both large and small data sets. The proposed enhancement minimizes the risk of disclosure while ensuring that the results of commonly performed statistical analyses are identical and equal for both the original and the perturbed data.     

A Simple Univariate Outlier Identification Procedure Designed for Large Samples

A simple univariate outlier identification procedure is presented for the detection of multiple outliers in large and moderate sized data sets. This procedure is a modification of the well-known boxplot outlier-labeling rule. Critical values are easy to obtain for the large sample case for a variety of useful distributions, including the normal, t, gamma, and Weibull. Simple adjustment formulas and graphs are provided for handling smaller samples. Basic probability properties are obtained mathematically and through simulation. Two data sets illustrate the procedure's application as a simple and effective screening tool for both moderate and large-sized univariate samples.     

ANALYSIS OF MASKED DATA IN A DEPENDENT COMPETING RISKS MODEL UNDER UNKNOWN ENVIRONMENT

ABSTRACT

System failure data is often analyzed to estimate component reliabilities. Due to cost and time constraints, the exact component causing the failure of the system cannot be identified in some cases. This phenomenon is called masking. Further, it is sometimes necessary for us to take account of the influence of the operating environment. Here we consider a series system, operating under unknown environment, of two components whose failure times follow the Marshall-Olkin bivariate exponential distribution. We present a maximum likelihood approach for obtaining estimators from the masked data for this system. From a simulation study, we found that the relative errors of the estimates are almost well behaved even for small or moderate expected number of systems whose cause of failure is identified.     

Influence analysis based on the case sensitivity function

The case sensitivity function approach to influence analysis is introduced as a natural smooth extension of influence curve methodology in which both the insights of geometry and the power of (convex) analysis are available. In it, perturbation is defined as movement between probability vectors defining weighted empirical distributions. A Euclidean geometry is proposed giving such perturbations both size and direction. The notion of the salience of a perturbation is emphasized. This approach has several benefits. A general probability case weight analysis results. Answers to a number of outstanding questions follow directly. Rescaled versions of the three usual finite sample influence curve measures—seen now to be required for comparability across different-sized subsets of cases—are readily available. These new diagnostics directly measure the salience of the (infinitesimal) perturbations involved. Their essential unity, both within and between subsets, is evident geometrically. Finally it is shown how a relaxation strategy, in which a high dimensional ( O ( ⁿC_m )) discrete problem is replaced by a low dimensional ( O ( n )) continuous problem, can combine with (convex) optimization results to deliver better performance in challenging multiple-case influence problems. Further developments are briefly indicated.