Cost-optimal performance of special reliability tests using prior knowledge

In the present paper we formulate a general statistical decision problem for reliability investigations and its specification for reliability tests with test period termi¬nated by time and failures,

The risk function includes the experimental costs as well as the expected financial expen¬ses caused by the decisions, Interpreted as     

An Examination of the Robustness to Non Normality of the EWMA Control Charts for the Dispersion

ABSTRACT

The EWMA control chart is used to detect small shifts in a process. It has been shown that, for certain values of the smoothing parameter, the EWMA chart for the mean is robust to non normality. In this article, we examine the case of non normality in the EWMA charts for the dispersion. It is shown that we can have an EWMA chart for dispersion robust to non normality when non normality is not extreme.     

Sensitivity Analyses of the Economic and Economic Statistical Designs of the Multivariate Synthetic T2 Chart

This article performs a sensitivity analyses of the synthetic T² chart using fractional factorial design, which integrates the interaction effects. We are interested in the effects of the input parameters on the optimal cost, chart's parameters, and average run lengths. We also look at the input parameters responsible for the increase in cost and improvement in statistical performance under statistical constraints, and investigate how the input parameters influence the binding effect of the statistical constraints. The sensitivity analyses of the synthetic T² chart are compared with that of the Hotelling's T² chart, and parameters responsible for the cost advantage of the synthetic T² chart are identified.     

One-sided EWMA control charts for monitoring Poisson processes with varying sample sizes

ABSTRACT

Recently considerable research has been devoted to monitoring increases of incidence rate of adverse rare events. This paper extends some one-sided upper exponentially weighted moving average (EWMA) control charts from monitoring normal means to monitoring Poisson rate when sample sizes are varying over time. The approximated average run length bounds are derived for these EWMA-type charts and compared with the EWMA chart previously studied. Extensive simulations have been conducted to compare the performance of these EWMA-type charts. An illustrative example is given.     

Robust weighted generalized estimating equations based on statistical depth

Most of the longitudinal data contain influential points and for analyzing them generalized and weighted generalized estimating equations (GEEs and WGEEs) are highly influenced by these points. An approach for dealing with outliers is having weight functions. In this article, we propose some new weights based on the statistical depth. These weights express centrality of points with respect to the whole sample with a smaller depth (larger depth) for the point far from the center (for the point near the center). The proposed approach leads to robust WGEE. These approaches are applied on two real datasets and some simulation studies.     

Discussion

This report is the product of the Task Force on State and Local Government Statistics formed by the ASA Committee on Government Statistics. The Task Force began its work in March 1985 because of a growing concern among ASA members that state and local governments were undertaking many statistical programs and functions of which the ASA had little knowledge and for which it had little role in supporting, and because of the potential and real impacts of federal policy changes and budget reductions on state statistical programs. The report examines the need for state and local government statistical policy, reviews current practice, summarizes elements of a statistical policy, proposes alternative models for organizing the statistical policy function, and makes recommendations for further action.     

A Note on the Calculation of Pr{X 1 < X 2 < ··· < Xk }

Suppose that X_i are independent random variables, and that X_i has cdf F_i (x), 1 ≤ i ≤ k. Many statistical problems involve the probability Pr{X ₁ < X ₂ < ··· < X_k }. In this note a numerical method is proposed for computing this probability.     

Statistical Artifacts in the Ratio of Discrete Quantities

The ratio is a familiar statistic, but it is often misused. One frequently overlooked problem occurs when ratioing two discrete (digitized) variables. Fine structure appears in the histogram of the ratio that can be very subtle, or can sometimes even dominate the histogram. It disappears when the numerator and/or denominator become continuous. This statistical artifact is not a binning error, nor is it removed by taking more data. It is important to be aware of the artifact in order to avoid misinterpretation of ratio data. We provide examples of the statistical artifact (including one from baseball) and discuss ways to avoid or minimize the problems it can cause.     

Applying Cognitive Theory to Statistics Instruction

This article presents five principles of learning, derived from cognitive theory and supported by empirical results in cognitive psychology. To bridge the gap between theory and practice, each of these principles is transformed into a practical guideline and exemplified in a real teaching context. It is argued that this approach of putting cognitive theory into practice can offer several benefits to statistics education: A means for explaining and understanding why reform efforts work; a set of guidelines that can help instructors make well-informed design decisions when implementing these reforms; and a framework for generating new and effective instructional innovations.     

The Significance of a Square-Root Rule

In this article, I comment on a rough square-root rule for statistical significance which turns out to be equivalent to testing whether an observation lies within one standard deviation of that expected.