A bootstrap view on dickey-fuller control charts for AR(1) series

Dickey-Fuller control charts aim at monitoring a random walk until a given time horizon to detect stationarity as early as possible. That problem appears in many fields, especially in econometrics and the analysis of economic equilibria. To improve upon asymptotic control limits (critical values), we study the bootstrap and establish its a.s. consistency for fixed alternatives. Simulations indicate that the bootstrap control chart works very well. --Autoregressive time series,control chart,invariance principle,least squares,resampling,unit root

Session 11 - Methods: \u3cem\u3eBootstrap Control Chart for Pareto Percentiles\u3c/em\u3e

Lifetime percentile is an important indicator of product reliability. However, the sampling distribution of a percentile estimator for any lifetime distribution is not a bell shaped one. As a result, the well-known Shewhart-type control chart cannot be applied to monitor the product lifetime percentiles. In this presentation, Bootstrap control charts based on maximum likelihood estimator (MLE) are proposed for monitoring Pareto percentiles. An intensive simulation study is conducted to compare the performance among the proposed MLE Bootstrap control chart and Shewhart-type control chart

Improved memory loading techniques for the TSRV display system

A recent upgrade of the TSRV research flight system at NASA Langley Research Center retained the original monochrome display system. However, the display memory loading equipment was replaced requiring design and development of new methods of performing this task. This paper describes the new techniques developed to load memory in the display system. An outdated paper tape method for loading the BOOTSTRAP control program was replaced by EPROM storage of the characters contained on the tape. Rather than move a tape past an optical reader, a counter was implemented which steps sequentially through EPROM addresses and presents the same data to the loader circuitry. A cumbersome cassette tape method for loading the applications software was replaced with a floppy disk method using a microprocessor terminal installed as part of the upgrade. The cassette memory image was transferred to disk and a specific software loader was written for the terminal which duplicates the function of the cassette loader

Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations

We prove asymptotic stability of shear flows close to the planar Couette flow in the 2D inviscid Euler equations on \Torus \times \Real. That is, given an initial perturbation of the Couette flow small in a suitable regularity class, specifically Gevrey space of class smaller than 2, the velocity converges strongly in L^2 to a shear flow which is also close to the Couette flow. The vorticity is asymptotically driven to small scales by a linear evolution and weakly converges as $t \rightarrow \pm\infty$. The strong convergence of the velocity field is sometimes referred to as inviscid damping, due to the relationship with Landau damping in the Vlasov equations. This convergence was formally derived at the linear level by Kelvin in 1887 and it occurs at an algebraic rate first computed by Orr in 1907; our work appears to be the first rigorous confirmation of this behavior on the nonlinear level.Comment: 78 page

The Weibull-Geometric distribution

In this paper we introduce, for the first time, the Weibull-Geometric distribution which generalizes the exponential-geometric distribution proposed by Adamidis and Loukas (1998). The hazard function of the last distribution is monotone decreasing but the hazard function of the new distribution can take more general forms. Unlike the Weibull distribution, the proposed distribution is useful for modeling unimodal failure rates. We derive the cumulative distribution and hazard functions, the density of the order statistics and calculate expressions for its moments and for the moments of the order statistics. We give expressions for the R\'enyi and Shannon entropies. The maximum likelihood estimation procedure is discussed and an algorithm EM (Dempster et al., 1977; McLachlan and Krishnan, 1997) is provided for estimating the parameters. We obtain the information matrix and discuss inference. Applications to real data sets are given to show the flexibility and potentiality of the proposed distribution

An Explanatory Study on the Non-Parametric Multivariate T2 Control Chart

Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T2 are correlated, the T2 chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is presented based on Hotelling’s T2 statistic then the performance of the bootstrap multivariate control chart is compared to a Hotelling’s T2 parametric multivariate control chart, a multivariate sign control chart, and a multivariate Wilcoxon control chart using a simulation study. Ultimately, the bootstrap multivariate control chart is used in an empirical example to study the process of sugar production

Cubic Rank Transmuted Modified Burr III Pareto Distribution: Development, Properties, Characterizations and Applications

In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. The potentiality of CRTMBIII-P distribution is demonstrated via its application to the real data sets: tensile strength of carbon fibers and strengths of glass fibers. Goodness of fit of this distribution through different methods is studied

Principal alarms in multivariate statistical process control

This paper describes a methodology for the simulation of multivariate out of control situations using in-control data. The method is based on finding the independent factors of the variability of the process, and shifting these factors one by one. These shifts are then translated in terms of the observed variables. The shifts provoked by the most important factors are called principal alarms. The principal alarms are plotted, visualizing the main deviations of the process. Also, a resampling procedure for ARL estimation using principal alarms is proposed. An application using a real industrial process, illustrates the usefulness of the methodology