Storage Life Prediction for a High-Performance Capacitor Using Multi-Phase Wiener Degradation Model

Capacitance is a critical performance characteristic of high-voltage-pulse capacitor which is used to store and discharge electrical energy rapidly. The capacitors usually are stored for a long period of time before put into use. Experimental result and engineering experience indicate that the capacitance increases with storage time and will eventually exceed the failure threshold, which means that the capacitor may fail during storage. This is a typical mode of degradation failure for long storage products. Further, the capacitance degradation path can be extrapolated in several stages based on the shifting characteristics. That is, the capacitance increases slowly or fluctuates in the initial storage stage that lasts about three months. Then it increases sharply in the middle stage which lasts about four months. After the two stages, the capacitor enters into the third stage in which capacitance increases constantly. This degradation phenomenon motivates us to study the storage life prediction method based on multi-phase degradation path model. The storage performance degradation mechanism of high-voltage-pulse capacitor was investigated, which provides the physical basis for multi-phase Wiener degradation model. Identification procedure for the transition points in the degradation path was proposed using maximum likelihood principle (MLP). The result of Kruskal-Wallis test which is the method to test whether two populations are consistent or not in statistics showed that the transition points are statistically effective. Other parameters in the multi-phase degradation model are estimated with maximum likelihood estimation (MLE) after the transition points have been specified. The multi-phase Inverse Gaussian (IG) distribution for storage life was deduced for the capacitor, and the point and interval estimation procedure for reliable storage life are constructed with bootstrap method. The efficiency and effectiveness of the proposed multi-phase degradation model is compared with storage life prediction under single-phase condition.     

Tests of hypotheses based on ranks in the general linear model

A unified approach is developed for testing hypotheses in the general linear model based on the ranks of the residuals. It complements the nonparametric estimation procedures recently reported in the literature. The testing and estimation procedures together provide a robust alternative to least squares. The methods are similar in spirit to least squares so that results are simple to interpret. Hypotheses concerning a subset of specified parameters can be tested, while the remaining parameters are treated as nuisance parameters. Asymptotically, the test statistic is shown to have a chi-square distribution under the null hypothesis. This result is then extended to cover a sequence of contiguous alternatives from which the Pitman efficacy is derived. The general application of the test requires the consistent estimation of a functional of the underlying distribution and one such estimate is furnished.     

The performance of multivariate CUSUM control charts with estimated parameters

In this paper, we study the effect of estimating the vector of means and the variance–covariance matrix on the performance of two of the most widely used multivariate cumulative sum (CUSUM) control charts, the MCUSUM chart proposed by Crosier [Multivariate generalizations of cumulative sum quality-control schemes, Technometrics 30 (1988), pp. 291–303] and the MC1 chart proposed by Pignatiello and Runger [Comparisons of multivariate CUSUM charts, J. Qual. Technol. 22 (1990), pp. 173–186]. Using simulation, we investigate and compare the in-control and out-of-control performances of the competing charts in terms of the average run length measure. The in-control and out-of-control performances of the competing charts deteriorate significantly if the estimated parameters are used with control limits intended for known parameters, especially when only a few Phase I samples are used to estimate the parameters. We recommend the use of the MC1 chart over that of the MCUSUM chart if the parameters are estimated from a small number of Phase I samples.     

Developing a variables repetitive group sampling plan based on process capability index C pk with unknown mean and variance

In this paper, variables repetitive group sampling plans are developed based on the process capability index C _pk when the quality characteristic follows a normal distribution with unknown mean and variance. The sampling plan parameters such as the sample size and the acceptance constant are determined to minimize the average sample number. Symmetric and asymmetric cases, in percent defectives due to two specification limits, are dealt with for specified combinations of acceptable quality level and limiting quality level. Tables are provided and examples are given to use proposed plans in practice.     

On constructing T 2 control charts for retrospective examination

In this paper we consider the issue of constructing retrospective T ² control chart limits so as to control the overall probability of a false alarm at a specified value. We describe an exact method for constructing the control limits for retrospective examination. We then consider Bonferroni-adjustments to Alt's control limit and to the standard x ² control limit as alternatives to the exact limit since it is computationally cumbersome to find the exact limit. We present the results of some simulation experiments that are carried out to compare the performance of these control limits. The results indicate that the Bonferroni-adjusted Alt's control limit performs better that the Bonferroni-adjusted x ² control limit. Furthermore, it appears that the Bonferroni-adjusted Alt's control limit is more than adequate for controlling the overall false alarm probability at a specified value.     

Decomposition of Variance for Spatial Cox Processes

Abstract. Spatial Cox point processes is a natural framework for quantifying the various sources of variation governing the spatial distribution of rain forest trees. We introduce a general criterion for variance decomposition for spatial Cox processes and apply it to specific Cox process models with additive or log linear random intensity functions. We moreover consider a new and flexible class of pair correlation function models given in terms of normal variance mixture covariance functions. The proposed methodology is applied to point pattern data sets of locations of tropical rain forest trees.     

Discrete Multicolour Random Mosaics with an Application to Network Extraction

We introduce a class of random fields that can be understood as discrete versions of multicolour polygonal fields built on regular linear tessellations. We focus first on a subclass of consistent polygonal fields, for which we show Markovianity and solvability by means of a dynamic representation. This representation is used to design new sampling techniques for Gibbsian modifications of such fields, a class which covers lattice‐based random fields. A flux‐based modification is applied to the extraction of the field tracks network from a Synthetic Aperture Radar image of a rural area.     

Strong Gaussian Approximations of Product-Limit and Quantile Processes for Strong Mixing and Censored Data

In this article, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and product-limit quantile process are constructed with rate O[(log n)^?λ] for some λ > 0. The strong Gaussian approximation of the product-limit process is then applied to derive the laws of the iterated logarithm for product-limit process.     

A Distribution-Free Control Chart Based on Order Statistics

In this article, we introduce a new distribution-free Shewhart-type control chart that takes into account the location of a single order statistic of the test sample (such as the median) as well as the number of observations in that test sample that lie between the control limits. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of the chart is that, due to its nonparametric nature, the false alarm rate and in-control run length distribution are the same for all continuous process distributions, and so will be naturally robust. Tables are provided for the implementation of the chart for some typical ARL values and false alarm rates. The empirical study carried out reveals that the new chart is preferable from a robustness point of view in comparison to a classical Shewhart-type chart and also the nonparametric chart of Chakraborti et al. (2004 Chakraborti , S. , van der Laan , P. , van de Wiel , M. A. ( 2004 ). A class of distribution-free control charts . J. Roy. Statist. Soc. Ser. C-Appl. Statist. 53 ( 3 ): 443 – 462 .[Web of Science ®] , [Google Scholar]).