Weibull分布兴趣参数的广义置信区间

Weibull分布可以用来描述疲劳失效、真空管失效和轴承失效等,是重要的寿命分布。本文研究了Weibull分布尺度参数、形状参数、分位数及可靠度函数的广义置信区间问题。利用广义枢轴量给出四个兴趣参数的广义置信区间。证明了由广义枢轴量确定的四个兴趣参数的广义置信区间具有频率意义下的实际置信水平。     

集成量纲分析的多元测量系统能力评价

多元测量系统分析是多元质量控制的重要内容。现有的研究主要是利用统计学的方法,如多元方差分析法和主成分法等进行分析评价。本文提出了基于量纲分析的多元测量系统能力评价方法,集成物理和统计分析方法,利用物理中量纲分析的方法研究产品各相关变量之间的物理关系,将多元测量系统问题转化为一元测量系统问题。从而可以利用一元测量系统能力评价的统计方法及指标来对测量系统的能力进行评估。同时,本文重复了纸飞机试验,并运用基于量纲分析的多元测量系统能力评价方法对纸飞机的测量系统进行了分析评价,验证了该方法的有效性。     

Cline分块矩阵的极小范数广义逆

矩阵广义逆的递推算法在统计推断、模式识别以及解析动力学等领域有着广泛的应用背景.本文利用范数极小化方法给出了计算Cline分块矩阵的极小范数广义逆及逆的两个一般递推表示式,推广了已有的结果.     

广义Pareto分布参数的Bootstrap置信区间及应用

针对广义Pareto分布应用于超阈值数据拟合时尾部数据较少的情况,将参数的极大似然估计与Bootstrap方法相结合,给出参数的Bootstrap置信区间。Bootstrap置信区间计算方法既可以通过重复抽样充分利用样本信息,又可以避免样本较少时估计量方差偏大的情况。理论证明参数的Bootstrap置信区间是渐近有效的。数值模拟结果表明在一定的置信度下,置信区间的区间长度和覆盖率比较合理。应用建立的Pareto模型对巴颜喀拉地震带震级数据进行分析,结果表明在相同的置信度下,采用Bootstrap方法计算的置信区间比由近似协方差矩阵计算的区间长度更短,这为广义Pareto模型描述地震震级分布的适用性提供了支撑。     

基于旋转装置的磁梯度张量测量方法

磁梯度张量是目前磁信息应用领域的研究热点,尤其在探测未爆弹(UXO)方面,具有更好的反演能力.本文提出了一种基于旋转装置的磁梯度张量测量方法,基于该方法的测量系统包含两个单轴磁力仪和一个旋转装置,两个磁力仪在相互平行的两个平面上,它们的敏感轴共线,但方向相反,且与平面存在固定夹角.测量时,两个磁力仪饶与平面垂直的同一个轴旋转,旋转半径相同,利用磁力仪的输出可解算得到磁梯度张量.该方法可减少磁梯度张量测量系统的磁力仪数量,从而节约成本,降低系统误差.仿真结果表明,基于该方法的测量系统可有效测得磁梯度张量,且测量精度优于十字形轴向差分测量阵列.     

基于评分法的测量系统能力评价

目前所用的测量系统能力评价方法是建立在正态性假设的基础上,如果测量系统误差不满足正态性,运用原来的评价指标在对测量系统能力进行评价的过程中会发生误判。将连续等级概率评分(CRPS)应用到测量系统分析评价当中,通过研究CRPS的相关特性,建立了基于CRPS评分法的测量系统能力评价指标,从而使测量系统误差非正态分布时,对测量系统能力进行评价的过程中不会发生误判。通过案例分析表明,当测量系统误差为正态分布时,运用CRPS和运用传统评价指标给出的评价结果是一致的,同时,CRPS评价方法能够有效实现非正态测量系统误差情形下的测量系统能力评价。     

基于Bootstrap方法的过程能力指数区间估计

针对传统统计过程控制方法的局限性,利用Bootstrap方法构建了过程能力指数的置信区间,分别对正态分布、指数分布进行仿真计算,对3种Bootstrap置信区间进行了比较。通过实证分析验证了在小样本条件下Bootstrap置信区间的有效性。     

测量不确定度评估及基于Monte Carlo法的数值计算

对于测量结果的不确定度评价主要依据的文件是ISO GUM,本文对GUM以及最新的利用MonteCarlo法基于概率密度函数(PDF)的传递评价测量不确定度的标准ISO GUM S1进行分析,阐述了两者评价测量不确定度的联系、基于Monte Carlo法的评价测量不确定度的数值计算方法.文中针对两个典型的例子,分别采用GUM与GUM S1规定的两种不确定度评定方法对其进行了不确定度评估,并对结果进行了比较.     

基于普通摄像头的心率测量系统设计

为了研究一种通过普通摄像头非接触地拍摄人脸获取人体心率的测量系统,提出基于光电容积描记法原理,从人脸图像序列中可以提取出含有脉搏成分的信号,对该信号进行小波滤波得到血液容积脉搏波,然后用改进的时间间隔差法计算得到心率值。实验结果证明,如果将脉搏血氧仪测量的心率作为标准值,该系统测量结果的95%置信区间为［-2.2139, 2.1539］,该系统与脉搏血氧仪的心率测量结果具有很高的一致性;通过调节光照强度和摄像头硬件参数等能够在一定程度上提高测量准确度。     

微流量测量方法及其技术的发展

归纳了近五年来基于MEMS技术的微流量传感器结构及性能参数。根据国际上热门的研究方法推断微流量测量技术可能的发展方向与研究趋势,即集成两种或两种以上的测量方法,实现优势互补,提高测量精度或扩大量程比。最后基于现有的技术基础,提出了融合科氏效应与差压效应的微流量测量方法,阐述了传感器的工作原理与理论基础,并对其可行性进行了分析与论证。     

Applying Bootstrap method to the types I–II errors in the measurement system

This paper attempts to evaluate different methods of calculating the type‐I and type‐II errors in the measurement system. Furthermore, we apply the Bootstrap method to construct the confidence intervals for the type‐I and type‐II errors. Also, the proposed method is compared with the generalized inference method. Several factors such as the sample size, the measurement error, the process mean, and the process variation are simulated to validate the performance. The simulation results show that both methods almost have the same performance. In addition, we develop a computer program that can evaluate the error of measurement system without changing information or data. Two case studies of the nano measurement data are used to demonstrate the application. The simulation results indicate that the sample size has an influence for all cases. The type‐I and type‐II errors are decreased when the measurement error is increased. The type‐I and type‐II errors are affected by the measurement error, the process mean, and the process deviation. The case studies show that the development of nano technology requires the immediate attention of the measurement capability. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of Field Reliability Based on Aggregate Lifetime Data

Because of the exponential distribution assumption, many reliability databases recorded data in an aggregate way. Instead of individual failure times, each aggregate data point is a summation of a series of collective failures representing the cumulative operating time of one component position from system commencement to the last component replacement. The data format is different from traditional lifetime data and the statistical inference is challenging. We first model the individual component lifetime by a gamma distribution. Confidence intervals for the gamma shape parameter can be constructed using a scaled χ² approximation to a modified ratio of the geometric mean to the arithmetic mean, while confidence intervals for the gamma rate and mean parameters, as well as quantiles, are obtained using the generalized pivotal quantity method. We then fit the data using the inverse Gaussian (IG) distribution, a useful lifetime model for failures caused by degradation. Procedures for point estimation and interval estimation of parameters are developed. We also propose an interval estimation method for the quantiles of an IG distribution based on the generalized pivotal quantity method. An illustrative example demonstrates the proposed inference methods. Supplementary materials for this article are available online.     

Reliability analysis for accelerated degradation data based on the Wiener process with random effects

On the basis of the principle of degradation mechanism invariance, a Wiener degradation process with random drift parameter is used to model the data collected from the constant stress accelerated degradation test. Small-sample statistical inference method for this model is proposed. On the basis of Fisher's method, a test statistic is proposed to test if there is unit-to-unit variability in the population. For reliability inference, the quantities of interest are the quantile function, the reliability function, and the mean time to failure at the designed stress level. Because it is challenging to obtain exact confidence intervals (CIs) for these quantities, a regression type of model is used to construct pivotal quantities, and we develop generalized confidence intervals (GCIs) procedure for those quantities of interest. Generalized prediction interval for future degradation value at designed stress level is also discussed. A Monte Carlo simulation study is used to demonstrate the benefits of our procedures. Through simulation comparison, it is found that the coverage proportions of the proposed GCIs are better than that of the Wald CIs and GCIs have good properties even when there are only a small number of test samples available. Finally, a real example is used to illustrate the developed procedures.     

Optimal confidence intervals on the variation for operators and gauge in manufacturing process with repeated measurements

It is necessary to measure the attributes of the parts in any manufacturing process. It is also important to monitor measurement system in the manufacturing process because repeated measurements of the attributes include variability as well as target value. This paper considers variabilities due to repeated measurements, operators, and gauge in a measurement system. The measurement system is statistically modeled as a two-factor mixed model with one covariate and interaction. That is, this model employs J operators randomly chosen to conduct measurements on I randomly selected parts from a manufacturing process. In this experiment each operator measures each part K times. This paper aims to provide engineering practitioners with statistically optimal confidence intervals on the variation due to operators and gauge resulted from a measurement system statistically modeled. The optimal confidence intervals are based on a moderate large sample method (MLS) and a generalized p-value method (GEN). The confidence intervals proposed can be useful tools to determine whether a manufacturing process is adequate for monitoring a measurement system.     

Confidence Intervals for Process Capability Indices for the Unbalanced One‐Way Random Effect ANOVA Model

Confidence intervals for process capability index C_pk are developed for the unbalanced one‐way random effect model using Bissell's approximation method. The proposed limit is compared with the generalized lower confidence limit obtained using the generalized pivotal quantity method. To assess the accuracy of the method, a simulation study is presented. The results are illustrated with an industrial example. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparing Confidence Intervals for Multivariate Process Capability Indices

Multivariate process capability indices (MPCIs) are needed for process capability analysis when the quality of a process is determined by several univariate quality characteristics that are correlated. There are several different MPCIs described in the literature, but confidence intervals have been derived for only a handful of these. In practice, the conclusion about process capability must be drawn from a random sample. Hence, confidence intervals or tests for MPCIs are important. With a case study as a start and under the assumption of multivariate normality, we review and compare four different available methods for calculating confidence intervals of MPCIs that generalize the univariate index C_p. Two of the methods are based on the ratio of a tolerance region to a process region, and two are based on the principal component analysis. For two of the methods, we derive approximate confidence intervals, which are easy to calculate and can be used for moderate sample sizes. We discuss issues that need to be solved before the studied methods can be applied more generally in practice. For instance, three of the methods have approximate confidence levels only, but no investigation has been carried out on how good these approximations are. Furthermore, we highlight the problem with the correspondence between the index value and the probability of nonconformance. We also elucidate a major drawback with the existing MPCIs on the basis of the principal component analysis. Our investigation shows the need for more research to obtain an MPCI with confidence interval such that conclusions about the process capability can be drawn at a known confidence level and that a stated value of the MPCI limits the probability of nonconformance in a known way. Copyright © 2011 John Wiley & Sons, Ltd.     

A note on “Parameter estimation for bivariate Weibull distribution using generalized moment method for reliability evaluation”

Yuan [Quality and Reliability Engineering International, 2018, doi: 10.1002/qre.2276] proposed a generalized moment method for parameter estimation of a particular bivariate Weibull distribution and derived corresponding confidence intervals. The expressions given for the confidence intervals do not appear correct. In this note, we correct the confidence intervals and recompute them for two real data sets.     

Generalized confidence intervals for process capability indices

The concept of generalized confidence intervals is used to derive lower confidence limits for some of the commonly used process capability indices. For the cases where approximate lower confidence limits are already available, numerical comparisons are made among the available approximations and the generalized lower confidence limit. The numerical results indicate that the generalized confidence interval does provide coverage probabilities very close to the nominal confidence level. Two examples are given to illustrate the results. Copyright © 2006 John Wiley & Sons, Ltd.     

Inference for dependence competing risks with partially observed failure causes from bivariate Gompertz distribution under generalized progressive hybrid censoring

Competing risks model is considered with dependence causes of failure in this paper. When the latent failure times are distributed by a bivariate Gompertz model, statistical inference for the unknown model parameters is studied from classical and Bayesian approaches, respectively. Under a generalized progressive hybrid censoring, maximum likelihood estimators of the unknown parameters together with the associated existence and uniqueness are established, and the approximate confidence intervals are also obtained based on asymptotic likelihood theory via the observed Fisher information matrix. Moreover, Bayes estimates and the highest posterior density credible intervals of the unknown parameters are also provided based on a flexible Gamma–Dirichlet prior, and Monte Carlo sampling method is also derived to compute associated estimates. Finally, simulation studies and a real-life example are given for illustration purposes.     

Inference on the Gamma Distribution

This study develops inferential procedures for a gamma distribution. Based on the Cornish–Fisher expansion and pivoting the cumulative distribution function, an approximate confidence interval for the gamma shape parameter is derived. The generalized confidence intervals for the rate parameter and other quantities such as mean are explored. The proposed generalized inferential procedures are extended to construct prediction limits for a single future measurement and for at least p of m measurements at each of r locations. The performance of the proposed procedures is evaluated using Monte Carlo simulation. The simulation results show that the proposed procedures are very satisfactory. Finally, three real examples are used to illustrate the proposed procedures. Supplementary materials for this article are available online.