Confidence Limits For Reliability Research Articles

Generalized fiducial inference for the lower confidence limit of reliability based on Weibull distribution

Reliability performance, especially the lower confidence limit of reliability, plays an important role in reliability assessment, and it is also of concern to researchers and engineers. In this article, a novel estimate of the lower confidence limit of the reliability for two-parameter Weibull distribution is proposed based on the generalized fiducial inference. The corresponding adaptive Metropolis-Hastings within Gibbs algorithm is provided to analyze the generalized fiducial lower confidence limit. The proposed lower confidence limit of the reliability is compared with that from frequentist method. In addition, this novel procedure is generalized to the series system and the parallel system which consists of identical Weibull components. Simulation results show that the proposed generalized fiducial lower confidence limit is more applicable than the frequentist method, especially for the case of small sample size. Finally, the MOS transistor lifetime data is used to illustrate the new procedure.

Fiducial Lower Confidence Limit of Reliability for a Power Distribution System

Reliability performance, especially the lower confidence limit of reliability, plays an important role in system risk and safety assessment. A good estimator of the lower confidence limit of system reliability can help engineers to make the right decisions. Based on the lifetime of the key component in a typical satellite intelligent power distribution system, the generalized fiducial method is adopted to estimate the lower confidence limit of the system reliability in this paper. First, the generalized pivotal quantity and the lower confidence limit of reliability for the key component are derived for the lifetimes of the exponential-type and Weibull-type components. Simulations show that the sample median is more appropriate than the sample mean when the lower confidence limit of reliability is estimated. Moreover, the lower confidence limit of reliability is obtained for the typical satellite intelligent power distribution system through the pseudo-lifetime data of the metallic oxide semiconductor field effect transistor. The lower confidence limit of reliability for this power distribution system at 15 years is 0.998, which meets the factory’s reliability requirement. Finally, through the comparison, a hot standby subsystem can be substituted with a cold standby subsystem to increase the lower confidence limit of the system reliability.

Higher-order normal approximation approach for highly reliable system assessment

In this study, the issue of system reliability assessment (SRA) based on component failure data is considered. In industrial statistics, the delta method has become a popular approach for confidence interval approximation. However, for high reliability systems, usually the assessment is confronted with very limited component sample size, variant multi-parameter lifetime models, and complex system structure. Along with strict requirement on assessment accuracy and computational efficiency, existing approaches barely work under these circumstances. In this article, a normal approximation approach is proposed for determining the lower confidence limit of system reliability using components’ time-to-failure data. The polynomial adjustment method is adopted to construct higher-order approximate confidence limit. The main contribution of this work is constructing an integrated methodology for SRA. Specifically, a reliability-based Winterbottom-extended Cornish-Fisher (R-WCF) expansion method for log-location-scale family is elaborated. The proposed methodology exceeds the efficient limitation of Cramer Rao’s theory. Numerical studies are conducted to illustrate the effectiveness of the proposed approach, and results show that the R-WCF approach is more efficient than the delta method for highly reliable system assessment, especially with ultra-small sample size. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transactions.

Exact confidence limit for complex system reliability based on component test data

ABSTRACTReliability analysis for complex system is one of the most concerned problems in industry. On account of high cost of testing we often obtain a small size of sample, even only test data for components. In this article, an exact method for system reliability assessment will be presented generalized from the Buehler confidence limit. We give a suggestion on the choice of statistic order based on an estimate of system reliability which only relies on the true value of even for multiparameter model. In addition, we present an algorithm to solve the function with constraint set up in Buehler method. A three-component application is given to illustrate the algorithm. We also present some simulation studies to compare our proposed method with other widely applied methods.

A Stress-Strength Time-Varying Correlation Interference Model for Structural Reliability Analysis Using Copulas

This paper proposes a stress-strength time-varying correlation interference model for structural reliability analysis using Copulas. First, the stochastic stress is developed by incorporating the interaction between basic variables and time variable into the quadratic response surface method, and the stochastic strength is characterized by the linear or exponential degradation model. Second, the Copula selection method is given, and we propose time-varying stable (unstable) model for Kendall's tau to describe the time-varying correlation characteristic. Third, the structural reliability estimation method is developed, especially the method for the nondifferentiable Copulas can be used to calculate the probability in any area for any type of Copula when the marginal distribution is continuous. Finally, the lower confidence limit of structural reliability is given based on the survival coefficient. The comparison results of the high-temperature structural reliability estimation from different situations are illustrated in the simulation example to demonstrate the availability of the proposed model.

The role of randomization tests in vegetation boundary detection with moving split‐window analysis

AbstractAimMoving split‐window (MSW) analysis is a frequently used tool for vegetation boundary detection. The statistical test of the method is, however, not satisfactory. We aimed to identify reliable confidence limits of MSW statistics.MethodsMultivariate transect data (representing forest, grassland and forest‐steppe habitats and some artificial data sets) were analysed using five dissimilarity functions and two randomization methods to find the most efficient procedure. We tested the normality of distribution of the dissimilarity values, and then compared the effect of plot randomization and random shift randomization on the power of the statistic. We evaluated the scale dependence of the dissimilarity/distance values and confidence limits.ResultsThe distribution of expected dissimilarity values deviated from a normal distribution, and in all analyses appeared to be skewed to the right. The rate of deviation depends on the data set, on the spatial scale (window size) and on the type of randomization. Expected mean dissimilarity decreased considerably with increasing window width when plot randomization was applied, but was more balanced if random shift was used. Consequently, normalized dissimilarity values increased rapidly with window width in plot randomization, causing extreme scale dependence and false significance. The analysis with random shift distinguished between significant and non‐significant peaks at every window size.ConclusionsWe suggest the use of the random shift permutation as a new method in the MSW analysis, since it minimizes the scale dependence of standardized dissimilarity values, making a clear distinction between significant and non‐significant discontinuities.

A review of micro-scale focused ion beam milling and digital image correlation analysis for residual stress evaluation and error estimation

Abstract In the past decade several versions of micro-scale residual stress analysis techniques have been developed based on Focused Ion Beam (FIB) milling at sample surface followed by Digital Image Correlation (DIC) for the determination of the resulting strain relief. Reliable and precise estimation of the error bounds on these measures is critical in determining the usefulness and accuracy of residual stress evaluation. Here we present an overview of the steps necessary for effective outlier removal, error propagation and estimation in order to provide reliable confidence limits for the stress value obtained. Error propagation analysis begins with DIC marker tracking errors that depend on imaging contrast and magnification, and can be improved with sub-pixel tracking and marker shift averaging. We demonstrate how the outliers and poorly tracked markers ought to be removed from the data set using correlation coefficient thresholding and/or correlation peak confidence intervals. Markers showing large displacements relative to their neighbours can also be identified as aberrant, and removed. By performing careful error propagation throughout the analysis chain we quantify the displacement and strain fields, and qualify them with the associated confidence intervals. These values, in combination with the elastic modulus confidence limits, are then used to provide the final confidence intervals for the determined residual stress values. The generic nature of the methodology presented ensures its suitability for all residual stress analysis techniques based on FIB milling and image correlation analysis. An example of implementation is presented for the micro-scale ring-core FIB–DIC approach.

WCF approach of reliability assessment for solid state power controller with accelerate degradation data

ABSTRACTThe lower confidence limit of system reliability plays an important role in system reliability assessment, and it is also of a concern to researchers and engineers. In this article, Winterbottom-Cornish-Fisher (WCF) method is applied to estimate the lower confidence limit of the reliability for Solid State Power Controller (SSPC). In order to do this, this article first fits the regression paths and extrapolates the pseudo lifetimes based on the degradation data of MOSFET. With the monotone coherent structure of SSPC and the cumulant properties of parameters, the lower confidence limit of SSPC reliability is derived from the pseudo lifetime of MOSFET.

Lower confidence limit for reliability based on grouped data using a quantile-filling algorithm

The aim of this paper is to propose an approach to constructing lower confidence limits for a reliability function and investigate the effect of a sampling scheme on the performance of the proposed approach. This is accomplished by using a data-completion algorithm and certain Monte Carlo methods. The data-completion algorithm fills in censored observations with pseudo-complete data while the Monte Carlo methods simulate observations for complicated pivotal quantities. The Birnbaum–Saunders distribution, the lognormal distribution and the Weibull distribution are employed for illustrative purpose. The results of three cases of data-analysis are presented to validate the applicability and effectiveness of the proposed methods. The first case is illustrated through simulated data, and the last two cases are illustrated through two real-data sets.

LOGISTIC FUNCTION PROFILE FIT: A least-squares program for fitting interface profiles to an extended logistic function

The extended logistic function provides a physically reasonable description of interfaces such as depth profiles or line scans of surface topological or compositional features. It describes these interfaces with the minimum number of parameters, namely, position, width, and asymmetry. Logistic Function Profile Fit (LFPF) is a robust, least-squares fitting program in which the nonlinear extended logistic function is linearized by a Taylor series expansion (equivalent to a Newton–Raphson approach) with no apparent introduction of bias in the analysis. The program provides reliable confidence limits for the parameters when systematic errors are minimal and provides a display of the residuals from the fit for the detection of systematic errors. The program will aid researchers in applying ASTM E1636-10, “Standard practice for analytically describing sputter-depth-profile and linescan-profile data by an extended logistic function,” and may also prove useful in applying ISO 18516: 2006, “Surface chemical analysis—Auger electron spectroscopy and x-ray photoelectron spectroscopy—determination of lateral resolution.” Examples are given of LFPF fits to a secondary ion mass spectrometry depth profile, an Auger surface line scan, and synthetic data generated to exhibit known systematic errors for examining the significance of such errors to the extrapolation of partial profiles.

Confidence Intervals for Difference Between Two Poisson Rates

In this article, we develop four explicit asymptotic two-sided confidence intervals for the difference between two Poisson rates via a hybrid method. The basic idea of the proposed method is to estimate or recover the variances of the two Poisson rate estimates, which are required for constructing the confidence interval for the rate difference, from the confidence limits for the two individual Poisson rates. The basic building blocks of the approach are reliable confidence limits for the two individual Poisson rates. Four confidence interval estimators that have explicit solutions and good coverage levels are employed: the first normal with continuity correction, Rao score, Freeman and Tukey, and Jeffreys confidence intervals. Using simulation studies, we examine the performance of the four hybrid confidence intervals and compare them with three existing confidence intervals: the non-informative prior Bayes confidence interval, the t confidence interval based on Satterthwait's degrees of freedom, and the Bayes confidence interval based on Student's t confidence coefficient. Simulation results show that the proposed hybrid Freeman and Tukey, and the hybrid Jeffreys confidence intervals can be highly recommended because they outperform the others in terms of coverage probabilities and widths. The other methods tend to be too conservative and produce wider confidence intervals. The application of these confidence intervals are illustrated with three real data sets.

Estimating gametic introgression rates in a risk assessment context: a case study with Scots pine relicts

The estimation of recent gene immigration is fundamental to a wide range of evolutionary and conservation studies. In a risk assessment context, gene flow estimation procedures are needed that are both accurate and readily amenable to formal evaluation of statistical uncertainty. However, genetic methods for estimating recent migration rates that are specific and have been thoroughly evaluated are scarce. Here we use an original and straightforward maximum-likelihood method to estimate recent uniparental gametic immigration from non-local plantations into an endangered population of the Iberian relict pine variety Pinus sylvestris var. nevadensis D. H. Christ. Our approach is not intended to ascertain population membership of individuals, but rather to obtain accurate immigration rate estimates with reliable confidence limits. We found very high (approximately 40%) pollen introgression at the seed-crop level into the Scots pine relict, and substantial (10-15%) male gametic introgression among naturally regenerated recruits. Using numerical simulation, we show that our method yields uniparental gametic immigration estimates that are expected to be virtually unbiased and usually accurate under our sampling conditions. Among four tested methods to estimate the confidence intervals for immigration estimates, the profile-likelihood method was the best, as it outperformed bootstrapping procedures and yielded coverage close to nominal limits under different sample sizes and migration rates. This study presents a method by which researchers can facilitate decision making within a gene flow risk assessment context.

Reliability inference and sample-size determination under double censoring for some two-parameter models

Assuming that some extreme sample values have been censored or discarded, a reliability analysis of several two-parameter models, as the exponential, Pareto and power-function laws, is presented. Explicit expressions for the distribution, density and moments of the natural generalized pivot of the true reliability are deduced. Its asymptotic normality is also shown. Reliability point estimates are derived by selecting summary features of the pivotal quantity. Reliability confidence limits, which are shown to provide exact coverage probabilities, are readily found by solving simple nonlinear equations. Quite accurate approximate limits are given in closed forms. In addition, a procedure for determining confidence intervals of shortest length is proposed. Reliability tests, which are carried out using generalized p -values, satisfy the conventional repeated-sampling property. Minimum sample sizes and decision rules of optimal reliability demonstration plans, which accept good (bad) products with a certain high (low) probability, are obtained via iterative methods. A numerical example is included for illustrative purposes.

Lower confidence limits for structure reliability

For a class of data often arising in engineering, we have developed an approach to compute the lower confidence limit for structure reliability with a given confidence level. Especially, in a case with no failure and a case with only one failure, the concrete computational methods are presented.

Parameter optimisation in constitutive equations for hot forging

Various methods for parameter optimisation in constitutive equations applied to the hot deformation of a popular α–β titanium alloy have been examined. The use of direct search and gradient methods are shown to be effective, even with a limited dataset, and reliable confidence limits can be computed in each case. However, a hybrid approach, whereby genetic algorithms are used to find an initial parameter starting point, and then a direct search (simplex) method is applied to obtain a global minimum, is particularly promising. For comparison, an artificial neural network approach, which does not require the use of any constitutive equations, has also been implemented.

A Lower Confidence Limit for Reliability of a Coherent System with Independent Exponential Components

In this paper, we solve an oldest open problem of finding estimate interval for system reliability via the CHA algorithm (Chaudhuri et al 2001) following the Easterling (Jour. Amer. Statist. Asso., 1972) approach. We consider a coherent system composed of exponential components; the components arc assumed to be statistically independent. A closed form expression for the standard error of the system reliability, for a given mission of duration, is obtained. The method of calculating the 100(1- α)% lower confidence limit for the system reliability is illustrated for a simple series system with three independent exponential components. Both methods of simulation and numerical integration techniques are used for calculations. This paper basically extends the results of Easterling to any coherent system.

Bootstrap tolerance and confidence limits for two-variable reliability using independent and weakly dependent observations

Tolerance and confidence limits are obtained for two-variable reliability, δ= P( Y< X), using the bootstrap method. X and Y are two random variables with unspecified distributions. Both independent and weakly dependent data cases are considered. Moving Block Bootstrap (MBB) method is used for the later case. Minitab macros are provided for obtaining tolerance and confidence limits. Simulation studies indicate the accuracy of the proposed tolerance and confidence limits.

Finding Confidence Limits on Population Growth Rates: Three Real Examples Revised

EcologyVolume 75, Issue 1 p. 255-260 Article Finding Confidence Limits on Population Growth Rates: Three Real Examples Revised Elena R. Alvarez-Buylla, Elena R. Alvarez-BuyllaSearch for more papers by this authorMontgomery Slatkin, Montgomery SlatkinSearch for more papers by this author Elena R. Alvarez-Buylla, Elena R. Alvarez-BuyllaSearch for more papers by this authorMontgomery Slatkin, Montgomery SlatkinSearch for more papers by this author First published: 01 January 1994 https://doi.org/10.2307/1939401Citations: 70AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume75, Issue1January 1994Pages 255-260 RelatedInformation

Terrestrial physical and chemical processes for liquid waste treatment

Experiences gained from full-scale evaluation of advanced treatment processes used for reclaiming wastewaters should help in the evaluation of potential treatment systems for treatment and reuse of water in space. Water Factory 21 is a 0.66 m 3s −1 (15 million gallons per day) water reclamation plant in California that has been in operation since 1976. The plant receives biologically treated wastewater. Lime treatment is effective for removal of heavy metals. Volatile organic constitutes are efficiently removed by air stripping. Non-volatile organic constituents are removed by activated carbon adsorption and reverse osmosis (RO). RO is a highly effective polishing step, and removes most of the remaining materials including inorganic salts, heavy metals, and organics. RO removed 85% of the total organic carbon, down to about 1 mg 1 −1, which is lower than in many treated drinking waters. The series of treatment processes used insured virus and pathogen removal, with lime treatment and chlorination together proving highly effective. Sufficient data has been collected to provide statistically reliable confidence limits to be set on the performance of each unit process.

Theory and counterexamples for confidence limits on system reliability

The general theory of optimal confidence limits for system reliability based on results of Buehler (1957) and Sudakov and references cited there (1974) is developed. Counterexamples to some results of Sudakov (1974), Winterbottom (1974) and Harris and Soms (1980, 1981) are exhibited. Numerical examples are given for two component series systems which show that the results hold for confidence levels used in practice.