A Monte-Carlo Technique for Estimating Lower Confidence Limits on System Reliability Using Pass-Fail Data

Several methods for estimating lower s-confidence limits (LCLs) for system reliability were examined using pass-fail data on the components. A new technique was used to obtain limits for selected systems. These limits were compared to those obtained by other methods. The new method was tested to verify its accuracy. Results indicate that the proposed technique is simple to understand, easy to implement, and accurate. One need only supply the component reliabilities, the number of component tests, and the desired level of s-confidence, to obtain, not only an estimated LCL of the system reliability, but also an idea of the accuracy of the estimate. Most of the other techniques are not valid in the case of zero-failures, whereas this method easily accommodates such a situation. This method is not restricted to series systems; it can easily handle parallel configurations.     

Sequential Testing of Components for System Reliability

It is often desirable to construct s-confidence limits for system reliability on the basis of data obtained from `pass-fail' tests on the components of the system. This paper presents a general method for sequentially testing the components that provides data from which these s-confidence limits can be easily derived. The method is applicable to any s-coherent system for which the reliability function is known. It is a generalization of a scheme given by Winterbottom and Verrall for systems composed of units arranged either in series or parallel.     

Approximate Tolerance Limits and Confidence Limits on Reliability for the Gamma Distribution

No exact method is known for determining tolerance limits or s-confidence limits for reliability for the gamma distribution when both parameters are unknown. Perhaps the simplest approximate method is to determine a tolerance limit assuming the shape parameter known and then replace the shape parameter with its ML estimate to obtain approximate limits. Simulated values of the true probability levels, achieved by this method, indicate that this method is not suitable, contrary to what has been anticipated. A second approach is to consider the corresponding tolerance limits assuming the distribution mean known and the shape parameter unknown, and then replace the distribution mean by the sample mean. This approach gives useful results for many practical cases. Simulated values of the true probability levels achieved are presented for some typical cases and limiting values are provided. This method appears satisfactory for all values of the shape parameter, for the common s-confidence levels, and moderate sample sizes.     

Approximate Confidence Intervals for Reliability of a Series System

Two solutions are proposed for estimating s-confidence intervals for reliability of a repairable series system comprised of non-constant failure rate components: 1) the system is treated as a sum of renewal processes with the mean and variance of total number of system failures being computed from the moments of failure times of the components; and 2) a pseudo-Bayesian solution is derived for the mean and variance of the log-reliability of a system of Weibull components. In both solution approaches, the central limit theorem is invoked for a sum of component random variables determined from test data such as number of failures or log-reliabilities. s-Confidence limits are then approximated using Gaussian probability tables. The intervals derived yield close-to-exact frequency limits, depending on such variables as number of test failures, number of components, and component parameters.     

A Comparison of Three Methods for Calculating Lower Confidence Limits on System Reliability Using Binomial Component Data

The Maximus, bootstrap, and Bayes methods can be useful in calculating lower s-confidence limits on system reliability using binomial component test data. The bootstrap and Bayes methods use Monte Carlo simulation, while the Maximus method is closed-form. The Bayes method is based on noninformative component prior distributions. The three methods are compared by means of Monte Carlo simulation using 20 simple through moderately complex examples. The simulation was generally restricted to the region of high reliability components. Sample coverages and average interval lengths are both used as performance measures. In addition to insights regarding the adequacy and desirability of each method, the comparison reveals the following regions of superior performance: 1. The Maximus method is generally superior for: a) moderate to large series systems of reliable components with small quantities of test data per component, and b) small series systems of repeated components. 2. The bootstrap method is generally superior for highly reliable and redundant systems. 3. The Bayes method is generally superior for: a) moderate to large series systems of reliable components with moderate to large numbers of component tests, and b) small series systems of reliable non-repeated components.     

Properties of Moment Estimators For the 3-Parameter Weibull Distribution

This paper gives a method of constructing moment estimators for the shape, scale, and location parameters of the 3-parameter Weibull distribution. These estimators are asymptotically s-normally distributed around the population values; the asymptotic covariance matrix is obtained. The estimators and their estimated covariance matrix can be constructed by using tables in the paper; the covariance matrix can then be used to construct s-confidence regions for the estimators.     

Comparison of Monte Carlo Techniques for Obtaining System-Reliability Confidence Limits

Digital computer techniques are developed using a) asymptotic distributions of maximum likelihood estimators, and b) a Monte Carlo technique, to obtain approximate system reliability s-confidence limits from component test data. 2-Parameter Weibull, gamma, and logistic distributions are used to model the component failures. The components can be arranged in any system configuration: series, parallel, bridge, etc., as long as one can write the equation for system reliability in terms of component reliability. Hypothetical networks of 3, 5, and 25 components are analyzed as examples. Univariate and bivariate asymptotic techniques are compared with a double Monte Carlo method. The bivariate asymptotic technique is shown to be fast and accurate. It can guide decisions during the research and development cycle prior to complete system testing and can be used to supplement system failure data.     

A Confidence Interval for the Barlow-Scheuer Reliability Growth Model

Barlow & Scheuer proposed a useful scheme for estimating reliability growth of a system undergoing developmental testing and offered a conservative lower s-confidence bound. This paper shows how a less conservative lower s-confidence bound can be found by using an equivalent model for system reliability.     

Failure Rate Calculations Using a Programmable Calculator

This paper describes a TI 59 program which calculates the acceleration factor between any two temperatures, equivalent unit-hours at one temperature based on actual test hours at a second temperature, the x2 approximation at any of seven s-confidence levels, and the s-confidence limit failure rate estimate in both %/1000 hours and FITs. The program allows numerous entries of separate sample results which the calculator stores and then performs a single failure rate estimate calculation. Required inputs are test temperature, temperature at which the failure rate estimate is desired, the activation energy, and the number of failures during the test. The equations for the program are reviewed and tables are included showing all labels and memories used, and the 355 program steps listing.     

Weibull Percentile Estimates and Confidence Limits from Singly Censored Data by Maximum Likelihood

This paper presents a simple chart that provides approximate large-sample s-confidence limits for the percentiles of a Weibull life distribution estimated by maximum likelihood from singly censored data. The chart also helps determine the appropriate sample size and length of a life test. The methods are illustrated with life data on a locomotive control.     

一种计算具有内圆柱导体矩形线特性阻抗的新方法

本文采用保角变换技术，将内外接多边形柱取代内圆导体，得到的传输线特性阻抗Ｚｃｉｎ，Ｚｃｏｕｔ作为真值Ｚｃ的上，下限（Ｚｃｉｎ．Ｚｃ．Ｚｃｏｕｔ），并研究了其相对偏差情况，从而得到了计算具有内圆导体矩形线特性阻抗的一种新方法，所得结果与文献的数据吻合良好，最大偏差＜０．５％。     

Reliability estimation and tolerance limits for Laplace distribution based on censored samples

In this paper, we first present an estimator for the reliability function based on the best linear unbiased estimators (BLUEs) of the location and scale parameters, μ and σ, for the Laplace distribution based on Type-II censored samples. We show that this estimator is almost unbiased at varying levels of reliability. Next, we determine through Monte Carlo simulations the values of the tolerance factor t_γ that are necessary for the construction of lower and upper tolerance limits for the distribution. We also illustrate how these tables for tolerance limits could be used to determine lower confidence limits for the reliability. Finally, we present an example to illustrate the methods of inference developed in this paper.     

Design of Close-to-Capacity Constrained Codes for Multi-Level Optical Recording

We report a new method for designing (M,d, k) constrained codes for use in multi-level optical recording channels. The method allow us to design practical codes, which have simple encoder tables and decoders having fixed window length. The codes presented here for the d = 1 and d = 2 cases, achieve higher storage densities than previously reported codes, and come within 0.3 - 0.7% of capacity.     

Survey of reliability and availability evaluation of complex networks using Monte Carlo techniques

Generally there are four main difficulties in evaluating complex large-scale system reliability, availability and MTBF: the system structure may be very complex; subsystems may follow various failure distributions; subsystems may conform to arbitrary failure and repair distributions for maintained systems; the failure data of subsystems are sometimes not sufficient, reliability test sample sizes tend to be small. It is difficult and often impossible to obtain s-confidence limits of them by classical statistics. Monte Carlo technique combined with Bayes method is a powerful tool to solve this kind of problems. In this survey, the typical existing Monte Carlo reliability, availability and MTBF simulation procedures, variance reduction methods, and random variate generation algorithms are analyzed and summarized. The advantages, drawbacks, accuracy and computer time of Monte Carlo simulation in evaluating reliability, availability and MTBF of a complex network are discussed. Finally, some conclusions are drawn and a general Monte Carlo reliability and MTTF assessment procedure is recommended.     

Bootstrap confidence regions for the expected ROCOF of a repairablesystem

Bootstrap methods are presented for constructing s-confidence regions for the s-expected ROCOF (rate of occurrence of failures) of a repairable system. This is based on the work of Cowling, et al. (1996) for the intensity function of a NHPP (nonhomogeneous Poisson process). The method is applied to the operating times of unscheduled maintenance actions for a diesel engine of the USS Grampus given by Lee (1980) and also analyzed by Crowder, et al. (1991)     

Estimation of Mission Reliability from Multiple Independent Grouped Censored Samples

Aircraft or missiles are flown for missions of varying durations. Data are collected at the end of each mission which indicate the mission duration and whether the equipment failed. The data are considered as multiple s-independent grouped censored samples with failure times unknown. The underlying failure model considered is the 2-parameter Weibull distribution. Maximum likelihood estimates are derived. The exponential distribution is used for comparison. Monte Carlo simulations are used to compare s-efficiency of estimates for grouped data with estimates if failure times were known. The asymptotic variance-covariance matrix was computed for the sampling conditions studied and was used to obtain lower s-confidence bounds on the system reliability.     

应用于压电能量收集器的PZT PZN系陶瓷材料

压电材料作为环境振动能量收集器的核心功能材料,是制备高性能能量收集器的关键。该文从提高能量收集效率入手,研究适合于能量转换的高性能压电陶瓷材料。采用两步合成工艺制备出了0.7Pb(Zr0.51Ti0.49)0.99O3-0.3Pb(Zn1/3Nb2/3)O3(PZT-PZN)压电陶瓷,研究了La2O3掺杂对其微观结构和机电性能的影响。实验结果表明,掺杂少量的La2O3能显著提高PZT-PZN陶瓷的压电系数(d33)、机电耦合系数(k31、kp)、介电常数(εr)等。当掺杂量为4%(摩尔分数)时,在1 200℃烧结PZT-PZN,显示出良好的压电和介电性能:d33=560pC/N,k31=0.376,kp=0.642,s1E1=16.5×10-12 m2/N,εr=3 125。     

A 1 log N parallel algorithm for detecting convex hulls on imageboards

By finding the maximum and minimum of {y(i)-mx(i)|1=/相似文献   

Application Tables for MIL-STD-461B

The complexity in application of ML-STD- is re-reduced by use of tables which summarize requirements of the standard. A separate table is provided for a group of limits applicable to each type of test procedure.     

Tables of normalized cutoff wavenumbers of elliptic cross sectionresonators

Current methods to evaluate the mode resonance of elliptic cross section resonators are cumbersome for design purposes. In this paper, tables for the cutoff wavenumbers of TE_nm and TM_nm modes for both even and odd modes are tabulated in a new way, that reveals a simple relation to the equivalent circular cross section resonator and makes interpolation results accurate. These tables range for n=0, ... 3 for even modes and n=1, ... 4 for odd modes, with m=1, ..., 5 for both. The tables cover 80 different modes for eccentricity in the range 0相似文献