Estimation of failure probability under a bivariate normal stress-strength distribution

The probability of a chance failure is a parameter of great importance for design reliability and is often examined through stress-strength models. The uniform minimum variance unbiased estimator for the same under a bivariate normal stress-strength distribution has been obtained.     

Estimation of reliability in multi-component stress-strength model following a Burr distribution

This paper draws inferences about the reliability in a multi-component stress-strength system when both stress and strength are independently identically distributed (idd) Burr random variables. We consider both maximum likelihood and Bayes estimators of the system reliability. The two estimators are compared numerically by obtaining empirical efficiencies with respect to the maximum likelihood estimator (MLE) by generating 1000 random samples by a Monte Carlo simulation. It is found that the Bayes estimators are better than the corresponding MLEs for small samples (n_i ≤ 7; i = 1, 2). Moreover, the robustness of the Bayes estimators to the change of the prior parameters is also considered.     

Estimation for a probabilistic stress-strength model

Estimation for an unknown strength distribution is considered in two situations: (1) independent identically distributed stresses are applied to the component until it fails (no cumulative damage); and (2) each applied stress causes damage to the component and damage cumulates until the component fails. Both situations lead to mixtures of probability distributions, with the strength distribution playing the role of the mixing distribution. Based on the observation of cycles to failure of several independent components and on the theory of mixtures of distributions, estimators of the mixing distributions are obtained using linear programming. In particular, the solution to the linear-programming problem yields a probability mass function which approximates the unknown strength distribution. From this estimate of the strength distribution, an estimate of the mean strength of the item can be obtained by the usual computation of the mean of a probability distribution. Hence, the results provide a method of estimating the mean strength, or other parameters of the strength distribution, without requiring observations directly on the strengths of the test components     

MVU estimators for some multivariate normal probability models: An application to stress-strength models

This paper is concerned with the minimum variance unbiased (MVU) estimators for some multivariate normal probability models which can be found useful in the interference theory of reliability.     

Estimation of probability density and distribution functions

First- and second-order stochastic gradient algorithms are developed for suitably approximating the unknown density and distribution functions of a random vector from a sequence of independent samples. The mean-square-error criterion and the integral-square-error criterion are used in the approximations. The rates of convergence and the approximation error are also evaluated.     

Estimation of reliability of stress-strength model with non-identical component strengths

An attempt has been made in this paper to estimate the reliability of an s-out-of-k system with non-identical component strengths when component strengths follow an exponential distribution. A further assumption is made that all the components are subjected to a common random stress which also follow an exponential distribution. Bayes and maximum likelihood estimators of such system reliability are considered. A Bayes estimate is obtained by using Lindley's approximation. Comparisons are made on the basis of efficiency and Pitman nearness probability through a Monte-Carlo study.     

On the series representation of bivariate probability density functions

A series representation is derived for a class of bivariate probability density functions. The representation uses orthonormal sets generated by the first-order density functions.     

Estimating component-defect probability from masked systemsuccess/failure data

Consider a system of k components that fails whenever there is a defect in at least one of the components. Due to cost and time constraints it is not feasible to learn exactly which components are defective. Instead, test procedures ascertain that the defective components belong to some subset of the k components. This phenomenon is termed masking. The authors describe a 2-stage procedure in which a sample of masked subsets is subjected to intensive failure analysis. This enables maximum-likelihood estimation of the defect probability of each individual component and leads to diagnosis of the defective components in future masked failures     

The distribution of the sample correlation from a complex normal

We obtain the density of the distribution of the sample correlation from a complex normal using a complex version of Cochran's theorem. We give “small sample” asymptotic expansions for its distribution.     

Estimation of a probability with guaranteed normalized mean absolute error

The estimation of a probability p from repeated Bernoulli trials is considered in this letter. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute error of the unbiased estimator of p. The results given permit the estimation of an arbitrary probability with a prescribed level of normalized mean absolute error.     

Bayes estimation of reliability in stress-strength model of Weibull distribution with equal scale parameters

The paper provides a Bayesian approach to inference about the reliability in a multicomponent stress-strength system. We consider Bayes' estimator of the system reliability from data consisting of a random sample from the stress distribution and one from the strength distribution when the two distributions are Weibull with equal and known scale parameters. The estimator of λ, ratio of two shape parameters, is also considered. The proposed estimators can be compared with the maximum likelihood estimators (mles). However, the comparison is carried out for single component stress-strength system and the Monte Carlo efficiencies are obtained. It is found that the proposed estimators are better than the corresponding mles.     

Simplified relationships for the probability distribution of the phase of a sine wave in narrow-band normal noise (Corresp.)

A new form of the probability distribution of the phase of a sine wave in narrow-band normal noise is derived. It leads to several different simple expressions for the probability distribution which render the previously required numerical integration of the probability density function unnecessary.     

A study on failure probability of a system including a protecting device

A method to estimate the failure probability is developed on a system including a protecting device, taking account of the delay time to a failure of the system and the initial non-operation time interval of the protecting device. An experimental demonstration was also carried out and a method to estimate the failure probability is analytically discussed in a system including a protecting device.     

Estimation of correct recognition probability by Bayes’ equation in case of not precisely known distribution density

A procedure of estimation of correct recognition probability by Bayes’ equation in the case of not precisely known distribution density is suggested. Expression for error estimation considering inaccuracy of determination of distribution density is obtained. Variants of estimation of correct recognition probability for different sample volumes are resulted.     

A table of the cumulative probability distribution of the phase of a sine wave in narrow-band normal noise (Corresp.)

A table, accurate to ten decimal digits, is provided for the absolute value of the modulo2piphase of a sine wave in narrow-band normal noise. Values are provided at angular increments of 10 degrees, and for values of the root-mean-square sinor-to-noise ratio from 0 to 5 in increments of 0.2.     

Testing equality of means in a bivariate normal population under possible presence of correlation coefficient

In this paper, we have considered for testing the hypothesis H₀: μ₁ = μ₂, in a bivariate normal population N(μ₁,μ₂,σ²,σ²,) when it is suspected that correlation coefficient , may be equal to zero. The expressions for the power and size have been obtained and recommendations regarding use or not of the proposed procedure have also been attempted.     

Fitting a multivariate failure time distribution

A class of continuous multivariate distributions is reviewed. It is derived in a survival/reliability context, where the dependence is modeled as random effects, viz, by an unobserved covariate common to the components in a system and assumed to follow a positive stable distribution. Accounting for censored data is straightforward. The class is well fitted to proportional hazard models, and distributions of minima are simple. An important subfamily is the multivariate Weibull distributions. The theory is illustrated with an example     

Estimation of raindrop size distribution from spaceborne Radar observations

The Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar uses surface reference method to estimate the attenuation encountered in the observation of radar reflectivity. The cumulative attenuation estimated from the surface reference method can be distributed along the radar range using a power law relation between the specific attenuation (k) and reflectivity factor (Z). A physical interpretation of the variability in the k-Z relation can be provided with the normalized drop size distributions. This paper describes an algorithm to estimate the drop size distribution (DSD) parameters from the measured attenuation and reflectivity values obtained from TRMM precipitation radar observations. Coincident data collected with ground polarimetric radar during the TRMM field campaigns is used to cross-validate the estimates of drop size distribution parameters obtained from the TRMM precipitation radar. The results of cross validation show fairly good agreement with the drop size distribution parameters retrieved from TRMM precipitation radar and the ground-radar-based estimates. The algorithm is subsequently used to generate monthly global maps of DSD. The global distribution of DSDs is critically important for development of retrieval algorithms used by the Global Precipitation Mission Radiometers.     

Estimation of probability density function using spectral analysis

The authors present a new bound on the estimation of the probability density function of random signals, using Woodward's theorem, correlation techniques and spectral analysis. The proposed method is based on the spectral analysis of the random process