A Method for Inferring Conditional Stochastic Failure Rates From the Time-History of Observed Failures

2011 ◽  
Author(s):  
David Thompson ◽  
Philippe Pe´bay
Keyword(s):  
First Principles ◽  
Synthetic Data ◽  
Time History ◽  
Random Variable ◽  
Cumulative Damage ◽  
Operating Conditions ◽  
Operating Condition ◽  
History Of ◽  
Mean And Variance ◽  
The Mean

Observed failures, rather than first principles, are used to estimate fatigue rates probabilistically conditioned on operating conditions. The method developed assumes that a normal random variable may be used to approximate the damage limit (remaining lifetime) of components subjected to cumulative damage and that when a component fails, its damage limit has vanished at a rate proportional to the amount of time spent at each operating condition experienced during its lifetime. By considering differences in cumulative damage between pairs of failed components, we obtain the relative rates at which damage is accumulated for each observed operating condition. When the differences in component lifetimes are dominated by variations in experienced conditions, it is possible to estimate absolute rates. Otherwise, variations in initial damage limits dominate and it is only possible to estimate the mean and variance of this distribution. We demonstrate the procedure on synthetic data, including a test for the dominant source of lifetime variations.

Stationary and Transient Response of Cylindrical Shells Under Random Excitation

1988 ◽  
Vol 110 (2) ◽  
pp. 205-209
Author(s):  
A. V. Singh
Keyword(s):  
Transient Response ◽  
Random Vibration ◽  
Time History ◽  
Wide Band ◽  
Random Excitation ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
History Of ◽  
The Mean ◽  
Random Vibration Analysis

This paper presents the random vibration analysis of a simply supported cylindrical shell under a ring load which is uniform around the circumference. The time history of the excitation is assumed to be a stationary wide-band random process. The finite element method and the condition of symmetry along the length of the cylinder are used to calculate the natural frequencies and associated mode shapes. Maximum values of the mean square displacements and velocities occur at the point of application of the load. It is seen that the transient response of the shell under wide band stationary excitation is nonstationary in the initial stages and approaches the stationary solution for large value of time.

Asymptotic properties of the number of replications of a paired comparison

1974 ◽  
Vol 11 (1) ◽  
pp. 43-52 ◽  
Author(s):  
V. R. R. Uppuluri ◽  
W. J. Blot
Keyword(s):  
Paired Comparison ◽  
Beta Function ◽  
Asymptotic Properties ◽  
Random Variable ◽  
Incomplete Beta Function ◽  
Discrete Random Variable ◽  
World Series ◽  
Mean And Variance ◽  
The Mean ◽  
Made In

A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta function with equal arguments is obtained. This expression is used in deriving asymptotic (m-large) expressions for the mean and variance. The standardized variate is shown to converge to the Gaussian distribution as m→ ∞. A result corresponding to the DeMoivre-Laplace limit theorem is proved. Finally applications are made to the genetic code problem, to Banach's Match Box Problem, and to the World Series of baseball.

Time Progression of Hemolysis of Erythrocyte Populations Exposed to Supraphysiological Temperatures

1979 ◽  
Vol 101 (3) ◽  
pp. 213-217 ◽  
Author(s):  
N. A. Moussa ◽  
E. N. Tell ◽  
E. G. Cravalho
Keyword(s):  
Statistical Model ◽  
Distribution Curve ◽  
Time History ◽  
Kinetic Scheme ◽  
First Order ◽  
Arrhenius Dependence ◽  
History Of ◽  
The Mean ◽  
Two Parameters ◽  
Microscope Stage

Populations of erythrocytes in solution were heated “instantaneously” to and maintained at temperatures in the range of 44 to 60°C on a microscope stage specifically designed for this purpose. Simultaneously, the visually observed hemolysis-time history of these cells was measured. The results were successfully correlated on the basis of two models: 1) a kinetic scheme assuming two sequential, first-order reactions by which the cells are first reversibly altered and then irreversibly damaged; and 2) a statistical model for which the number of cells that are damaged at each instant is assumed to be normally distributed. From the experimental data the rate constants for the two reactions in the kinetic model were determined and were found to have an Arrhenius dependence on temperature. By applying the statistical model to the data, we were able to determine the mean and standard deviation of the distribution curve for this model. The logarithms of these latter two parameters vary with temperature in a linear fashion.

The Largest Missing Value in a Sample of Geometric Random Variables

2014 ◽  
Vol 23 (5) ◽  
pp. 670-685 ◽  
Author(s):  
MARGARET ARCHIBALD ◽  
ARNOLD KNOPFMACHER
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Missing Value ◽  
Asymptotic Expressions ◽  
Mean And Variance ◽  
The Mean ◽  
Special Case

We consider samples of n geometric random variables with parameter 0 < p < 1, and study the largest missing value, that is, the highest value of such a random variable, less than the maximum, that does not appear in the sample. Asymptotic expressions for the mean and variance for this quantity are presented. We also consider samples with the property that the largest missing value and the largest value which does appear differ by exactly one, and call this the LMV property. We find the probability that a sample of n variables has the LMV property, as well as the mean for the average largest value in samples with this property. The simpler special case of p = 1/2 has previously been studied, and verifying that the results of the present paper coincide with those previously found for p = 1/2 leads to some interesting identities.

STATISTICAL INFERENCE FOR K INDEPENDENT, HOMOGENEOUS ARITHMETIC PROCESSES

2000 ◽  
Vol 07 (03) ◽  
pp. 223-236 ◽  
Author(s):  
FRANCIS KIT-NAM LEUNG
Keyword(s):  
Stochastic Process ◽  
Linear Regression ◽  
Renewal Process ◽  
Random Variable ◽  
Simple Linear Regression ◽  
Variable Formula ◽  
Mean And Variance ◽  
The Mean ◽  
Time Continuum ◽  
Area Of Application

For k=1,…, K, a stochastic process {An,k, n =1, 2,…} is an arithmetic process (AP) if there exists some real number, d, so that {An,k +(n-1)d, n =1, 2,…} is a renewal process (RP). AP is a stochastically monotonic process and can be used to model a point process, i.e., point events occurring in a haphazard way in time (or space), especially with a trend. For example, the events may be failures arising from a deteriorating machine; and such a series of failures is distributed haphazardly along a time continuum. In this paper, we discuss estimation procedures for K independent, homogeneous APs. Two statistics are suggested for testing whether K given processes come from a common AP. If this is so, we can estimate the parameters d, [Formula: see text] and [Formula: see text] of the AP based on the techniques of simple linear regression, where [Formula: see text] and [Formula: see text] are the mean and variance of the first average random variable [Formula: see text], respectively. In this paper, the procedures are, for the most part, discussed in reliability terminology. Of course, the methods are valid in any area of application, in which case they should be interpreted accordingly.

scholarly journals Estimation of Hazard Rate and Mean Residual Life Ordering for Fuzzy Random Variable

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
S. Ramasubramanian ◽  
P. Mahendran
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Mean Residual Life ◽  
Mean And Variance ◽  
The Mean ◽  
Hazard Rate Ordering ◽  
Fuzzy Random

L2-metric is used to find the distance between triangular fuzzy numbers. The mean and variance of a fuzzy random variable are also determined by this concept. The hazard rate is estimated and its relationship with mean residual life ordering of fuzzy random variable is investigated. Additionally, we have focused on deriving bivariate characterization of hazard rate ordering which explicitly involves pairwise interchange of two fuzzy random variablesXandY.

Characterizing Journey Time Performance on Urban Metro Systems under Varying Operating Conditions

2019 ◽  
Vol 2673 (7) ◽  
pp. 516-528
Author(s):  
Ramandeep Singh ◽  
Daniel J. Graham ◽  
Richard J. Anderson
Keyword(s):  
Service Quality ◽  
Performance Metrics ◽  
Operating Conditions ◽  
Journey Time ◽  
Time Performance ◽  
Mean And Variance ◽  
The Mean ◽  
Metro Systems ◽  
Afternoon Peak ◽  
Public Transport Service

Automated fare collection (AFC) data provide opportunities for improved measurement of public transport service quality from the passenger perspective. In this paper, AFC data from the London Underground are used to measure service quality through an analysis of journey time performance under regular and incident-affected operating conditions. The analysis involves two parts: (i) parametrically defining the shape of journey time distributions, and (ii) defining three performance metrics based on the moments of the distributions to measure the mean and variance of journey times. The metrics show that mean journey times are longest during the afternoon peak across all lines analyzed, and are more variable during the afternoon and off-peak periods depending on the line. Under incident conditions, mean journey times range from 8% to 39% longer compared with regular conditions, depending on the line. Overall, the main application of this work is that the metrics presented here can be directly applied by operators to quantify customer journey time performance, and can be further extended for industry-wide application to compare performance across metro networks.

The statistical analysis of direct repeats in nucleic acid sequences

1985 ◽  
Vol 22 (1) ◽  
pp. 15-24 ◽  
Author(s):  
Rakesh Shukla ◽  
R. C. Srivastava
Keyword(s):  
Nucleic Acid ◽  
Evolutionary History ◽  
Probability Model ◽  
Asymptotic Distributions ◽  
Direct Repeats ◽  
Dna And Rna ◽  
The Central Limit Theorem ◽  
History Of ◽  
Mean And Variance ◽  
The Mean

Sequence symmetries in DNA and RNA are being discovered at an increasing rate. Conjectures and hypotheses are being proposed for their possible structural and functional role in the nucleic acid. In this paper a probability model is studied which evaluates the probabilities of various repeats occurring by chance alone. Expressions are derived for the mean and variance of the statistics employed. The central limit theorem for dependent trials is used to obtain the asymptotic distributions. An indication is given of how to use the model to search for various gene amplification events in the evolutionary history of the sequences.

Aortic Pressure Estimation With Electro-Mechanical Circulatory Assist Devices

1993 ◽  
Vol 115 (2) ◽  
pp. 187-194 ◽  
Author(s):  
J. F. Gardner ◽  
M. Ignatoski ◽  
U. Tasch ◽  
A. J. Snyder ◽  
D. B. Geselowitz
Keyword(s):  
Initial Conditions ◽  
Circulatory System ◽  
Time History ◽  
Aortic Pressure ◽  
Operating Conditions ◽  
Observer Performance ◽  
Mean Deviation ◽  
Mock Circulatory System ◽  
The Mean

An adaptive technique for the estimation of the time history of aortic pressure (from applied voltage and position feedback) has been designed, implemented, and bench tested using the Penn State Electric Ventricular Assist Device (EVAD). This method, known in the field of automatic control as a dynamic observer, utilizes gains which were determined using experimental data collected while the EVAD was running on a mock circulatory system. An adaptive scheme provides the observer with a method of changing its initial conditions on a stroke-by-stroke basis which improves observer performance. In both determining the feedback gains and developing the adaptation scheme, a range of beat rates and pressure loads was taken into account to yield satisfactory observer performance over a range of operating conditions. The observer was implemented, its performance was verified in vitro and results are reported. In the six experimental operating conditions, the beat rate ranged from 56-104 beats per minute (bpm) and the span of the mean systolic aortic pressure was 10.7-18.7 kPa (80–140 mmHg). For these cases, the mean deviation between the actual and estimated aortic pressure during the latter two-thirds of systole was 0.41 kPa (3.1 mmHg).

scholarly journals Heteroscedastic Ensemble Postprocessing

2014 ◽  
Vol 142 (9) ◽  
pp. 3484-3502 ◽  
Author(s):  
Elizabeth A. Satterfield ◽  
Craig H. Bishop
Keyword(s):  
Posterior Distribution ◽  
Synthetic Data ◽  
Error Variance ◽  
Sample Variance ◽  
Ensemble Prediction ◽  
Analytic Approximation ◽  
True Error ◽  
Ensemble Forecasts ◽  
Mean And Variance ◽  
The Mean

Ensemble variances provide a prediction of the flow-dependent error variance of the ensemble mean or, possibly, a high-resolution forecast. However, small ensemble size, unaccounted for model error, and imperfections in ensemble generation schemes cause the predictions of error variance to be imperfect. In previous work, the authors developed an analytic approximation to the posterior distribution of true error variances, given an imperfect ensemble prediction, based on parameters recovered from long archives of innovation and ensemble variance pairs. This paper shows how heteroscedastic postprocessing enables climatological information to be blended with ensemble forecast information when information about the distribution of true error variances given an ensemble sample variance is available. A hierarchy of postprocessing methods are described, each graded on the amount of information about the posterior distribution of error variances used in the postprocessing. These homoscedastic methods are used to assess the value of knowledge of the mean and variance of the posterior distribution of error variances to ensemble postprocessing and explore sensitivity to various parameter regimes. Testing was performed using both synthetic data and operational ensemble forecasts of a Gaussian-distributed variable, to provide a proof-of-concept demonstration in a semi-idealized framework. Rank frequency histograms, weather roulette, continuous ranked probability score, and spread-skill diagrams are used to quantify the value of information about the posterior distribution of error variances. It is found that ensemble postprocessing schemes that utilize the full distribution of error variances given the ensemble sample variance outperform those that do not.

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