The negative log-gamma prior distribution for Bayesian assessment of system reliability

2017 ◽  
Vol 232 (3) ◽  
pp. 308-319 ◽  
Author(s):  
Roger Zoh ◽  
Alyson Wilson ◽  
Scott Vander Wiel ◽  
Earl Lawrence
Keyword(s):  
Data Collection ◽  
Gamma Distribution ◽  
System Reliability ◽  
Prior Distribution ◽  
Scale Parameter ◽  
Time Varying ◽  
Prior Distributions ◽  
Reliability Problem ◽  
Series Systems

This paper presents the negative log-gamma distribution as a prior distribution useful for Bayesian assessment of system reliability. When the scale parameter is held fixed, the negative log-gamma distribution is closed under products, making it convenient for specifying priors for series systems. In particular, for series systems, negative log-gamma component priors can be specified to give an exact desired system prior and vice versa. We consider pass/fail data at the system and component levels for both static and time-varying data collection schemes and propose two new prior distributions for analyzing time-varying reliability. Finally, we consider an application of the negative log-gamma to a missile reliability problem and illustrate diagnostics useful for developing the priors.

scholarly journals Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation

1989 ◽  
Vol 12 (4) ◽  
pp. 797-804
Author(s):  
M. E. Ghitany ◽  
W. H. Laverty
Keyword(s):  
Mean Square Error ◽  
Gamma Distribution ◽  
Bayesian Approach ◽  
Prior Distribution ◽  
Scale Parameter ◽  
Random Variable ◽  
Minimum Variance ◽  
Reliability Estimation ◽  
Mean Square ◽  
The Mean

In this paper we discuss the behavlor of the statisticR^(t), the uniformly minimum variance unbiased (UMVU) estimate for the reliability of gamma distribution with unknown scale parameterσwhen an outlier observation is present. Given the outlier effect onσ, we determine bounds for the mean and mean square error (MSE) of R(t). A semi-Bayesian approach is discussed when the outlier effect onσis treated as a random variable having a prior distribution of beta type. Results of the exponential distribution (Sinha [1]) are given as particular cases of our results.

scholarly journals Integrated sample-handling and mounting system for fixed-target serial synchrotron crystallography

2021 ◽  
Vol 77 (5) ◽  
pp. 628-644
Author(s):  
Gabrielle Illava ◽  
Richard Jayne ◽  
Aaron D. Finke ◽  
David Closs ◽  
Wenjie Zeng ◽  
...  
Keyword(s):  
Data Collection ◽  
Integrated System ◽  
Ease Of Use ◽  
Time Varying ◽  
Fixed Target ◽  
Sample Handling ◽  
Small Crystals ◽  
Fixed Orientation ◽  
Common Problems ◽  
Liquid Flows

Serial synchrotron crystallography (SSX) is enabling the efficient use of small crystals for structure–function studies of biomolecules and for drug discovery. An integrated SSX system has been developed comprising ultralow background-scatter sample holders suitable for room and cryogenic temperature crystallographic data collection, a sample-loading station and a humid `gloveless' glovebox. The sample holders incorporate thin-film supports with a variety of designs optimized for different crystal-loading challenges. These holders facilitate the dispersion of crystals and the removal of excess liquid, can be cooled at extremely high rates, generate little background scatter, allow data collection over >90° of oscillation without obstruction or the risk of generating saturating Bragg peaks, are compatible with existing infrastructure for high-throughput cryocrystallography and are reusable. The sample-loading station allows sample preparation and loading onto the support film, the application of time-varying suction for optimal removal of excess liquid, crystal repositioning and cryoprotection, and the application of sealing films for room-temperature data collection, all in a controlled-humidity environment. The humid glovebox allows microscope observation of the sample-loading station and crystallization trays while maintaining near-saturating humidities that further minimize the risks of sample dehydration and damage, and maximize working times. This integrated system addresses common problems in obtaining properly dispersed, properly hydrated and isomorphous microcrystals for fixed-orientation and oscillation data collection. Its ease of use, flexibility and optimized performance make it attractive not just for SSX but also for single-crystal and few-crystal data collection. Fundamental concepts that are important in achieving desired crystal distributions on a sample holder via time-varying suction-induced liquid flows are also discussed.

Fatigue Reliability and Inspection of TLP Tendon System

1991 ◽  
Vol 28 (02) ◽  
pp. 99-110
Author(s):  
Maria Celia C. Ximenes
Keyword(s):  
Order Statistics ◽  
System Reliability ◽  
Fatigue Reliability ◽  
Tension Leg Platform ◽  
Reliability Problem ◽  
Failure Path ◽  
Solution Methods

The collapse of a tension leg platform (TLP) tendon system due to progressive fatigue of several joints is investigated. Two solution methods for the system reliability problem are proposed. The first method is based on the failure path approach and the second on the order statistics approach. The effects of redundancy and uncertainties involved in the problem are analyzed. Inspection of selected joints is also included in order to evaluate its impact on system reliability.

scholarly journals A channel-based perspective on conjugate priors

2020 ◽  
Vol 30 (1) ◽  
pp. 44-61 ◽  
Author(s):  
B. Jacobs
Keyword(s):  
Statistical Model ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Closure Property ◽  
Bayesian Probability ◽  
Conjugate Prior ◽  
Prior Distributions ◽  
Graphical Language ◽  
Conjugate Priors ◽  
Abstract Formulation

AbstractA desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions – say Gaussians – as the prior distribution. When the updating takes place via a statistical model, one calls the class of prior distributions the ‘conjugate priors’ of the model. This paper gives (1) an abstract formulation of this notion of conjugate prior, using channels, in a graphical language, (2) a simple abstract proof that such conjugate priors yield Bayesian inversions and (3) an extension to multiple updates. The theory is illustrated with several standard examples.

scholarly journals Integrating Probability and Nonprobability Samples for Survey Inference

2020 ◽  
Vol 8 (1) ◽  
pp. 120-147 ◽  
Author(s):  
Arkadiusz Wiśniowski ◽  
Joseph W Sakshaug ◽  
Diego Andres Perez Ruiz ◽  
Annelies G Blom
Keyword(s):  
Data Collection ◽  
Linear Model ◽  
Survey Data ◽  
Simulated Data ◽  
Empirical Literature ◽  
Informative Priors ◽  
Small Probability ◽  
Prior Distributions ◽  
Probability Sampling ◽  
Mean Squared Errors

Abstract Survey data collection costs have risen to a point where many survey researchers and polling companies are abandoning large, expensive probability-based samples in favor of less expensive nonprobability samples. The empirical literature suggests this strategy may be suboptimal for multiple reasons, among them that probability samples tend to outperform nonprobability samples on accuracy when assessed against population benchmarks. However, nonprobability samples are often preferred due to convenience and costs. Instead of forgoing probability sampling entirely, we propose a method of combining both probability and nonprobability samples in a way that exploits their strengths to overcome their weaknesses within a Bayesian inferential framework. By using simulated data, we evaluate supplementing inferences based on small probability samples with prior distributions derived from nonprobability data. We demonstrate that informative priors based on nonprobability data can lead to reductions in variances and mean squared errors for linear model coefficients. The method is also illustrated with actual probability and nonprobability survey data. A discussion of these findings, their implications for survey practice, and possible research extensions are provided in conclusion.

scholarly journals Robust Bayesian Sensitivity Analysis for Case–Control Studies with Uncertain Exposure Misclassification Probabilities

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Timothy Shin Heng Mak ◽  
Nicky Best ◽  
Lesley Rushton
Keyword(s):  
Prior Distribution ◽  
Odds Ratio ◽  
Case Control ◽  
Sensitivity Analyses ◽  
Feasible Region ◽  
Exposure Misclassification ◽  
Case Control Studies ◽  
Unknown Parameters ◽  
Prior Distributions ◽  
Posterior Inference

AbstractExposure misclassification in case–control studies leads to bias in odds ratio estimates. There has been considerable interest recently to account for misclassification in estimation so as to adjust for bias as well as more accurately quantify uncertainty. These methods require users to elicit suitable values or prior distributions for the misclassification probabilities. In the event where exposure misclassification is highly uncertain, these methods are of limited use, because the resulting posterior uncertainty intervals tend to be too wide to be informative. Posterior inference also becomes very dependent on the subjectively elicited prior distribution. In this paper, we propose an alternative “robust Bayesian” approach, where instead of eliciting prior distributions for the misclassification probabilities, a feasible region is given. The extrema of posterior inference within the region are sought using an inequality constrained optimization algorithm. This method enables sensitivity analyses to be conducted in a useful way as we do not need to restrict all of our unknown parameters to fixed values, but can instead consider ranges of values at a time.

scholarly journals Distribution of Myosin Attachment Times Predicted from Viscoelastic Mechanics of Striated Muscle

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Bradley M. Palmer ◽  
Yuan Wang ◽  
Mark S. Miller
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Shape Parameter ◽  
Striated Muscle ◽  
Scale Parameter ◽  
Viscoelastic Model ◽  
A Value ◽  
Temporal Events ◽  
Single Exponential

We demonstrate that viscoelastic mechanics of striated muscle, measured as elastic and viscous moduli, emerge directly from the myosin crossbridge attachment time,tatt, also called time-on. The distribution oftattwas modeled using a gamma distribution with shape parameter,p, and scale parameter,β. At 5 mM MgATP,βwas similar between mouseα-MyHC (16.0±3.7 ms) andβ-MyHC (17.9±2.0 ms), andpwas higher (P<0.05) forβ-MyHC (5.6±0.4no units) compared toα-MyHC (3.2±0.9). At 1 mM MgATP,papproached a value of 10 in both isoforms, butβrose only in theβ-MyHC (34.8±5.8 ms). The estimated meantatt(i.e.,pβproduct) was longer in theβ-MyHC compared toα-MyHC, and became prolonged in both isoforms as MgATP was reduced as expected. The application of our viscoelastic model to these isoforms and varying MgATP conditions suggest thattattis better modeled as a gamma distribution due to its representing multiple temporal events occurring withintattcompared to a single exponential distribution which assumes only one temporal event withintatt.

A Novel Time-Variant Reliability Analysis Method Based on Failure Processes Decomposition for Dynamic Uncertain Structures

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Shui Yu ◽  
Zhonglai Wang
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Dynamic Properties ◽  
Limit State ◽  
Quadratic Function ◽  
State Function ◽  
Analysis Method ◽  
Engineering Structures ◽  
Reliability Problem ◽  
Time Invariant

Abstract Due to the uncertainties and the dynamic parameters from design, manufacturing, and working conditions, many engineering structures usually show uncertain and dynamic properties. This paper proposes a novel time-variant reliability analysis method using failure processes decomposition to transform the time-variant reliability problems to the time-invariant problems for dynamic structures under uncertainties. The transformation is achieved via a two-stage failure processes decomposition. First, the limit state function with high dimensional input variables and high order temporal parameters is transformed to a quadratic function of time based on the optimized time point in the first-stage failure processes decomposition. Second, based on the characteristics of the quadratic function and reliability criterion, the time-variant reliability problem is then transformed to a time-invariant system reliability problem in the second-stage failure processes decomposition. Then, the kernel density estimation (KDE) method is finally employed for the system reliability evaluation. Several examples are used to verify the effectiveness of the proposed method to demonstrate its efficiency and accuracy.

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