Statistical models for protein validation using tandem mass spectral data and protein amino acid sequence databases

The purpose of this work is to develop and verify statistical models for protein identification using peptide identifications derived from the results of tandem mass spectral database searches. Recently we have presented a probabilistic model for peptide identification that uses hypergeometric distribution to approximate fragment ion matches of database peptide sequences to experimental tandem mass spectra. Here we apply statistical models to the database search results to validate protein identifications. For this we formulate the protein identification problem in terms of two independent models, two-hypothesis binomial and multinomial models, which use the hypergeometric probabilities and cross-correlation scores, respectively. Each database search result is assumed to be a probabilistic event. The Bernoulli event has two outcomes: a protein is either identified or not. The probability of identifying a protein at each Bernoulli event is determined from relative length of the protein in the database (the null hypothesis) or the hypergeometric probability scores of the protein's peptides (the alternative hypothesis). We then calculate the binomial probability that the protein will be observed a certain number of times (number of database matches to its peptides) given the size of the data set (number of spectra) and the probability of protein identification at each Bernoulli event. The ratio of the probabilities from these two hypotheses (maximum likelihood ratio) is used as a test statistic to discriminate between true and false identifications. The significance and confidence levels of protein identifications are calculated from the model distributions. The multinomial model combines the database search results and generates an observed frequency distribution of cross-correlation scores (grouped into bins) between experimental spectra and identified amino acid sequences. The frequency distribution is used to generate p-value probabilities of each score bin. The probabilities are then normalized with respect to score bins to generate normalized probabilities of all score bins. A protein identification probability is the multinomial probability of observing the given set of peptide scores. To reduce the effect of random matches, we employ a marginalized multinomial model for small values of cross-correlation scores. We demonstrate that the combination of the two independent methods provides a useful tool for protein identification from results of database search using tandem mass spectra. A receiver operating characteristic curve demonstrates the sensitivity and accuracy level of the approach. The shortcomings of the models are related to the cases when protein assignment is based on unusual peptide fragmentation patterns that dominate over the model encoded in the peptide identification process. We have implemented the approach in a program called PROT_PROBE.     

2D C/SiC复合材料的可靠性评价

采用概率论和数理统计方法, 以研究分析2D C/SiC复合材料的弯曲强度分布规律为切入点, 比较了失效概率预测值与实验值, 用可靠度、 风险函数和可靠强度评价了该材料可靠性。通过线性回归分析和拟合优度检验得到正态、 对数正态和三参数Weibull分布模型均可表征其弯曲强度分布规律; 确定了该材料弯曲强度失效概率、 可靠度函数、 风险函数和可靠强度的数学模型中的参数, 可以预测给定强度条件和许用可靠度条件下的多种可靠性指标; 材料弯曲强度均值的三种模型预测值与实测值最大相对误差仅0.07%, 计算得到的失效概率曲线与实验弯曲强度的失效分布均符合很好。      

人的可靠性综合分析模式及应用

提高系统可靠性的关键步骤是提高系统中人的可靠性,这需要对人的可靠性进行分析。当前分析人的可靠性主要依靠运用各类HRA模型,这些模型各有优缺点。为了研究航空人为差错,选取了具有代表性的3个HRA模型,对人的可靠性分析模型THERP（technique for human error rate prediction)、CREAM（cognitive reliability and error analysis method)、IDAC(information decision and action)进行了分析。将3种模型进行比较,找出它们的优劣之处,结合3种模型的优点,建立了以THERP模型、CREAM模型以及IDAC模型为主体的人的可靠性综合分析模式,并将该分析模式在航空人为差错分析上进行了应用,并给出实例说明该分析模式的应用。     

The Effect of Estimation Error on Risk‐Adjusted Survival Time CUSUM Chart Performance

Research on risk‐adjusted control charts has gained great interest in healthcare settings. Based on monitored variables (binary outcome or survival times), risk‐adjusted cumulative sum (CUSUM) charts are divided into Bernoulli and survival time CUSUM charts. The effect of estimation error on control chart performance has been systematically studied for Bernoulli CUSUM but not for survival time CUSUM in continuous time. We investigate the effect of estimation error on the performance of risk‐adjusted survival time CUSUM scheme in continuous time with the cardiac surgery data. The impact is studied with the use of the median run lengths (medRLs) and the standard deviation (SD) of medRLs for different sample sizes, specified in‐control median run length, adverse event rate and patient variability. Results show that estimation error affects the performance of risk‐adjusted survival time CUSUM chart significantly and the performance is more sensitive to the specified in‐control median run length (medRL₀) and adverse event rate. To take the estimation error into account, the practitioners can bootstrap many samples from Phase I data and then determine the threshold that can guarantee at least a medRL₀ with certain probability under which false alarms occur less frequently and meanwhile out‐of‐control alarms don't signal too slow. Moreover, additional event occurrences can be used to update the estimation but should be from in‐control process. Finally, non‐parametric bootstrap can be applied to reduce model misspecification error. Copyright © 2015 John Wiley & Sons, Ltd.     

Reduction of the Effect of Estimation Error on In‐control Performance for Risk‐adjusted Bernoulli CUSUM Chart with Dynamic Probability Control Limits

The in‐control performance of any control chart is highly associated with the accuracy of estimation for the in‐control parameter(s). For the risk‐adjusted Bernoulli cumulative sum (CUSUM) chart with a constant control limit, it had been shown that the estimation error could have a substantial effect on the in‐control performance. In our study, we examine the effect of estimation error on the in‐control performance of the risk‐adjusted Bernoulli CUSUM chart with dynamic probability control limits (DPCLs). Our simulation results show that the in‐control performance of risk‐adjusted Bernoulli CUSUM chart with DPCLs is also affected by the estimation error. The most important factors affecting estimation error are the specified desired in‐control average run length, the Phase I sample size, and the adverse event rate. However, the effect of estimation error is uniformly smaller for the risk‐adjusted Bernoulli CUSUM chart with DPCLs than for the corresponding chart with a constant control limit under various realistic scenarios. In addition, we found a substantial reduction in the mean and variation of the standard deviation of the in‐control run length when DPCLs are used. Therefore, use of DPCLs has yet another advantage when designing a risk‐adjusted Bernoulli CUSUM chart. Copyright © 2016 John Wiley & Sons, Ltd.     

Looking for errors of omission and commission or The Hunting of the Snark revisited

Since the early 1990s, considerable effort has been spent to understand what is meant by an “error of commission” (EOC), to complement the traditional notion of an “error of omission” (EOO). This paper argues that the EOO–EOC dyad, as an artefact of the PSA event tree, is insufficient for human reliability analysis (HRA) for several reasons: (1) EOO–EOC fail to distinguish between manifestation and cause; (2) EOO–EOC refer to classes of incorrect actions rather than to specific instances; (3) there is no unique way of classifying an event using EOO–EOC; (4) the set of error modes that cannot reasonably be classified as EOO is too diverse to fit into any single category of its own. Since the use of EOO–EOC leads to serious problems for HRA, an alternative is required. This can be found in the concept of error modes, which has a long history in risk analysis. A specific system for error mode prediction was tested in a simulator experiment. The analysis of the results showed that error modes could be qualitatively predicted with sufficient accuracy (68% correct) to propose this method as a way to determine how operator actions can fail in PSA-cum-HRA. Although this still leaves the thorny issue of quantification, a consistent prediction of error modes provides a better starting point for determining probabilities than the EOO–EOC dyad. It also opens a possibility for quantification methods where the influence of the common performance conditions is prior to and more important than individual failure rates.     

Matrix-based system reliability method and applications to bridge networks

Using a matrix-based system reliability (MSR) method, one can estimate the probabilities of complex system events by simple matrix calculations. Unlike existing system reliability methods whose complexity depends highly on that of the system event, the MSR method describes any general system event in a simple matrix form and therefore provides a more convenient way of handling the system event and estimating its probability. Even in the case where one has incomplete information on the component probabilities and/or the statistical dependence thereof, the matrix-based framework enables us to estimate the narrowest bounds on the system failure probability by linear programming. This paper presents the MSR method and applies it to a transportation network consisting of bridge structures. The seismic failure probabilities of bridges are estimated by use of the predictive fragility curves developed by a Bayesian methodology based on experimental data and existing deterministic models of the seismic capacity and demand. Using the MSR method, the probability of disconnection between each city/county and a critical facility is estimated. The probability mass function of the number of failed bridges is computed as well. In order to quantify the relative importance of bridges, the MSR method is used to compute the conditional probabilities of bridge failures given that there is at least one city disconnected from the critical facility. The bounds on the probability of disconnection are also obtained for cases with incomplete information.     

RISK DISK: A PC decision aid for human performance analysis

RISK DISK_CR is a set of IBM compatible PC diskettes that provide estimates from data, of the probabilities that certain tasks are finished within relevant time limits (windows) by different agents (crews). An important application is to performance of time-sensitive safety-related human interactions required during nuclear power plant operation.

The probability of satisfactory performance may be assessed from nuclear plant-specific data, augmented by other relevant data as desired, using modified log-normal and Weibull models. Procedures for assessing model fit, and for deriving informative error bounds, are made available.

There is no implication that RISK DISK actually calculates risk, in the sense of probability of an event multiplied by its consequence or penalty.     

Treatment of uncertainties in space nuclear risk assessment with examples from Cassini mission applications

By means of several examples from a recent comprehensive space nuclear risk analysis of the Cassini mission, a scenario and consequence representational framework is presented for risk analysis of space nuclear power systems in the context of epistemic and aleatory uncertainties. The framework invites the use of probabilistic models for the calculation of both event probabilities and scenario consequences. Each scenario is associated with a frequency that may include both aleatory and epistemic uncertainties. The outcome of each scenario is described in terms of an end state vector. The outcome of each scenario is also characterized by a source term. In this paper, the source term factors of interest are number of failed clads in the space nuclear power system, amount of fuel released and amount of fuel that is potentially respirable. These are also subject to uncertainties. The 1990 work of Apostolakis is found to be a useful formalism from which to derive the relevant probabilistic models. However, an extension to the formalism was necessary to accommodate the situation in which aleatory uncertainty is represented by changes in the form of the probability function itself, not just its parameters. Event trees that show reasonable alternative accident scenarios are presented. A grouping of probabilities and consequences is proposed as a useful structure for thinking about uncertainties. An example of each category is provided. Concluding observations are made about the judgments involved in this analysis of uncertainties and the effect of distinguishing between aleatory and epistemic uncertainties.     

On the ensemble crossing rate approach to time variant reliability analysis of uncertain structures

The ‘ensemble’ up-crossing rate technique consists of averaging the rate at which a random load process up-crosses a deterministic barrier level over the resistance distribution at successive time points. Averaging over the resistance makes the assumption of independent up-crossings less appropriate. As a result, first passage failure probabilities may become excessively conservative in problems with other than extremely low failure probabilities. The ensemble up-crossing rate technique has a significant potential in simplifying the solution of time variant reliability problems under resistance degradation. However, little is known about the quality of this approximation or its limits of application. In the paper, a Monte Carlo simulation-based methodology is developed to predict the error in the approximation. An error parameter is identified and error functions are constructed. The methodology is applied to a range of time-invariant and time-variant random barriers, and it is shown that the error in the original ensemble up-crossing rate approximation is largely reduced. The study provides unprecedented insight into characteristics of the ensemble up-crossing rate approximation.     

基于非Gauss风载的高耸结构风振可靠性分析

基于风载非Gauss模型推导了Davenport谱下结构脉动风载的五阶统计矩表达。通过响应概率特征函数和Fourier变换,求得Gram-Charlier级数形式的振形位移和速度响应联合概率统计分布。利用Rice公式和Poisson假设,研究了不同风载模型对高耸结构风振可靠性分析结果的影响。算例分析表明:高耸结构风振可靠性分析需要采用风载非Gauss模型;模态位移和速度响应的联合概率统计分布在截断于五阶Hermite多项式时具有较好精度;可以引入模态位移与速度独立性假设以简化高耸结构风振可靠性分析,计算结果是偏于安全的。     

Error-based stopping criterion for the combined adaptive Kriging and importance sampling method for reliability analysis

Metamodel-based method is a wise reliability analysis technique because it uses the metamodel to substitute the actual limit state function under the predefined accuracy. Adaptive Kriging (AK) is a famous metamodel in reliability analysis for its flexibility and efficiency. AK combined with the importance sampling (IS) method abbreviate as AK–IS can extremely reduce the size of candidate sampling pool in the updating process of Kriging model, which makes the AK-based reliability method more suitable for estimating the small failure probability. In this paper, an error-based stopping criterion of updating the Kriging model in the AK–IS method is constructed and two considerable maximum relative error estimation methods between the failure probability estimated by the current Kriging model and the limit state function are derived. By controlling the maximum relative error, the accuracy of the estimate can be adjusted flexibly. Results in three case studies show that the error-based stopping criterion based AK–IS method can achieve the predefined accuracy level and simultaneously enhance the efficiency of updating the Kriging model.     

Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states-perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of "excess" zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to "excess" zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed-and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros.     

Product quality inspection in Bernoulli lines: analysis,bottlenecks, and design

This paper is devoted to serial production lines consisting of producing and inspection machines that obey the Bernoulli reliability and Bernoulli quality models. Such production lines are encountered in automotive assembly and painting operations where the downtime is relatively short and the defects are due to uncorrelated random events. For these systems, this paper develops analytical methods for performance analysis, bottleneck identification, and design. In addition, insights into the nature of bottlenecks in such systems are provided, and an empirical rule for placing an inspection machine that maximises the production rate of non-defectives is formulated.     

Human reliability analysis for manned submersible diving process based on CREAM and Bayesian network

The diving mission of manned submersibles is a long‐term, high‐intensity work that is affected by many factors and is in a narrow confined space. In order to improve the reliability of oceanauts' safe operations, this paper is based on the cognitive reliability and error analysis method (CREAM) and the Bayesian network method to study the human errors of the diving mission. First, we construct a Bayesian network framework of the diving process by analyzing the diving steps. Second, the CREAM is applied to calculate the prior probability of each root node's error. Then, the backward reasoning ability of the Bayesian network is used to calculate the posterior probabilities and identify the top few risk nodes. Finally, we obtained the top few risk factors. Among them, we find that the light distribution design in the risk nodes is the more influential risk factor, so a brief design is made on them.     

Some Tests for Variance Components Using Generalized p Values

The concept of a generalized p value, introduced by Tsui and Weerahandi, is applied for testing hypotheses in two situations, testing the significance of a variance component in a general balanced mixed model when an exact F test does not exist and comparing randomeffects variance components in two independent balanced mixed models. Extensions to the unbalanced cases are also indicated. The proposed test is compared with the test based on the Satterthwaite approximation through their simulated Type I error probabilities. The simulations indicate that the test based on the generalized p value hasType I error probabilities less than the chosen significance level most of the time, whereas the Type I error probabilities of the Satterthwaite approximate test can be much larger than the significance level. The results are illustrated using two examples.     

Reliability Modelling of Multiple Repairable Units

This paper proposes a model selection framework for analysing the failure data of multiple repairable units when they are working in different operational and environmental conditions. The paper provides an approach for splitting the non‐homogeneous failure data set into homogeneous groups, based on their failure patterns and statistical trend tests. In addition, when the population includes units with an inadequate amount of failure data, the analysts tend to exclude those units from the analysis. A procedure is presented for modelling the reliability of a multiple repairable units under the influence of such a group to prevent parameter estimation error. We illustrate the implementation of the proposed model by applying it on 12 frequency converters in the Swedish railway system. The results of the case study show that the reliability model of multiple repairable units within a large fleet may consist of a mixture of different stochastic models, that is, the homogeneous Poisson process/renewal process, trend renewal process, non‐homogeneous Poisson process and branching Poisson processes. Therefore, relying only on a single model to represent the behaviour of the whole fleet may not be valid and may lead to wrong parameter estimation. Copyright © 2015 John Wiley & Sons, Ltd.     

Reliability Forecasting of a Load‐Haul‐Dump Machine: A Comparative Study of ARIMA and Neural Networks

Both the autoregressive integrated moving average (ARIMA or the Box–Jenkins technique) and artificial neural networks (ANNs) are viable alternatives to the traditional reliability analysis methods (e.g., Weibull analysis, Poisson processes, non‐homogeneous Poisson processes, and Markov methods). Time series analysis of the times between failures (TBFs) via ARIMA or ANNs does not have the limitations of the traditional methods such as requirements/assumptions of a priori postulation and/or statistically independent and identically distributed observations for TBFs. The reliability of an LHD unit was investigated by analysis of TBFs. Seasonal autoregressive integrated moving average (SARIMA) was employed for both modeling and forecasting the failures. The results were compared with a genetic algorithm‐based (ANNs) model. An optimal ARIMA model, after a Box–Cox transformation of the cumulative TBFs, outperformed ANNs in forecasting the LHD's TBFs. Copyright © 2015 John Wiley & Sons, Ltd.     

Real-time monitoring of events applied to syndromic surveillance

Abstract

This article focuses on monitor plans aimed at the early detection of the increase in the frequency of events. The literature recommends either monitoring the time between events (TBE) if events are rare or counting the number of events per unit non-overlapping time intervals otherwise. Some authors advocate using the Bernoulli model for rare events, applying presence or absence of events within non-overlapping and exhaustive time intervals. This Bernoulli model does improve the real-time monitoring assessment of these events compared to counting events over a larger interval, making them less rare. However this approach became inefficient if more than one event starts occurring within the intervals. Monitoring TBE is the real-time option for outbreak detection, because outbreak information is accumulated when an event occurs. This is preferred to waiting for the end of a period to count events. If the TBE reduces significantly, then the incidence of these events increases significantly. This article explores this TBE option relative to using the monitoring of counts when the TBEs are either Exponentially, Gamma or Weibull distributed for moderately low count scenarios. The article will discuss and compare the approaches of using an Exponentially Weighted Moving Average (EWMA) statistic for the TBEs to the EWMA of counts. Several robust options will be considered when the future change in event frequency is unknown. Our goal is to have a robust monitoring plan which is able to efficiently detect many different levels of shifts. These robust plans are compared to the more traditional event monitoring plans for both small and large changes in the event frequency.     

A Bayesian model averaging method for software reliability modeling and assessment

The software reliability modeling is of great significance in improving software quality and managing the software development process. However, the existing methods are not able to accurately model software reliability improvement behavior because existing single model methods rely on restrictive assumptions and combination models cannot well deal with model uncertainties. In this article, we propose a Bayesian model averaging (BMA) method to model software reliability. First, the existing reliability modeling methods are selected as the candidate models, and the Bayesian theory is used to obtain the posterior probabilities of each reliability model. Then, the posterior probabilities are used as weights to average the candidate models. Both Markov Chain Monte Carlo (MCMC) algorithm and the Expectation–Maximization (EM) algorithm are used to evaluate a candidate model's posterior probability and for comparison purpose. The results show that the BMA method has superior performance in software reliability modeling, and the MCMC algorithm performs better than EM algorithm when they are used to estimate the parameters of BMA method.