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Estimation of Failure Probability and Its Applications in Lifetime Data Analysis (2011)

Han, Ming

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-6. Published 2011 Jan 01. doi: 10.1155/2011/719534.

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Publikationsdatum: 2011-01-01

Beschreibung: Since Lindley and Smith introduced the idea of hierarchical prior distribution, some results have been obtained on hierarchical Bayesian method to deal with lifetime data. But all those results obtained by means of hierarchical Bayesian methods involve complicated integration compute. Though some computing methods such as Markov Chain Monte Carlo (MCMC) are available, doing integration is still very inconvenient for practical problems. This paper introduces a new method, named E-Bayesian estimation method, to estimate failure probability. In the case of one hyperparameter, the definition of E-Bayesian estimation of the failure probability is provided; moreover, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation and the property of E-Bayesian estimation of the failure probability are also provided. Finally, calculation on practical problems shows that the provided method is feasible and easy to perform.

Print ISSN: 1687-7144

Digitale ISSN: 1687-7152

Thema: Mathematik

Publiziert von Hindawi

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Bayes Estimation of Change Point in Discrete Maxwell Distribution (2011)

Pandya, Mayuri ; Pandya, Hardik

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-8. Published 2011 Jan 01. doi: 10.1155/2011/395034.

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Publikationsdatum: 2011-01-01

Beschreibung: A sequence of independent lifetimes X1,…,Xm,Xm+1,…,Xn was observed from Maxwell distribution with reliability r1(t) at time t but later, it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in reliability r2(t) at time t. The Bayes estimators of m, θ1, θ2 are derived under different asymmetric loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

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Thema: Mathematik

Publiziert von Hindawi

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On MEMS Reliability and Failure Mechanisms (2011)

Fonseca, Daniel J. ; Sequera, Miguel

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-7. Published 2011 Jan 01. doi: 10.1155/2011/820243.

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Publikationsdatum: 2011-01-01

Beschreibung: Microelectromechanical systems (MEMS) are a fast-growing field in microelectronics. MEMS are commonly used as actuators and sensors with a wide variety of applications in health care, automotives, and the military. The MEMS production cycle can be classified as three basic steps: (1) design process, (2) manufacturing process, and (3) operating cycle. Several studies have been conducted for steps (1) and (2); however, information regarding operational failure modes in MEMS is lacking. This paper discusses reliability in the context of MEMS functionality. It also presents a brief review of the most relevant failure mechanisms for MEMS.

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Thema: Mathematik

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Estimation of Reliability for a Two Component Survival Stress-Strength Model (2011)

Munoli, S. B. ; Mutkekar, Rohit R.

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-8. Published 2011 Jan 01. doi: 10.1155/2011/721962.

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Publikationsdatum: 2011-01-01

Beschreibung: The reliability function for a parallel system of two identical components is derived from a stress-strength model, where failure of one component increases the stress on the surviving component of the system. The Maximum Likelihood Estimators of parameters and their asymptotic distribution are obtained. Further the Maximum Likelihood Estimator and Bayes Estimator of reliability function are obtained using the data from a life-testing experiment. Computation of estimators is illustrated through simulation study.

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Thema: Mathematik

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On the Charting Procedures:T2Chart and DD-Diagram (2011)

Hajlaoui, Mekki

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-8. Published 2011 Jan 01. doi: 10.1155/2011/830764.

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Publikationsdatum: 2011-01-01

Beschreibung: Multivariate analysis is increasingly used to include all dimensions of quality concept, in light of rapid development of customer requirements. With the recent advances in information technology and in recording, large amounts of multivariate data are now needed to be analyzed. Many charting procedures are based on Mahalanobis distance, but their applicability relies heavily on the requirement of normality and their performance is related to the choice of a type I error rate. An alternative charting scheme based on data depth is pursued and its performance is assessed through a real example. This performance and that of aT2chart for individual observations are discussed. Using the centre-outward ranking, this new method named DD-diagram is used to detect any multivariate quality datum that one of its components exceeds its limiting variation interval. For a given error-free sample, the DD-diagram can be used to signal out any point of another observed sample taken from a multivariate quality process. This new scheme based on data depth uses a properly chosen limiting variation line orLvaluein order to evaluate the outlyingness of every point in the observed sample in all directions of the consideredP-variates of quality process.

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Thema: Mathematik

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Coding ATC Incident Data Using HFACS: Intercoder Consensus (2011)

Wang, Liang ; Wang, Yaohua ; Yang, Xiaoqiang ; [weitere]

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-8. Published 2011 Jan 01. doi: 10.1155/2011/379129.

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Publikationsdatum: 2011-01-01

Beschreibung: Reliability studies for coding contributing factors of incident reports in high hazard industries are rarely conducted and reported. Although the Human Factors Analysis and Classification System (HFACS) appears to have a larger number of such studies completed than most other systems doubt exists as the accuracy and comparability of results between studies due to aspects of methodology and reporting. This paper reports on a trial conducted on HFACS to determine its reliability in the context of military air traffic control (ATC). Two groups participated in the trial: one group comprised of specialists in the field of human factors, and the other group comprised air traffic controllers. All participants were given standardized training via a self-paced workbook and then read 14 incident reports and coded the associated findings. The results show similarly low consensus for both groups of participants. Several reasons for the results are proposed associated with the HFACS model, the context within which incident reporting occurs in real organizations and the conduct of the studies.

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Thema: Mathematik

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A Confidence Region for Zero-Gradient Solutions for Robust Parameter Design Experiments (2011)

Cheng, Aili ; Peterson, John ; Chitturi, Pallavi

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-11. Published 2011 Jan 01. doi: 10.1155/2011/537543.

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Publikationsdatum: 2011-01-01

Beschreibung: One of the key issues in robust parameter design is to configure the controllable factors to minimize the variance due to noise variables. However, it can sometimes happen that the number of control variables is greater than the number of noise variables. When this occurs, two important situations arise. One is that the variance due to noise variables can be brought down to zero The second is that multiple optimal control variable settings become available to the experimenter. A simultaneous confidence region for such a locus of points not only provides a region of uncertainty about such a solution, but also provides a statistical test of whether or not such points lie within the region of experimentation or a feasible region of operation. However, this situation requires a confidence region for the multiple-solution factor levels that provides proper simultaneous coverage. This requirement has not been previously recognized in the literature. In the case where the number of control variables is greater than the number of noise variables, we show how to construct critical values needed to maintain the simultaneous coverage rate. Two examples are provided as a demonstration of the practical need to adjust the critical values for simultaneous coverage.

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Thema: Mathematik

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8

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Bayes Estimation of Two-Phase Linear Regression Model (2011)

Pandya, Mayuri ; Bhatt, Krishnam ; Andharia, Paresh

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-9. Published 2011 Jan 01. doi: 10.1155/2011/357814.

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Publikationsdatum: 2011-01-01

Beschreibung: Let the regression model be Yi=β1Xi+εi, where εi are i. i. d. N (0,σ2) random errors with variance σ2〉0 but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in slope, regression parameter β2. The problem of study is when and where this change has started occurring. This is called change point inference problem. The estimators of m, β1,β2 are derived under asymmetric loss functions, namely, Linex loss & General Entropy loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

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Thema: Mathematik

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Probabilistic Modeling of Fatigue Damage Accumulation for Reliability Prediction (2011)

Rathod, Vijay ; Yadav, Om Prakash ; Rathore, Ajay ; [weitere]

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-10. Published 2011 Jan 01. doi: 10.1155/2011/718901.

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Publikationsdatum: 2011-01-01

Beschreibung: A methodology for probabilistic modeling of fatigue damage accumulation for single stress level and multistress level loading is proposed in this paper. The methodology uses linear damage accumulation model of Palmgren-Miner, a probabilistic S-N curve, and an approach for a one-to-one transformation of probability density functions to achieve the objective. The damage accumulation is modeled as a nonstationary process as both the expected damage accumulation and its variability change with time. The proposed methodology is then used for reliability prediction under single stress level and multistress level loading, utilizing dynamic statistical model of cumulative fatigue damage. The reliability prediction under both types of loading is demonstrated with examples.

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Thema: Mathematik

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On Three Competing Maintenance Actions and the Related Condition Control (2011)

Hagmark, Per-Erik

Hindawi

In: International Journal of Quality, Statistics, and Reliability. 2011; 2011: 1-6. Published 2011 Jan 01. doi: 10.1155/2011/637079.

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Publikationsdatum: 2011-01-01

Beschreibung: This paper considers three competing maintenance actions: corrective after failure, condition-based preventive to avoid failure, and scheduled. A stochastic model is set for the time relationship between corrective and preventive maintenance. This model defines a version of the so-called random signs censoring, and it leads to natural goodness measures for condition control. The effect of condition control on important observable and unobservable indicators is studied. The latter half of the paper considers static Weibull models for the time to failure and the effect of condition control; the main contribution is a calculation method that derives the four model parameters from four figures of input data. Corresponding parameter experimentation is demonstrated on maintenance cost analysis and condition control design.

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Thema: Mathematik

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