Smooth empirical Bayes estimation of observation error variances in linear systems

A smooth empirical Bayes estimator was developed for estimating the unknown random scale component of each of a set of observation error variances. It is shown that the estimator possesses a smaller average squared error loss than other estimators for a discrete time linear system

Detecting trends and patterns in reliability data over time using exponentially weighted moving-averages

A simple, easy-to-use graphical method is presented for use in determining if there is any statistically significant trend or pattern over time in an underlying Poisson event rate of occurrence or binomial failure on demand probability. The method is based on the combined use of both an exponentially weighted moving-average (EWMA) and a Shewhart chart. Two nuclear power plant examples are introduced and used to illustrate the method. The false alarm probability and power when using the combined procedure are also determined for both cases using Monte Carlo simulation. The results indicate that the combined procedure is quite effective in rapidly detecting either a small or large step increase in the Poisson rate or binomial probability over time

Comparing PRAs with operating experience

Probabilistic Risk Assessment is widely used to estimate the frequencies of rare events, such as nuclear power plant accidents. An obvious question concerns the extent to which PRAs conform to operating experience--that is, do PRAs agree with reality? The authors discuss a formal methodology to address this issue and examine its performance using plant-specific data

Exploratory comparison of methods for combining failure-rate data from different data sources

Thirteen methods are considered for use in pooling failure-rate data from different data sources. A Bayesian approach is taken in which two distinct sources of variation are assumed to be present; namely, prior variation between data sources and statistical error variation within each data source. An exploratory Monte Carlo simulation is used to compare the performance of the methods when used to construct both pooled point and 90% interval estimates of the failure-rate. The results indicated that those methods based on simple averaging techniques are satisfactory when only a small number of data sources are to be pooled. When there are fifteen or more data sets to be pooled, more sophisticated methods, which incorporate additional model structure, are superior. An example is given to illustrate the use of each of the proposed methods

A Fully Bayesian Approach for Combining Multilevel Failure Information in Fault Tree Quantification and Corresponding Optimal Resource Allocation

This paper presents a fully Bayesian approach that simultaneously combines basic event and statistically independent higher event-level failure data in fault tree quantification. Such higher-level data could correspond to train, sub-system or system failure events. The full Bayesian approach also allows the highest-level data that are usually available for existing facilities to be automatically propagated to lower levels. A simple example illustrates the proposed approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm

Extended likelihood inference in reliability

Extended likelihood methods of inference are developed in which subjective information in the form of a prior distribution is combined with sampling results by means of an extended likelihood function. The extended likelihood function is standardized for use in obtaining extended likelihood intervals. Extended likelihood intervals are derived for the mean of a normal distribution with known variance, the failure-rate of an exponential distribution, and the parameter of a binomial distribution. Extended second-order likelihood methods are developed and used to solve several prediction problems associated with the exponential and binomial distributions. In particular, such quantities as the next failure-time, the number of failures in a given time period, and the time required to observe a given number of failures are predicted for the exponential model with a gamma prior distribution on the failure-rate. In addition, six types of life testing experiments are considered. For the binomial model with a beta prior distribution on the probability of nonsurvival, methods are obtained for predicting the number of nonsurvivors in a given sample size and for predicting the required sample size for observing a specified number of nonsurvivors. Examples illustrate each of the methods developed. Finally, comparisons are made with Bayesian intervals in those cases where these are known to exist

Spectrophotometric Calibration of pH Electrodes in Seawater Using Purified m-Cresol Purple

This work examines the use of purified meta-cresol purple (mCP) for direct spectrophotometric calibration of glass pH electrodes in seawater. The procedures used in this investigation allow for simple, inexpensive electrode calibrations over salinities of 20–40 and temperatures of 278.15–308.15 K without preparation of synthetic Tris seawater buffers. The optimal pH range is ∼7.0–8.1. Spectrophotometric calibrations enable straightforward, quantitative distinctions between Nernstian and non-Nernstian electrode behavior. For the electrodes examined in this study, both types of behavior were observed. Furthermore, calibrations performed in natural seawater allow direct determination of the influence of salinity on electrode performance. The procedures developed in this study account for salinity-induced variations in liquid junction potentials that, if not taken into account, would create pH inconsistencies of 0.028 over a 10-unit change in salinity. Spectrophotometric calibration can also be used to expeditiously determine the intercept potential (i.e., the potential corresponding to pH 0) of an electrode that has reliably demonstrated Nernstian behavior. Titrations to ascertain Nernstian behavior and salinity effects can be undertaken relatively infrequently (∼weekly to monthly). One-point determinations of intercept potential should be undertaken frequently (∼daily) to monitor for stable electrode behavior and ensure accurate potentiometric pH determinations

Experimental modeling of hypoxia in pregnancy and early postnatal life

The important role of equilibrium of environmental factors during the embryo-fetal period is undisputable. Women of reproductive age are increasingly exposed to various environmental risk factors such as hypoxia, prenatal viral infections, use of drugs, smoking, complications of birth or stressful life events. These early hazards represent an important risk for structural and/or functional maldevelopment of the fetus and neonates. Impairment of oxygen/energy supply during the pre- and perinatal period may affect neuronal functions and induce cell death. Thus when death of the newborn is not occurring following intrauterine hypoxia, various neurological deficits, including hyperactivity, learning disabilities, mental retardation, epilepsy, cerebral palsy, dystonia etc., may develop both in humans and in experimental animals. In our animal studies we used several approaches for modeling hypoxia in rats during pregnancy and shortly after delivery, i.e. chronic intrauterine hypoxia induced by the antiepileptic drug phenytoin, neonatal anoxia by decreased oxygen saturation in 2-day-old pups. Using these models we were able to test potential protective properties of natural (vitamin E, melatonin) and synthetic (stobadine) compounds. Based on our results, stobadine was also able to reduce hypoxia-induced hyperactivity and the antioxidant capacity of stobadine exceeded that of vitamin E and melatonin, and contrary to vitamin E, stobadine had no adverse effects on developing fetus and offspring