Curtailment Procedures Research Articles

Drivers of flight altitude during nocturnal bird migration over the North Sea and implications for offshore wind energy

AbstractEach year, millions of birds migrate nocturnally over the North Sea basin, an area designated for significant offshore wind energy development. Wind turbines can harm aerial wildlife through collisions and barrier effects, especially when birds fly at low altitudes below the wind turbine rotor tip. We aim to quantify seasonal and nightly differences in flight altitudes of nocturnal bird migration over the North Sea and identify how weather influences low‐altitude flight to inform wind turbine curtailment procedures for reducing bird fatalities. We used bird tracking radars at Borssele and Luchterduinen offshore wind parks, 22 and 23 km from the western Dutch coast, to monitor altitude distributions during migration. We show that median flight altitude was higher in spring compared to autumn at Borssele (spring: 285.5 m, autumn: 169.2 m; p < .001, effect size [ES] = 0.0001) and Luchterduinen (spring: 133.8 m, autumn: 126.0 m; p < .001, ES = 0.002) and below wind turbine rotor tip in both seasons. On most nights in both seasons, the majority of migrants flew predominantly at low altitudes, except for intense migration nights in spring in Borssele where, on 87% of these nights, migration mainly occurred at high altitudes. The most important predictors of low‐altitude migration in both seasons were day of year and wind assistance. Birds chose altitudes with the most favorable wind conditions for migration in both seasons. The relationship between day of year and low‐altitude migration fraction suggests that different species migrate at different altitudes. In spring, birds were flying lower at the beginning and the end of the night, reflecting departures and arrivals of birds, while radar location in autumn was a good predictor of low‐altitude flights, indicating that different local migratory axes have distinct altitude distributions. Our findings suggest that mitigation measures offshore may be more effective during autumn than spring, especially on nights with more supportive wind conditions at altitudes below 300 m.

Designing efficient Bayesian sampling plans for exponential distributions based on samples under a (n, t) simple step-stress test

This article studies a method about how to design an efficient Bayesian sampling plan based on samples collected through a (n, t)-sampling scheme with a simple step-stress accelerated life test (ALT). For brevity, such a step-stress accelerated life test is called (n, t)-SSALT. A Bayesian sampling plan (BSP) derived through the (n, t)-SSALT is called BSPA. First, we derive the BSPA with data collected through a (n, t)-SSALT for a general loss function. Given gamma and Jeffreys prior distributions, an explicit expression of the Bayes decision function under a certain loss function is derived. By applying a curtailment procedure to the preceding Bayes decision function, an on-line new Bayes decision function and Bayesian sampling plan, called an efficient Bayesian sampling plan (EBSPA), are constructed. It is shown that the Bayes risk of EBSPA is less than or equal to that of BSPA. This indicates that the EBSPA is more efficient than the BSPA. Comparisons among some BSPAs and the proposed EBSPA are given. The numerical results indicate that, in terms of Bayes risks, the EBSPA significantly outperforms the BSPA.

Designing efficient Bayesian sampling plans based on the simple step-stress test under random stress-change time for censored data

ABSTRACT This paper studies the problem about how to design an efficient Bayesian sampling plan based on a simple step-stress test with a random stress-change time for censored data. For brevity, the step-stress test with random stress-change time is briefly called SSRSCT. A Bayesian sampling plan (BSP) through the SSRSCT is called BSPA. First, we derive the BSPA with data based on Type-II censoring for a general loss function. Given gamma and noninformative uniform prior distributions, an explicit expression of the Bayes decision function under a certain loss function is derived. By applying a curtailment procedure to the preceding Bayes decision function, a new Bayesian sampling plan, called an efficient Bayesian sampling plan (EBSPA), is constructed. It is shown that the Bayes risk of EBSPA is less than or equal to that of BSPA. This indicates that EBSPA is more efficient than the BSPA. Comparisons among some BSPAs and the proposed EBSPA are given. Monte Carlo simulations are carried out, and results indicate that the EBSPA outperforms those BSPAs. The EBSPA is recommended.

Making Renewables Work: Operational Practices and Future Challenges for Renewable Energy as a Major Power Source in Japan

Japan has been experiencing a rapid deployment of photovoltaics (PVs) since the Feed-In Tariff (FIT) Scheme for Renewable Energy was launched in July 2012 . The increasing penetration levels of variable renewable generation, especially PVs and wind, have been affecting power system operations in each of Japan's 10 balancing areas. To accommodate this rapid growth in variable generation, the government established the Working Group on Grid Connection of Renewable Energy in 2014 to continually discuss and make timely decisions about these operational issues, including capacity connections, operation enhancement and asset improvement in each balancing area, and inevitable curtailment procedures for renewable generation.

Designing Bayesian sampling plans for censored data under products sold with warranty

ABSTRACTThis paper deals with the problem of designing Bayesian sampling plan with censored data under products sold with warranty. For exponential distributions with Type-II censored samples, a Bayesian sampling plan (BSP) is derived. Then, a curtailment procedure is applied to modify the Bayes decision procedure of the BSP to obtain a curtailed Bayes decision function, and an efficient Bayesian sampling plan (EBSP) is constructed. It is shown that the resulting curtailed Bayes decision function is equivalent to the Bayes decision function of BSP, and the risk of EBSP is less than or equal to that of BSP. Monte Carlo simulations are carried out. Numerical comparisons between the two sampling plans BSP and EBSP are provided. Numerical results also illustrate that the performance of EBSP is always better than that of BSP if the time cost is included in the loss function.

Selection among Bernoulli populations in comparison with a standard

In this article we consider the problem of comparing several Bernoulli populations in order to identify the population producing the largest success probability that is also larger than a given standard. We propose a fixed sample size procedure for which we develop the probability of a correct selection and the least favorable configuration. We also propose a curtailed version of the fixed sample size procedure and show that the curtailed procedure reaches the same probability of a correct selection as the fixed sample size procedure, while using fewer observations. We provide tables to implement the procedures and illustrate them via an example. We use simulations to estimate the savings by the curtailment procedure.

Status of wind in Pennsylvania: Social and environmental impacts of wind

abstract With the push for renewable energy at the turn of the century, windmills have become a commonplace part of the landscape in Pennsylvania. Due to their size and footprint, the turbines have both social and environmental costs. To reduce or negate many of the potentially adverse impacts of wind farm development and operation, a number of significant studies are conducted in both the pre- and postconstruction phases of the development process. These studies will be discussed and reviewed. Many of the preconstruction studies are requirements for wind farm development to be permitted. Impacts on both wildlife and the landscape can be significantly reduced or eliminated with careful project design, from proper wind farm siting and habitat avoidance measures, and through proper erosion control design. With proper development techniques and implementation practices, this “impact reduction” extends through the conclusion of the projects’ construction phase and into the generation phase. Proper implementation of curtailment procedures on a wind-farm-by-wind-farm or site-by-site basis significantly reduces bird and bat impacts through the projects’ active generation phase.

Curtailed Bayesian sampling plans for exponential distributions based on Type-II censored samples

ABSTRACTThis paper studies the problem of designing a curtailed Bayesian sampling plan (CBSP) with Type-II censored data. We first derive the Bayesian sampling plan (BSP) for exponential distributions based on Type-II censored samples in a general loss function. For the conjugate prior with quadratic loss function, an explicit expression for the Bayes decision function is derived. Using the property of monotonicity of the Bayes decision function, a new Bayesian sampling plan modified by the curtailment procedure, called a CBSP, is proposed. It is shown that the risk of CBSP is less than or equal to that of BSP. Comparisons among some existing BSPs and the proposed CBSP are given. Monte Carlo simulations are conducted, and numerical results indicate that the CBSP outperforms those early existing sampling plans if the time loss is considered in the loss function.

Bayesian sampling plans for exponential distributions with interval censored samples

ABSTRACTThis article studies the problem of designing Bayesian sampling plans (BSP) with interval censored samples. First, an algorithm for deriving the conventional BSP is proposed. The BSP is shown to possess some monotonicity. Based on the BSP and using the property of monotonicity, a new sampling plan modified by the curtailment procedure is proposed. The resulting curtailed Bayesian sampling plan (CBSP) can reduce the duration time of life test experiment, and it is optimal in the sense that its associated Bayes risk is smaller than the Bayes risk of the BSP if the cost of the duration time of life test experiment is considered. A numerical example to compute the Bayes risks of BSP and CBSP and related quantities is given. Also, a Monte Carlo simulation study is performed to illustrate the performance of the CBSP compared with the BSP. The simulation results demonstrate that our proposed CBSP has better performance because it has smaller risk. The CBSP is recommended. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 604–616, 2015

Curtailment in single-arm two-stage phase II oncology trials

Two-stage designs that allow for early stopping if the treatment is ineffective are commonly used in phase II oncology trials. A limitation of current designs is that early stopping is only allowed at the end of the first stage, even if it becomes evident during the trial that a significant result is unlikely. One way to overcome this limitation is to implement stochastic curtailment procedures that enable stopping the trial whenever the conditional power is below a pre-specified threshold θ. In this paper, we present the results for implementing curtailment rules in either only the second stage or both stages of the designs. In total, 102 scenarios with different parameter settings were investigated using conditional power thresholds θ between 0 and 1 in steps of 0.01. An increase in θ results not only in a decrease of the actual Type I error rate and power but also of the expected sample size. Therefore, a reasonable balance has to be found when selecting a specific threshold value in the planning phase of a curtailed two-stage design. Given that the effect of curtailment highly depends on the underlying design parameters, no general recommendation for θ can be made. However, up to θ=0.2, the loss in power was less than 5% for all investigated scenarios while savings of up to 50% in expected sample size occurred. In general, curtailment is most appropriate when the outcome can be observed fast or when accrual is slow so that adequate information for making early and frequent decisions is available.

Discussion on “A Hybrid Selection and Testing Procedure with Curtailment for Comparative Clinical Trials” by Elena M. Buzaianu and Pinyuen Chen

Professors Buzaianu and Chen provided some selection procedures in the multi-treatment clinical trials set up having a control, with binary responses, using curtailment procedure. In this present discussion article, we discuss the possibility of using different possible sampling designs, including the adaptive designs, and the possibility of using inverse sampling in the set up of Buzaianu and Chen. We also indicate the necessity of extending the approach for non-Bernoulli responses.

A Hybrid Selection and Testing Procedure with Curtailment for Comparative Clinical Trials

In this paper we use the idea of strong curtailment to define a hybrid selection and testing procedure for finding the best among several experimental Bernoulli populations, provided that it is better than a control Bernoulli population. Our curtailment procedure is based on the fixed-sample-size selection and testing procedure proposed by Thall et al. (1988). Our curtailment procedure reaches the same probability of a correct selection as the original procedure, but requires fewer observations.

Curtailment Procedure for Selecting Among Bernoulli Populations

Dunnett (1984) proposed a fixed sample-size procedure for selecting the best population among several Bernoulli experimental populations in comparison with a control Bernoulli population. Having as a reference point Dunnett's procedure (1984), we propose a closed sequential procedure that takes fewer observations but achieves the same probability of a correct selection as the original procedure.

A general formulation for a one-sided group sequential design

A major contribution to the statistical literature on group sequential designs was provided by Pampallona and Tsiatis who developed closed form functions that can be used to iteratively calculate the boundary points of a family of popular group sequential designs. A related area of interest is the use of conditional probability calculations to make interim decisions in stochastic curtailment procedures. The purpose of the paper is to develop group sequential designs based on conditional probabilities, to compare our results to the general closed form family of designs developed by Pampallona and Tsiatis, and to relate these to commonly used stochastic curtailment procedures. The problem and its solution are formulated and derived mathematically. A graphical interpretation of the results provides the reader with an alternative mechanism to understand the results and their significance. One-sided group sequential design boundary points, as closed form functions, are derived from conditional probability statements. These conditional probability statements can be interpreted as the probability, at the final analysis, of reversing the conclusion reached at an interim state. Under mild constraints, these boundary points are identical to the Pampallona and Tsiatis boundary points. At any interim stage when a boundary point is attained or surpassed we suggest a graphical approach to examine the conditional probability of reversing the interim decision at the final stage versus a range of possible parameter values. For stochastic curtailment procedures, we recommend relaxing (increasing) the conditional probability levels to at least 0.50 so that early stopping is at least as likely as for the O'Brien-Fleming procedure. The results are limited to one-sided group sequential designs. Conditional probabilities of reversing interim decisions provides a useful concept to develop group sequential designs and to evaluate stochastic curtailment procedures.

Conditional Rejection Probabilities of Student's t‐test and Design Adaptations

AbstractFor clinical trials with interim analyses conditional rejection probabilities play an important role when stochastic curtailment or design adaptations are performed. The conditional rejection probability gives the conditional probability to finally reject the null hypothesis given the interim data. It is computed either under the null or the alternative hypothesis. We investigate the properties of the conditional rejection probability for the one sided, one sample t‐test and show that it can be non monotone in the interim mean of the data and non monotone in the non‐centrality parameter for the alternative. We give several proposals how to implement design adaptations (that are based on the conditional rejection probability) for the t‐test and give a numerical example. Additionally, the conditional rejection probability given the interim t‐statistic is investigated. It does not depend on the unknown σ and can be used in stochastic curtailment procedures. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Improving NERC Transmission Loading Relief Procedures

NERC's curtailment procedure can be significantly improved by curtailing more of those transactions with a bigger influence on the congested flowgates, and by curtailing multilateral packaged transactions as a package rather than on a bilateral basis.

Multiple Imputation for Early Stopping of a Complex Clinical Trial

It is desirable to have procedures available for stopping a clinical trial early if there appears to be no treatment effect. Conditional power procedures allow for early stopping in favor of the null hypothesis if the probability of rejecting H0 at the planned end of the trial given the current data and a value of the parameter of interest is below some threshold level. Lan, Simon, and Halperin (1982, Communications in Statistics C1, 207-219) proposed a stochastic curtailment procedure that calculates the conditional power under the alternative hypothesis. Alternatively, predictive power procedures incorporate information from the observed data by averaging the conditional power over the posterior distribution of the parameter. For complex problems in which explicit evaluation of conditional power is not possible, we propose treating the problem of projecting the outcome of a trial given the current data as a missing data problem. We then complete the data using multiple imputation and thus eliminate the need for explicit calculation of conditional power. We apply this method to AIDS Clinical Trials Group (ACTG) protocol 118 and to several simulated clinical trials.

Repeated confidence intervals and prediction intervals using stochastic curtailment

Jennlson and Turnbull (1984,1989) proposed procedures for repeated confidence intervals for parameters of interest In a clinical trial monitored with group sequential methods. These methods are extended for use with stochastic curtailment procedures for two samples in the estimation of differences of means, differences of proportions, odds ratios, and hazard ratios. Methods are described for constructing 1) confidence intervals for these estimates at repeated times In the course of a trial, and 2) prediction intervals for predicted estimates at the end of a trial. Specific examples from several clinical trials are presented.

Upper bounds for type I and type II error rates in conditional power calculations

Stochastic curtailment procedures are used to monitor accumulating data in long term clinical trials. These procedures allow one to calculate the conditional probability under H0 (or alternative hypothesis, Ha) given current data, of rejecting (accepting) H0 at the end of the trial. One might stop early and reject (accept) H0 if this probability is equal to or greater than γ (γ'). Lan, Simon and Halperin (1982) have shown that if α and β are the type I and type II errors , respectively, then the type I (type II) error using a stochastic curtailment method is equal to or less than α/γ (β/γ'). This upper bound is based on an unlimited number of interim looks. In fact, there are usually a small number of looks. Lower upper bounds using only the standard normal distribution table are presented. A computer program to obtain these bounds is available from the authors.

Curtailed versions of randomized binomial tests

Consider a fixed sample size uniformly most powerful test of Ho: p ≤ po versus H1 : p > po, where p is a Bernoulli parameter. If the test is non randomized, an optimally curtailed version stops sampling as soon as the final decision is certain. If the test is andomized, the optimal curtailment procedure is more complex. This paper gives a Simple, complete characterization of weakly admissible curtailments of such randomized tests.