A Bayesian adaptive dose-finding algorithm for balancing individual- and population-level ethics in Phase I clinical trials

Multiple Bayesian adaptive designs have been proposed for Phase I clinical trials since the continual reassessment method (CRM) was proposed by O’Quigley et al. (1990). Focused on dose-finding in cancer studies, the CRM seeks to allocate new patients to an estimated maximum tolerable dose (MTD). Later, Whitehead and Brunier (1995 Whitehead, J. and Brunier, H. (1995). Continual Reassessment Method: Bayesian Decision Procedures for Dose Determining Experiments, Statistics in Medicine 14: 885–893.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) applied Bayesian decision theory to maximize statistical information for the MTD when allocating new patients. The two allocation rules reflect conflicting perspectives. The CRM emphasizes individual-level ethics, whereas the method of Whitehead and Brunier (1995 Whitehead, J. and Brunier, H. (1995). Continual Reassessment Method: Bayesian Decision Procedures for Dose Determining Experiments, Statistics in Medicine 14: 885–893.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) emphasizes population-level ethics. In the design of a Phase I clinical trial to investigate hyperthermic intraperitoneal chemotherapy (HIPEC) we sought to compromise the two perspectives. To this end, we propose a novel dose allocation design referred to as the balanced information gain method. We first decompose the loss function used by Whitehead and Brunier and then modify it with a tuning parameter that allows a trialist to differentially weigh individual- and population-level ethics based on their particular clinical setting. Simulation studies show that the proposed design provides a reasonable compromise between the distribution of the estimated MTD and the distribution of the number of observed adverse events per trial when compared to the two existing methods.     

Two-stage procedures for the bounded risk point estimation of the parameter and hazard rate in two families of distributions

Two families of distributions are considered that cover a large number of probability distributions useful in investigations involving reliability studies and survival analyses. The problem of bounded risk point estimation of the parameter and hazard rate function of the two families of distribution is handled. Motivated by Mukhopadhyay and Pepe (2006 Mukhopadhyay, N. and Pepe, W. (2006). Exact Bounded Risk Estimation When the Terminal Sample Size and Estimator Are Dependent: The Exponential Case, Sequential Analysis 25: 85–101.[Taylor &; Francis Online] , [Google Scholar]), Roughani and Mahmoudi (2015 Roughani, G. and Mahmoudi, E. (2015). Exact Risk Evaluation of the Two-Stage Estimation of the Gamma Scale Parameter under Bounded Risk Constraint, Sequential Analysis 34: 387–405.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), and Mahmoudi and Lalehzari (2017 Mahmoudi, E. and Lalehzari, R. (2017). Bounded Risk Estimation of the Hazard Rate Function of the Exponential Distribution: Two-Stage Procedure, Sequential Analysis 36: 38–54.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), two-stage procedures are developed based on the maximum likelihood estimator (MLE) as well as uniformly minimum variance unbiased estimator (UMVUE). The estimation problem based on the minimum mean square estimator (MMSE) is also considered. We establish that the MMSE of the parameter and hazard rate provides a smaller risk.     

2-Aminothiophenol as building blocks for novel heterocycles

Herein, the chemistry of 2-aminothiophenol has been utilized in the synthesis of several interesting products such as oxidation and reaction with π-deficient compounds. On oxidizing 2-aminothiophenol by sodium hypochlorite furnishes 2-[(2-aminophenyl)-dithio]aniline. Treatment of the obtained product with acetyl chloride affords N-(2-[2-(acetylamino)-phenyl-disulphanyl)-phenyl]acetamide. Reaction of the former acetamide with POCl₃ yields 2-methyl-1,3-benzothiazole. Moreover, (3,4,8,9)-dibenzo-2,7-dithia-5,10-diaza4 Field, L. and Lawson, J. E. 1958. J. Am. Chem. Soc., 80: 838[Crossref], [Web of Science ®] , [Google Scholar] 4 Field, L. and Lawson, J. E. 1958. J. Am. Chem. Soc., 80: 838[Crossref], [Web of Science ®] , [Google Scholar] 4 Field, L. and Lawson, J. E. 1958. J. Am. Chem. Soc., 80: 838[Crossref], [Web of Science ®] , [Google Scholar]propellane is formed on reacting the target 2-aminothiophenol with cyclohexane-1,2-dione, whereas its reactions with electron π-acceptors such as 2,3-dichloro-1,4-naphthoquinone (DCHNQ), 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ), tetra-cyanoethylene (TCNE), and 1-(dicyanomethylen)acenaphthen-2-one yield various heterocycles.     

AN IMPROVEMENT TO THE SSF MODEL FOR PREDICTION OF LIGHT PARTICLE DISPERSION

This study investigates the predicted motion of small, light particles using the stochastic separated flow models proposed by Shuen et al. (1983 Shuen , J. S. , Chen , L. D. , and Faeth , G. M. ( 1983 ). Evaluation of a stochastic model of particle dispersion in a turbulent round jet , AIChE J. , 29 , 167 – 170 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) and Lightstone and Raithby (1998 Lightstone , M. F. and Raithby , G. D. ( 1998 ). A stochastic model of particle dispersion in a turbulent gaseous environment , Combust. Flame , 113 , 424 – 441 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). Model predictions are compared to the benchmark experiment of Snyder and Lumley (1971 Snyder , W. H. and Lumley , J. L. ( 1971 ). Some measurements of particle velocity autocorrelation functions in a turbulent flow , J. Fluid Mech. , 48 , 41 – 71 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) for particles released from a point source in grid-generated turbulence. It is found that the predictions of particle velocity variance and dispersion exhibit nonphysical waves. This behavior is explored in order to understand its mathematical basis arising from the model formulation. A modification to the model is presented. The modified model is successful in removing the characteristic waves.     

Multistage estimation of the difference of locations of two negative exponential populations under a modified Linex loss function: Real data illustrations from cancer studies and reliability analysis

We have designed modified two-stage and purely sequential strategies to estimate the difference of location parameters from two independent negative exponential populations having unknown but proportional scale parameters under a modified Linex loss function. This article extends one-sample methodologies of Mukhopadhyay and Bapat (2016 Mukhopadhyay, N. and Bapat, S. R. (2016). Multistage Point Estimation Methodologies for a Negative Exponential Location under a Modified Linex Loss Function: Illustrations with Infant Mortality and Bone Marrow Data, Sequential Analysis 35: 175–206. http://dx.doi.org/10.1080/07474946.2016.1165532.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], Sequential Analysis). Some preliminary results are established along the lines of Mukhopadhyay and Hamdy (1984 Mukhopadhyay, N. and Hamdy, H. I. (1984). On Estimating the Difference of Location Parameters of Two Negative Exponential Distributions, Canadian Journal of Statistics 12: 67–76.[Crossref] , [Google Scholar], Canadian Journal of Statistics) and Mukhopadhyay and Darmanto (1988 Mukhopadhyay, N. and Darmanto, S. (1988). Sequential Estimation of the Difference of Means of Two Negative Exponential Populations, Sequential Analysis 7: 165–190.[Taylor &; Francis Online] , [Google Scholar], Sequential Analysis). We have resorted to Mukhopadhyay and Duggan (1997 Mukhopadhyay, N. and Duggan, W. T. (1997). Can a Two-Stage Procedure Enjoy Second Order Properties? Sankhya, Series A 59: 435–448. [Google Scholar], Sankhya, Series A) in developing asymptotic second-order properties for the modified two-stage methodology and to nonlinear renewal theory of Lai and Siegmund (1977 Lai, T. L. and Siegmund, D. (1977). A Nonlinear Renewal Theory with Applications to Sequential Analysis I, Annals of Statistics 5: 946–954.[Crossref], [Web of Science ®] , [Google Scholar], 1979 Lai, T. L. and Siegmund, D. (1979). A Nonlinear Renewal Theory with Applications to Sequential Analysis II, Annals of Statistics 7: 60–76.[Crossref], [Web of Science ®] , [Google Scholar], Annals of Statistics) and Woodroofe (1977 Woodroofe, M. (1977). Second Order Approximation for Sequential Point and Interval Estimation, Annals of Statistics 5: 984–995.[Crossref], [Web of Science ®] , [Google Scholar], Annals of Statistics) in addressing analogous properties under the purely sequential methodology. Then, we supplement with extensive sets of data analysis via computer simulations validating that both modified two-stage and purely sequential methods perform very well. Both methodologies are also illustrated and implemented using real datasets from cancer studies and reliability analysis.     

BUBBLE COMPUTATION,GRANULAR TEMPERATURES,AND REYNOLDS STRESSES

Bubbles were simulated in a two-dimensional fluidized bed with a constant inlet velocity using two computer codes, the IIT code and the MFIX code. The computational results were compared to the Jung et al. (2005 Jung , J. , Gidaspow , D. , and Gamwo , I. K. (2005). Measurement of two kinds of granular temperatures, stresses and dispersion in bubbling beds, Ind. Eng. Chem. Res. , 44, 1329–1341 [CROSSREF] [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) experiments in a thin bubbling bed of 530 μm glass beads. The use of higher order numerics produces better bubble resolution due to smaller numerical diffusion. The computed bubble sizes and their distributions agreed with the experiments. The simulations show that there is no bubble formation for sufficiently elastic particles.

CFD computations and previous experiments show that in the bubbling fluidized beds there exist two random oscillations. The first kind is due to random oscillations of particles and is measured by the conventional granular temperature. The second one is due to motion of bubbles and gives rise to Reynolds type stresses. It is shown that the particle granular temperature is much smaller than the bubble-like granular temperature computed from the average of the normal Reynolds stresses, measured by Cody using a shot noise technique.     

EVALUATION OF LAGRANGIAN PARTICLE DISPERSION MODELS IN TURBULENT FLOWS

This work evaluates the performance of Lagrangian turbulent particle dispersion models based on the Langevin equation. A family of Langevin models, extensively reported in the open literature, decompose the fluctuating fluid velocity seen by the particle in two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, i.e., the closure is at the level of the fluid velocity seen by the particle. We will call those models generically the “standard model.” On the other hand, the model proposed by Minier and Peirano (2001 Minier , J. P. and Peirano , E. ( 2001 ). The PDF approach to turbulent polydisperesed two-phase flows , Phys. Rep. , 352 , 1 – 214 .[Crossref], [Web of Science ®] , [Google Scholar]) is considered; this approach is based on the probability density function (PDF) and performs the closure at the level of the acceleration of the fluid seen by the particle. The formulation of a Langevin equation model for the increments of fluid velocity seen by the particle allows capturing some underlying physics of particle dispersion in general turbulent flows while keeping simple the mathematical manipulation of the stochastic model, avoiding some pitfalls, and simplifying the derivation of macroscopic relations. The performance of the previous dispersion models is evaluated in the configurations of grid-generated turbulence (Snyder and Lumley, 1971 Snyder , W. H. and Lumley , J. L. ( 1971 ). Some measurements of particle-velocity autocorrelation functions in a turbulent flow , J. Fluid Mech. , 48 , 41 – 71 .[Crossref], [Web of Science ®] , [Google Scholar]; Wells and Stock, 1983 Wells , M. R. and Stock , D. E. ( 1983 ). The effect of crossing trajectories on the dispersion of particles in a turbulent flow , J. Fluid Mech. , 136 , 31 – 62 .[Crossref], [Web of Science ®] , [Google Scholar]), simple shear flow (Hyland et al., 1999), and confined axisymmetric jet flow laden with solids (Hishida and Maeda, 1987 Hishida , K. and Maeda , M. ( 1987 ). Turbulent characteristics of gas-solids two-phase confined jet: Effect of particle density , Jpn. J. Multiph. Flow , 1 , 56 – 69 . [Google Scholar]).     

Quantification of Carboxylic and Carbonyl Functional Groups in Organic Aerosol Infrared Absorbance Spectra

Atmospheric aerosols are one of the least understood components of the climate system and incur adverse health effects on susceptible populations. Organic aerosols can make up as much as 80% of atmospheric aerosols (Lim and Turpin 2002 Lim, H. J. and Turpin, B. J. 2002. Origins of Primary and Secondary Organic Aerosol in Atlanta: Results’ of Time-Resolved Measurements During the Atlanta supersite experiment. Environ. Sci. Technol., 36: 4489–4496. 10.1021/es0206487[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), and so its quantification and characterization plays an important role in reducing our uncertainty with regards to aerosol impacts on health and climate. As the number of organic molecules in the atmosphere are diverse in number (Hamilton et al. 2004 Hamilton, J. F., Webb, P. J., Lewis, A. C., Hopkins, J. R., Smith, S. and Davy, P. 2004. Partially Oxidised Organic Components in Urban Aerosol using GCXGC-TOF/MS. Atmos. Chem. Phys., 4: 1279–1290. [Crossref], [Web of Science ®] , [Google Scholar]), we advance a functional group representation of organic molecules as measured by Fourier transform infrared spectroscopy (FTIR) to characterize the chemical composition of particle samples. This study describes and evaluates the algorithm introduced by Russell et al. (2009 Russell, L. M., Takahama, S., Liu, S., Hawkins, L. N., Covert, D. S.Quinn, P. K. 2009. Oxygenated Fraction and Mass of Organic Aerosol from Direct Emission and Atmospheric Processing Measured on the R/V Ronald Brown During TEXAQS/GoMACCS 2006. J. Geophys. Res.-Atmos., 114: D00F05 10.1029/2008JD011275[Crossref], [Web of Science ®] , [Google Scholar]) for apportionment and quantification of oxygenated (carbonyl and hydroxyl) functional groups from infrared absorption spectra. Molar absorptivities for carbonyl and hydroxyl bonds in carboxylic groups are obtained for several dicarboxylic compounds, and applied to a multifunctional compound and mixture to demonstrate the applicability of this method for more complex samples. Furthermore, functional group abundances of two aldehydic compounds, 2-deoxy-d-ribose and glyceraldehyde, atomized from aqueous solution are in quantitative agreement with number of bonds predicted after transformation of these compounds into diols. The procedure for spectra interpretation and quantitative analysis is described through the context of an algorithm in which contributions of background and analyte absorption to the infrared spectrum are apportioned by the superposition of lineshapes constrained by laboratory measurements.

Copyright 2013 American Association for Aerosol Research     

A simulation model for settling tanks with varying cross-sectional area

A quasi-one-dimensional model of the process of continuous sedimentation in clarifier-thickeners (settlers) with variable cross-sectional area is presented. The partial differential equation (PDE) model extends the settler model advanced by Bürger et al. (2013 Bürger, R., Diehl, S., Farås, S., Nopens, I., and Torfs, E. (2013). A consistent modelling methodology for secondary settling tanks: A reliable numerical method, Water Sci. Technol. 68(1), 192–208.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), which assumes a constant cross section. A reliable numerical method that handles the special features of the nonlinear PDE is presented along with an advantageous time-step condition for continuous and batch sedimentation under the condition of a variable cross-sectional area. Simulations of continuous sedimentation show the effect of change of cross-sectional area in the concentration inside the vessel and in the underflow. Simulations of batch settling in cones illustrate the versatility of the numerical scheme to include a vertex, where the area shrinks to zero.     

Nonparametric partially random sequential test under Phase II sampling: An illustration to monitor water samples for arsenic contamination

We introduce a class of nonparametric two-sample tests based on a new partially sequential sampling scheme. Existing partially sequential procedures based on inverse sampling schemes, pioneered by Wolfe (1977 Wolfe, D. A. (1977). On a Class of Partially Sequential Two Sample Test Procedure, Journal of American Statistical Association 72: 202–205.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Orban and Wolfe (1980 Orban, J. and Wolfe, D. A. (1980). Distribution Free Partially Sequential Placement Procedure, Communications in Statistics - Theory &; Methods 9: 883–902.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), are updated in the light of random sequential sampling techniques, proposed by Mukhopadhyay and de Silva (2008 Mukhopadhyay, N. and de Silva, B. M. (2008). Theory and Applications of a New Methodology for the Random Sequential Probability Ratio Test, Statistical Methodology 5: 424–453.[Crossref] , [Google Scholar]). In a quality control setup, the present procedure can be looked upon as a Phase II on-line monitoring with rational subgroups of variable sizes where standards are unknown. We consider a training sample of prefixed size m as Phase I observations and adopt a random sequential sampling in Phase II. We discuss statistical methodologies in detail and provide some asymptotic results. Numerical results based on Monte Carlo are presented to justify asymptotic theory. We computationally investigate the power performances of the proposed test against some fixed alternative. We illustrate our procedure with real data related to water samples for monitoring arsenic contamination. Some concluding remarks along with possible future research problems are offered     

Asymptotic exponentiality of the first exit time of the Shiryaev–Roberts diffusion with constant positive drift

We consider the first exit time of a Shiryaev–Roberts diffusion with constant positive drift from the interval [0,A] with A>0 fixed. We show that the moment generating function (Laplace transform) of a suitably standardized version of the first exit time converges to that of the unit-mean exponential distribution as A→+∞. The proof is explicit in that the moment generating function of the first exit time is first expressed analytically and in a closed form and then the desired limit as A→+∞ is evaluated directly. The result is of importance in the area of quickest change-point detection, and its discrete-time counterpart has been previously established—although in a different manner—by Pollak and Tartakovsky (2009a Pollak, M. and Tartakovsky, A. G. (2009a). Asymptotic Exponentiality of the Distribution of First Exit Times for a Class of Markov Processes with Applications to Quickest Change Detection, Theory of Probability and Its Applications 53: 430–442.[Crossref], [Web of Science ®] , [Google Scholar]).     

Methodology for Performance Evaluation of Dust Control Systems with an Application to Electrostatic Precipitators

A general methodology is presented that enables rigorous estimation of the total collection efficiency and the size distribution of particles penetrating dust control systems. This methodology assumes lognormal inlet particle-size distributions and can be used with fractional efficiency formulations that predict, under such conditions, lognormal outlet particle-size distributions. Multimodal inlet particle distributions can be accommodated additively. This methodology is applied to Electrostatic Precipitator Systems (ESPs), with the Nobrega et al. (2004) Nobrega, S. W., Falaguasta, M. C. R. and Coury, J. R. 2004. A Study of a Wire-Plate Electrostatic Precipitator Operating in the Removal of Polydispersed Particles. Braz. J. Chem. Eng., 21(2): 275–284. [Crossref], [Web of Science ®] , [Google Scholar] model selected for predicting their fractional efficiencies. For ease of use, a graphical solution has been developed for the Nobrega et al. fractional efficiency relations, but its availability is not a prerequisite for the application of the general methodology. For the latter, the fractional efficiencies corresponding to three particle diameters need to be estimated and this can be done either graphically or numerically using the model of Nobrega et al. or any other fractional efficiency formulation of interest.

Fine particles emerge as the most important pollutant worldwide in terms of human health, creating thus the need for credible particle size-specific inventories. In line with the above, a generic and rigorous method, capable of producing size-specific emission estimates from uncontrolled and controlled sources, has been developed (Economopoulou and Economopoulos 2001 Economopoulou, A. A. and Economopoulos, A. P. 2001. Method for Estimating Size-Specific Particulate Emission Inventories. J. Environ. Eng., ASCE, 127: 1139–1148. [Crossref], [Web of Science ®] , [Google Scholar]). For controlled sources, this method relies on the development of easy to use models that predict the total efficiency and the lognormal size distribution of particles penetrating the control systems used. Such models have already been developed for dry cyclone separators (Economopoulou and Economopoulos 2002a Economopoulou, A. A. and Economopoulos, A. P. 2002a. Rapid Performance Evaluation and Optimal Sizing of Dry Cyclone Separators. J. Environ. Eng., ASCE, 128: 275–285. [Crossref], [Web of Science ®] , [Google Scholar], 2002b Economopoulou, A. A. and Economopoulos, A. P. 2002b. Size Distribution of Particles Penetrating Dry Cyclone Separators. J. Environ. Eng., ASCE, 128: 919–928. [Crossref], [Web of Science ®] , [Google Scholar]) and venturi scrubbers (Economopoulou and Harrison 2007a Economopoulou, A. A. and Harrison, R. M. 2007a. Graphical Analysis of the Performance of Venturi Scrubbers for Particle Abatement. Part I: Rapid Collection Efficiency Evaluation. Aerosol Sci. Technol., 41: 51–62. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 2007b Economopoulou, A. A. and Harrison, R. M. 2007b. Graphical Analysis of the Performance of Venturi Scrubbers for Particle Abatement. Part II: Size Distribution of Penetrating Particles. Aerosol Sci. Technol., 41: 63–74. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The present methodology extends the use of the inventory methodology to ESP-controlled sources and, in addition, it provides a generalized basis for covering other types of control systems with any fractional efficiency formulation considered appropriate.     

Adhesive Contact of a Compliant Sphere to an Elastic Coated Substrate: The Thin Film Limit

Experimental results for adhesive contacts on substrates coated with elastomeric thin films have recently been obtained by Tardivat and Léger [1 Tardivat , C. and Léger L. , J. Adhesion Sci. Technol. 15 , 1055 – 1078 ( 2001 ).[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] by the so-called Johnson-Kendall-Roberts (JKR) test, which provides both adhesion energy and elastic modulus. These data show that on substrates coated with thin films the adhesion and effective elastic modulus of the sphere depend upon the film thickness. In keeping with the experimental conditions, we try to interpret these data using a simple model [4 Barthel , E. and Perriot , A. , J. Phys. D: Appl. Phys. 40, 1059–1067 (2007).[Crossref] , [Google Scholar]] in the thin film limit, i.e., when the film thickness is small compared with the contact radius. Although the film does impact the local crack tip stress field, we show that no effect on the macroscopic contact variables is expected for the adhesion to coated substrates in such confined geometries. The deviations from the experimental results are ascribed to the idealized contact boundary conditions assumed in the model.     

Experimental study and hydrodynamic modeling of countercurrent liquid–solid system with batch liquid

It is known that a transient effluent outlet concentration is obtained with a batch of adsorbent solids in any operation. A preferred steady state outlet concentration can be achieved with a continuous flow of solids. In the present work, information on pressure profiles, the total pressure drop across the column and holdup of solids are experimentally obtained for various solid flow rates, particle sizes and densities in a countercurrent liquid–solid system. These experimental results are compared with the prediction obtained using a phenomenological model containing continuity and momentum balance equations. The dominant drag force term was expressed in terms of various drag equations. The drag expression developed by Foscolo et al. (1983 Foscolo, P. U., Gibilaro, L. G., and Waldram, S. P. (1983). A unified model for particulate expansion of fluidized beds and flow in fixed porous media, Chem. Eng. Sci., 38(8), 1251–1260.[Crossref], [Web of Science ®] , [Google Scholar]) could predict the axial profiles of pressure drop and holdup, and the effect of various parameters on total pressure drop and solid holdup most satisfactorily.     

Thermal Effects in Evaporation from Binary Liquid Mixtures

Thermal effects are considered assuming a volatile component evaporates from a binary liquid mixture in a very long tube. The work is an extension of the work of Chebbi and Selim (2006 Chebbi, R., and Selim, M. S. (2006). The Stefan problem of evaporation of a volatile component from a binary liquid mixture, Heat Mass Transfer, 42(3), 238–247.[Crossref], [Web of Science ®] , [Google Scholar]) (isothermal case) to include evaporative cooling. A similarity solution is provided for the gas–liquid interface temperature and the temperature profiles in the liquid and gas phases. The analysis accounts for the motion of the gas–liquid interface and shows evaporative cooling as expected. The magnitude of evaporative cooling is found significant when volatility of the volatile component is sufficiently high. The validity of the approximations used in the solution is addressed.     

ARL-unbiased geometric and CCCG control charts

In order to control increases and decreases in a parameter in a timely fashion, a chart should be set in such way that the average run length (ARL) curve attains a maximum in the in-control situation.

This article proposes not only a geometric (or cumulative count of conforming, CCC) chart but also a CCC chart under group inspection (CCC_G) for which all out-of-control ARL values are smaller than the in-control ARL and thus provides an improvement on the designs described in L. Zhang et al. (2004 Zhang, L., Govindaraju, K., Bebbington, M. and Lai, C. D. (2004). On the Statistical Design of Geometric Control Charts, Quality Technology &; Quantitative Management 2: 233–243.[Taylor &; Francis Online] , [Google Scholar]) and C. W. Zhang et al. (2012 Zhang, C. W., Xie, M., and Jin, T. (2012). An Improved Self-starting Cumulative Count of Conforming Chart for Monitoring High-Quality Processes under Group Inspection, International Journal of Production Research 50: 7026–7043.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Moreover, by exploring the notions of uniformly most powerful unbiased tests with randomization probabilities, we are able not only to eliminate the bias of the ARL function of the geometric charts but also to bring their in-control ARL exactly to a prespecified value.

Instructive examples are provided to illustrate the e?ciency of the proposed charts.     

Some optimal variance stopping problems revisited with an application to the Italian Ftse-Mib stock index

Optimal variance stopping (O.V.S.) problems are a new class of optimal stopping problems that differ from the classical ones because of their non linear (quadratic) dependence on the expectation operator. These problems were introduced by Pedersen (2011 Pedersen, J. L. (2011). Explicit Solutions to Some Optimal Variance Stopping Problems, Stochastics 83: 505–518.[Taylor &; Francis Online] , [Google Scholar]), who provided an effective solution method and derived the explicit solutions to the O.V.S. problem for some important examples of diffusion processes. In this article, we analyze the examples of Pedersen (2011 Pedersen, J. L. (2011). Explicit Solutions to Some Optimal Variance Stopping Problems, Stochastics 83: 505–518.[Taylor &; Francis Online] , [Google Scholar]) in light of the results in Buonaguidi (2015 Buonaguidi, B. (2015). A Remark on Optimal Variance Stopping Problems, Journal of Applied Probability 52: 1187–1194.[Crossref], [Web of Science ®] , [Google Scholar]), where an alternative method for solving an O.V.S. problem was developed: this method is based on the solution of a constrained optimal stopping problem, whose maximization, over all the admissible constraints, returns the solution to the O.V.S. problem. Using real data on the Italian Ftse-Mib stock index, we also discuss how the solution to the O.V.S. problem for a geometric Brownian motion can be used in trading strategies.     

Asymptotically optimal procedures in multivariate Bayesian sequential estimation

In this article, we consider the problem of multivariate Bayesian sequential estimation of the unknown mean vector. We propose a robust sequential procedure without using the prior information or any auxiliary data, which is similar to multivariate non-Bayesian sequential estimation by M. Ghosh et al. (1976 Ghosh, M., Sinha, B. K., and Mukhopadhyay, N. (1976). Multivariate Sequential Point Estimation, Journal of Multivariate Analysis 6: 281–294.[Crossref], [Web of Science ®] , [Google Scholar]). The proposed procedure, depending only on the present data but not on its distribution, is shown to be asymptotically as well as or better than the optimal fixed-sample-size procedures for the arbitrary distributions and asymptotically pointwise optimal and asymptotically optimal for multivariate exponential family with a large class of prior distributions.     

Numerical Modeling of Nanoparticle Collection Efficiency of Single-Stage Wire-in-Plate Electrostatic Precipitators

The numerical models for predicting the collection efficiency of particles in the size range of 0.3 ～ 10.0 μm in electrostatic precipitators (ESPs) have been well developed. However, for nanoparticles, or particles with the diameter below 100 nm, the existing models can't predict the collection efficiency very well because the electric field and ion concentration distribution were not simulated, or charging models were not adopted appropriately to calculate particle charges. In this study, a 2-D numerical model was developed to predict the nanoparticle collection efficiency in single-stage wire-in-plate ESPs. Laminar flow field was solved by using the Semi-Implicit Method for Pressure-Linked Equation (SIMPLER Method), while electric field strength and ion concentration distribution were solved based on Poisson and diffusion-convection equations, respectively. The charged particle concentration distribution and the particle collection efficiency were then calculated based on the convection-diffusion equation with particle charging calculated by Fuchs diffusion charging theory. The simulated collection efficiencies of 6–100 nm nanoparticles were compared with the experimental data of Huang and Chen (2002 Huang, S. H. and Chen, C. C. 2002. Ultrafine Aerosol Penetration through Electrostatic Precipitators.. Environ. Sci. Technol., 36: 4625–4632. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) for a wire-in-plate dry ESP (aerosol flow rate: 100 L/min, applied voltage: ?15.5 ～ –21.5 kV). Good agreement was obtained. The simulated particle collection efficiencies were further shown to agree with the experimental data obtained in the study for a wire-in-plate wet ESP (Lin et al. 2010 Lin, G. Y., Tsai, C. J., Chen, S. C., Tzu, M. C. and Li, S. N. 2010. An Efficient Single-Stage Wet Electrostatic Precipitator for Fine and Nanosized Particle Control.. Aerosol Sci. Technol, 44: 38–45. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) (aerosol flow rate: 5 L/min, applied voltage: +3.6 ～+4.3 kV) using monodisperse NaCl particles of 10 and 50 nm in diameter. It is expected that the present model can be used to facilitate the design of ESPs for nanoparticle control and electrostatic nanoparticle samplers.