VSSI X̄ charts with sampling at fixed times

A standard X̄ chart for controlling the process mean takes samples of size n0 at specified, equally-spaced, fixed-time points. This article proposes a modification of the standard X chart that allows one to take additional samples, bigger than n0, between these fixed times. The additional samples are taken from the process when there is evidence that the process mean moved from target. Following the notation proposed by Reynolds (1996a) and Costa (1997) we shortly call the proposed X chart as VSSIFT X chart where VSSIFT means variable sample size and sampling intervals with fixed times. The X chart with the VSSIFT feature is easier to be administered than a standard VSSI X chart that is not constrained to sample at the specified fixed times. The performances of the charts in detecting process mean shifts are comparable. Copyright © 1998 by Marcel Dekker, Inc.

Adaptive control charts for attributes

We develop a general model for adaptive c, np, u and p control charts in which one, two or three design parameters (sample size, sampling interval and control limit width) switch between two values, according to the most recent process information. For a given in-control average sampling rate and a given false alarm rate, the adaptive chart detects changes in the process much faster than a chart with fixed parameters. Moreover, this study also offers general guidance on how to choose an effective design.

Double sampling X̄ control chart for a first order autoregressive process

In this paper we propose the Double Sampling X̄ control chart for monitoring processes in which the observations follow a first order autoregressive model. We consider sampling intervals that are sufficiently long to meet the rational subgroup concept. The Double Sampling X̄ chart is substantially more efficient than the Shewhart chart and the Variable Sample Size chart. To study the properties of these charts we derived closed-form expressions for the average run length (ARL) taking into account the within-subgroup correlation. Numerical results show that this correlation has a significant impact on the chart properties.

Preliminary results concerning the VSS X- chart with unknow in-control parameters

The VSS X- chart is known to perform better than the traditional X- control chart in detecting small to moderate mean shifts in the process. Many researchers have used this chart in order to detect a process mean shift under the assumption of known parameters. However, in practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. In this paper, we evaluate the (run length) performances of the VSS X- control chart when the process parameters are estimated and we compare them in the case where the process parameters are assumed known. We draw the conclusion that these performances are quite different when the shift and the number of samples used during the phase I are small. ©2010 IEEE.

Step size control for efficient discrete element simulation

The step size determines the accuracy of a discrete element simulation. The position and velocity updating calculation uses a pre-calculated table and hence the control of step size can not use the integration formulas for step size control. A step size control scheme for use with the table driven velocity and position calculation uses the difference between the calculation result from one big step and that from two small steps. This variable time step size method chooses the suitable time step size for each particle at each step automatically according to the conditions. Simulation using fixed time step method is compared with that of using variable time step method. The difference in computation time for the same accuracy using a variable step size (compared to the fixed step) depends on the particular problem. For a simple test case the times are roughly similar. However, the variable step size gives the required accuracy on the first run. A fixed step size may require several runs to check the simulation accuracy or a conservative step size that results in longer run times. (C) 2001 Elsevier Science Ltd. All rights reserved.

Effect of training-sample size and classification difficulty on the accuracy of genomic predictors.

Introduction: As part of the MicroArray Quality Control (MAQC)-II project, this analysis examines how the choice of univariate feature-selection methods and classification algorithms may influence the performance of genomic predictors under varying degrees of prediction difficulty represented by three clinically relevant endpoints. Methods: We used gene-expression data from 230 breast cancers (grouped into training and independent validation sets), and we examined 40 predictors (five univariate feature-selection methods combined with eight different classifiers) for each of the three endpoints. Their classification performance was estimated on the training set by using two different resampling methods and compared with the accuracy observed in the independent validation set. Results: A ranking of the three classification problems was obtained, and the performance of 120 models was estimated and assessed on an independent validation set. The bootstrapping estimates were closer to the validation performance than were the cross-validation estimates. The required sample size for each endpoint was estimated, and both gene-level and pathway-level analyses were performed on the obtained models. Conclusions: We showed that genomic predictor accuracy is determined largely by an interplay between sample size and classification difficulty. Variations on univariate feature-selection methods and choice of classification algorithm have only a modest impact on predictor performance, and several statistically equally good predictors can be developed for any given classification problem.

Shewhart's control charts and process capability ratio applied to a sewage treatment station

The current study used statistical methods of quality control to evaluate the performance of a sewage treatment station. The concerned station is located in Cascavel city, Paraná State. The evaluated parameters were hydrogenionic potential, settleable solids, total suspended solids, chemical oxygen demand and biochemical oxygen demand in five days. Statistical analysis was performed through Shewhart control charts and process capability ratio. According to Shewhart charts, only the BOD(5.20) variable was under statistical control. Through capability ratios, we observed that except for pH the sewage treatment station is not capable to produce effluents under characteristics that fulfill specifications or standard launching required by environmental legislation.

Bayesian sample size for exploratory clinical trials incorporating historical data

This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored. Copyright (C) 2007 John Wiley & Sons, Ltd.

A new chart for monitoring the covariance matrix of bivariate processes

In this article we consider a control chart based on the sample variances of two quality characteristics. The points plotted on the chart correspond to the maximum value of these two statistics. The main reason to consider the proposed chart instead of the generalized variance |S| chart is its better diagnostic feature, that is, with the new chart it is easier to relate an out-of-control signal to the variables whose parameters have moved away from their in-control values. We study the control chart efficiency considering different shifts in the covariance matrix. In this way, we obtain the average run length (ARL) that measures the effectiveness of a control chart in detecting process shifts. The proposed chart always detects process disturbances faster than the generalized variance |S| chart. The same is observed when the size of the samples is variable, except in a few cases in which the size of the samples switches between small size and very large size.

Joint control charts for monitoring location and dispersion

The T-2 and the generalized variance vertical bar S vertical bar charts are used for monitoring the mean vector and the covariance matrix of multivariate processes. In this article, we propose for bivariate processes the use of the T-2 and the VMAX charts. The points plotted on the VMAX chart correspond to the maximum of the sample variances of the two quality characteristics. The reason to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar is the user's familiarity with the computation of simple sample variances; we can't say the same with regard to the computation of the generalized variance vertical bar S vertical bar.

Estudo das propriedades dos gráficos de controle bivariados com amostragem dupla

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gráficos de controle de X para monitoramento de processos autocorrelacionados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dispersion and size control of layered double hydroxide nanoparticles in aqueous solutions

We report a simple but efficient method to prepare stable homogeneous suspensions containing monodispersed MgAl layered double hydroxide (LDH) nanoparticles that have wide promising applications in cellular drug ( gene) delivery, polymer/LDH nanocomposites, and LDH thin films for catalysis, gas separation, sensing, and electrochemical materials. This new method involves a fast coprecipitation followed by controlled hydrothermal treatment under different conditions and produces stable homogeneous LDH suspensions under variable hydrothermal treatment conditions. Moreover, the relationship between the LDH particle size and the hydrothermal treatment conditions ( time, temperature, and concentration) has been systematically investigated, which indicates that the LDH particle size can be precisely controlled between 40 and 300 nm by adjusting these conditions. The reproducibility of making the identical suspensions under identical conditions has been confirmed with a number of experiments. The dispersion of agglomerated LDH aggregates into individual LDH crystallites during the hydrothermal treatment has been further discussed. This method has also been successfully applied to preparing stable homogeneous LDH suspensions containing various other metal ions such as Ni2+, Fe2+, Fe3+, Co2+, Cd2+, and Gd3+ in the hydroxide layers and many inorganic anions such as Cl-, CO32-, NO3-, and SO42-.

Calculation of sample size for stroke trials assessing functional outcome: comparison of binary and ordinal approaches

Background Many acute stroke trials have given neutral results. Sub-optimal statistical analyses may be failing to detect efficacy. Methods which take account of the ordinal nature of functional outcome data are more efficient. We compare sample size calculations for dichotomous and ordinal outcomes for use in stroke trials. Methods Data from stroke trials studying the effects of interventions known to positively or negatively alter functional outcome – Rankin Scale and Barthel Index – were assessed. Sample size was calculated using comparisons of proportions, means, medians (according to Payne), and ordinal data (according to Whitehead). The sample sizes gained from each method were compared using Friedman 2 way ANOVA. Results Fifty-five comparisons (54 173 patients) of active vs. control treatment were assessed. Estimated sample sizes differed significantly depending on the method of calculation (Po00001). The ordering of the methods showed that the ordinal method of Whitehead and comparison of means produced significantly lower sample sizes than the other methods. The ordinal data method on average reduced sample size by 28% (inter-quartile range 14–53%) compared with the comparison of proportions; however, a 22% increase in sample size was seen with the ordinal method for trials assessing thrombolysis. The comparison of medians method of Payne gave the largest sample sizes. Conclusions Choosing an ordinal rather than binary method of analysis allows most trials to be, on average, smaller by approximately 28% for a given statistical power. Smaller trial sample sizes may help by reducing time to completion, complexity, and financial expense. However, ordinal methods may not be optimal for interventions which both improve functional outcome

Treatment trials for neonatal seizures: the effect of design on sample size

Neonatal seizures are common in the neonatal intensive care unit. Clinicians treat these seizures with several anti-epileptic drugs (AEDs) to reduce seizures in a neonate. Current AEDs exhibit sub-optimal efficacy and several randomized control trials (RCT) of novel AEDs are planned. The aim of this study was to measure the influence of trial design on the required sample size of a RCT. We used seizure time courses from 41 term neonates with hypoxic ischaemic encephalopathy to build seizure treatment trial simulations. We used five outcome measures, three AED protocols, eight treatment delays from seizure onset (Td) and four levels of trial AED efficacy to simulate different RCTs. We performed power calculations for each RCT design and analysed the resultant sample size. We also assessed the rate of false positives, or placebo effect, in typical uncontrolled studies. We found that the false positive rate ranged from 5 to 85% of patients depending on RCT design. For controlled trials, the choice of outcome measure had the largest effect on sample size with median differences of 30.7 fold (IQR: 13.7–40.0) across a range of AED protocols, Td and trial AED efficacy (p<0.001). RCTs that compared the trial AED with positive controls required sample sizes with a median fold increase of 3.2 (IQR: 1.9–11.9; p<0.001). Delays in AED administration from seizure onset also increased the required sample size 2.1 fold (IQR: 1.7–2.9; p<0.001). Subgroup analysis showed that RCTs in neonates treated with hypothermia required a median fold increase in sample size of 2.6 (IQR: 2.4–3.0) compared to trials in normothermic neonates (p<0.001). These results show that RCT design has a profound influence on the required sample size. Trials that use a control group, appropriate outcome measure, and control for differences in Td between groups in analysis will be valid and minimise sample size.