The Variable Sample Size (X)over-bar Chart with Estimated Parameters

The VSS X chart, dedicated to the detection of small to moderate mean shifts in the process, has been investigated by several researchers under the assumption of known process parameters. 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 chart when the process parameters are estimated, we compare them in the case where the process parameters are assumed known and we propose specific optimal control chart parameters taking the number of Phase I samples into account.

X̄ charts with variable sample size

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours. This article considers the properties of the X̄ chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) X̄ chart are obtained using Markov chains. The VSS X̄ chart is substantially quicker than the traditional X̄ chart in detecting moderate shifts in the process.

X̄ chart with variable sample size and sampling intervals

Recent theoretical studies have shown that the X̄ chart with variable sampling intervals (VSI) and the X̄ chart with variable sample size (VSS) are quicker than the traditional X̄ chart in detecting shifts in the process. This article considers the X̄ chart with variable sample size and sampling intervals (VSSI). It is assumed that the amount of time the process remains in control has exponential distribution. The properties of the VSSI X̄ chart are obtained using Markov chains. The VSSI X̄ chart is even quicker than the VSI or VSS X̄ charts in detecting moderate shifts in the process.

Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals

Recent studies have shown that the X̄ chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both the X̄ and R charts. A Markov chain model is used to determine the properties of the joint X and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint X̄ and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.

Modelling polymers with side chains: MEH-PPV and P3HT

Modelling polymers with side chains is always a challenge once the degrees of freedom are very high. In this study, we present a successful methodology to model poly[2-methoxy-5-(2′-ethyl-hexyloxy)-p-phenylenevinylene] (MEH-PPV) and poly[3-hexylthiophene] (P3HT) in solutions, taking into account the influence of side chains on the polymer conformation. Molecular dynamics and semi-empirical quantum mechanical methods were used for structure optimisation and evaluation of optical properties. The methodology allows to describe structural and optical characteristics of the polymers in a satisfactory way, as well as to evaluate some usual simplifications adopted for modelling these systems. Effective conjugation lengths of 8-14.6 and 21 monomers were obtained for MEH-PPV and P3HT, respectively, in accordance with experimental findings. In addition, anti/syn conformations of these polymers could be predicted based on intrinsic interactions of the lateral branches. © 2013 Copyright Taylor and Francis Group, LLC.