Variable Sample Size Control Charts for Monitoring the Multivariate Coefficient of Variation Based on Median Run Length and Expected Median Run Length

The monitoring of a well-functioning process system has always held significant importance. In recent times, there has been notable attention towards employing control charts to oversee both univariate and multivariate coefficients of variation (MCV). This shift is in response to the concern of erroneous outcomes that can arise when traditional control charts are applied under the condition of dependent mean and standard deviation, as highlighted by prior research. To address this, the remedy lies in adopting the coefficient of variation. Furthermore, this study underscores the application of MCV in scenarios where multiple quality attributes are simultaneously under surveillance within an industrial process. This aspect has demonstrated considerable enhancement in chart performance, especially when incorporating the variable sample size (VSS) feature into the MCV chart. Adaptive VSS, evaluated through metrics like median run length (MRL) and expected median run length (EMRL), is also integrated for MCV monitoring. In contrast to earlier studies that predominantly focused on average run length (ARL), this research acknowledges the potential inaccuracies in ARL measurement. In this study, two optimal designs for VSS MCV charts are formulated by minimizing two criteria: firstly, MRL; and secondly, EMRL, both accounting for deterministic and unknown shift sizes. Additionally, to assess the distribution's variability in run lengths, the study provides the 5th and 95th percentiles. The research delves into two VSS schemes: one with a defined small sample size (nS), and another with a predetermined large sample size (nL) for the initial subgroup (n(1)). The approach taken involves the development of a Markov chain method for designing and deriving performance measures of the proposed chart. These measures include MRL and EMRL. Moreover, a comparative analysis between the proposed chart's performance and the standard MCV chart (STD) is presented in terms of MRL and EMRL criteria. The outcomes illustrate the superiority of the proposed chart over the STD MCV chart for all shift sizes, whether they are upward or downward, and when n(1) equals nS or nL

Characterization of in vivo human skin in response to mechanical indentation using optical coherence tomography

The biomechanical response of skin can reflect not only health or localized pathology, but also systemic disease or an abnormal physiological condition of an individual. Both the intrinsic stiffness of the solid constituents and the time-evolved redistribution of fluid within skin tissue can influence the biomechanical response to external forces. Therefore, it is important not only to evaluate the responding skin dynamics upon mechanical perturbation, but also to understand the intrinsic viscoelastic properties and fluid dynamics in the skin. While the clinical diagnosis of skin pathologies relies mostly on visual inspection and manual palpation, a more quantitative tissue characterization is highly desirable. Optical coherence tomography (OCT) is an interferometry-based imaging modality that offers an imaging resolution (cellular level) that surpasses those of most standard clinical imaging tools and has shown to be able suitable for in vivo skin imaging. Therefore, this thesis investigates OCT-guided characterization of the biomechanical response of skin, as well as the viscoelastic properties and the characteristics of local fluid transport. Quantitative analysis metrics were developed and demonstrated on in vivo human subjects, and a significant difference between the mechanically-perturbed and non-perturbed skins is revealed. Additionally, the quantitative results exhibit differences in the post-indentation scenarios between the young skin and the aged skin. Functional OCT techniques, such as optical coherence elastography (OCE) and Doppler OCT, are demonstrated to assess the stiffness and fluid dynamics of in vivo human tissue as well. The OCE results successfully reveal the stiffness at different anatomical sites, and the Doppler OCT shows the existence of the micro-vessels. This thesis research demonstrates the feasibility of quantitative skin characterization, the assessment of skin elasticity, and the revelation of fluid flows. With these information combined, a more objective and potentially more accurate diagnosis tool for skin pathologies may be possible in the future