Reliability Estimation for the Remained Stress-Strength Model under the Generalized Exponential Lifetime Distribution

A stress-strength reliability model compares the strength and stresses on a certain system; it is used not only primarily in reliability engineering and quality control but also in economics, psychology, and medicine. In this paper, a novel extension of stress-strength models is presented. The mew model is applied under the generalized exponential distribution. The maximum likelihood estimator, asymptotic distribution, and Bayesian estimation are obtained. A comprehensive simulation study along with real data analysis is performed for illustrating the importance of the new stress-strength model.

The Lindy effect in psychology: Network dynamics reinforce depression over time

This paper studies the factors that sustain mental disorders by taking a network approach. The network theory suggests that mental disorders are networks of symptoms that causally interact (Borsboom, 2017). Symptom networks share certain dynamics with other complex systems: abrupt transitions between stable states, critical slowing down and hysteresis (Cramer et al., 2016). These findings suggest that symptom networks that have transitioned to a pathological state tend to remain that state. We argue that this tendency leads to the Lindy effect in symptom networks. The Lindy effect means that the conditional probability of surviving beyond a time point, given survival until that time point, increases over time (Taleb, 2014). In other words, time benefits future survival. A symptom network is considered to have survived until a time point if it has remained in a pathological state until that point. We first show how the Lindy effect is formalised by examining the stopping time distribution of Brownian motion with an absorbing barrier (Cook, 2012; Taleb, 2018). Specifically, we describe the hazard function of the stopping time distribution and make a distinction between "strong Lindy" and "weak Lindy". Strong Lindy is a monotonically decreasing hazard function whereas weak Lindy means an inverted-U shaped hazard function. Then, major depressive disorder (MDD) networks were simulated, manipulating the level of symptom connectivity. As before, the presence of the Lindy effect in these networks were tested using hazard functions, and in addition, survival probabilities conditioned on time. Afterwards, we fit a distribution to the network lifetimes. The lifetime distribution of strongly connected networks were heavy tailed and showed the Lindy effect; the longer a network had been depressed, the more likely it was to remain depressed. The lifetime distribution of weakly connected networks were light tailed and did not show the Lindy effect. After discussing caveats and alternative explanations of the findings, we conclude that network dynamics and the resulting Lindy effect can explain several findings in psychology such as the chronicity of depression (Swaminath, 2009) and the frequency distribution of remission times (Simon, 2000; Patten et al., 2010).

Altering the distribution of excited-state lifetimes in aminated GFP chromophores by Ag nanohole arrays

Fluorescence of the modified GFP chromophore diethyl-ABDI-BF2 dispersed in PMMA matrix is studied on top of glass, continuous and perforated optically thin silver films. In polymer, the fluorescence decay kinetics becomes non-exponential and can be described by the distribution of rate constants. The results demonstrate shortening of the excited state lifetime in the presence of silver and broadening of the lifetime distribution caused by the nanoholes.

Investigation of Factors Causing Nonuniformity in Luminescence Lifetime of Fast-Responding Pressure-Sensitive Paints

Factors that cause nonuniformity in the luminescence lifetime of pressure-sensitive paints (PSPs) were investigated. The lifetime imaging method of PSP does not theoretically require wind-off reference images. Therefore, it can improve measurement accuracy because it can eliminate errors caused by the deformation or movement of the model during the measurement. However, it is reported that the luminescence lifetime of PSP is not uniform on the model, even under uniform conditions of pressure and temperature. Therefore, reference images are used to compensate for the nonuniformity of the luminescence lifetime, which significantly diminishes the advantages of the lifetime imaging method. In particular, fast-responding PSPs show considerable variation in luminescence lifetime compared to conventional polymer-based PSPs. Therefore, this study investigated and discussed the factors causing the nonuniformity of the luminescence lifetime, such as the luminophore solvent, luminophore concentrations, binder thickness, and spraying conditions. The results obtained suggest that the nonuniformity of the luminophore distribution in the binder caused by the various factors mentioned above during the coating process is closely related to the nonuniformity of the luminescence lifetime. For example, when the thickness of the binder became thinner than 8 μm, the fast-responding PSPs showed a tendency to vary significantly in the luminescence lifetime. In addition, it was found that the luminescence lifetime of fast-responding PSP could be changed in the depth direction of the binder depending on the coating conditions. Therefore, it is important to distribute the luminophore uniformly in the binder layer to create PSPs with a more uniform luminescence lifetime distribution.

Neutrosophic entropy measures for the Weibull distribution: theory and applications

Entropy is a standard measure used to determine the uncertainty, randomness, or chaos of experimental outcomes and is quite popular in statistical distribution theory. Entropy methods available in the literature quantify the information of a random variable with exact numbers and lacks in dealing with the interval value data. An indeterminate state of an experiment generally generates the data in interval form. The indeterminacy property of interval-valued data makes it a neutrosophic form data. This research proposed some modified forms of entropy measures for an important lifetime distribution called Weibull distribution by considering the neutrosophic form of the data. The performance of the proposed methods is assessed via a simulation study and three real-life data applications. The simulation and real-life data examples suggested that the proposed methodologies of entropies for the Weibull distribution are more suitable when the random variable of the distribution is in an interval form and has indeterminacy or vagueness in it.