Stochastic Comparisons of Lifetimes of Series and Parallel Systems with Dependent Heterogeneous MOTL-G Components under Random Shocks

To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of two series (parallel) systems with dependent or independent heterogeneous Marshall–Olkin Topp Leone G (MOTL-G) components under random shocks. Further, the effect of heterogeneity of the shape parameters of MOTL-G components and surviving probabilities from random shocks on the reliability of series and parallel systems in the sense of the usual stochastic and hazard rate orderings is investigated. First, we establish the usual stochastic and hazard rate orderings for the lifetimes of series and parallel systems when components are statistically dependent. Second, we also adopt the usual stochastic ordering to compare the lifetimes of the parallel systems under the assumption that components are statistically independent. The theoretical findings show that the weaker heterogeneity of shape parameters in terms of the weak majorization order results in the larger reliability of series and parallel systems and indicate that the more heterogeneity among the transformations of surviving probabilities from random shocks according to the weak majorization order leads to larger lifetimes of the parallel system. Finally, several numerical examples are provided to illustrate the main results, and the reliability of series system is analyzed by the real-data and proposed methods.

Demographic shifts, inter-group contact, and environmental conditions drive language extinction and diversification

Humans currently collectively use thousands of languages1,2. The number of languages in a given region (i.e. language “richness”) varies widely3–7. Understanding the processes of diversification and homogenization that produce these patterns has been a fundamental aim of linguistics and anthropology. Empirical research to date has identified various social, environmental, geographic, and demographic factors associated with language richness3. However, our understanding of causal mechanisms and variation in their effects over space has been limited by prior analyses focusing on correlation and assuming stationarity3,8. Here we use process-based, spatially-explicit stochastic models to simulate the emergence, expansion, contraction, fragmentation, and extinction of language ranges. We varied combinations of parameter settings in these computer-simulated experiments to evaluate the extent to which different processes reproduce observed patterns of pre-colonial language richness in North America. We find that the majority of spatial variation in language richness can be explained by models in which environmental and social constraints determine population density, random shocks alter population sizes more frequently at higher population densities, and population shocks are more frequently negative than positive. Language diversification occurs when populations split after reaching size limits, and when ranges fragment due to population contractions following negative shocks or due to contact with other groups that are expanding following positive shocks. These findings support diverse theoretical perspectives arguing that language richness is shaped by environmental and social conditions, constraints on group sizes, outcomes of contact among groups, and shifting demographics driven by positive innovations, such as new subsistence strategies, or negative events, such as war or disease.

Random Walk Analysis in a Reliability System under Constant Degradation and Random Shocks

In this paper, we study a reliability system subject to occasional random shocks hitting an underlying device in accordance with a general marked point process with position dependent marking. In addition, the system ages according to a linear path that eventually fails even without any external shocks that accelerate the total failure. The approach for obtaining the distribution of the failure time falls into the area of random walk analysis. The results obtained are in closed form. A special case of a marked Poisson process with exponentially distributed marks is discussed that supports our claim of analytical tractability. The example is further confirmed by simulation. We also provide a classification of the literature pertaining to various reliability systems with degradation and shocks.

Optimal Age-Based Preventive Maintenance Policy for a System Subject to Cumulative Damage Degradation and Random Shocks

This research investigates the problem of cumulative degradation and random shocks a system like a centrifugal pump may experience during normal and adverse operating conditions. An accelerated life testing method was employed to determine the degradation of the pump under cumulative damage degradation and random shocks conditions. An age- Based policy was used to determine the optimum time interval that will minimize the total expected cost of the system. The random shock increases the number of failures and hence reduces the reliability of the system. The total expected preventive maintenance cost obtained varies from N1700.00 (One thousand seven hundred naira) to N16,000.00 (sixteen thousand naira), depending on the shock and shock duration. The methodology presented is useful and thus recommended for use to study cumulative damage degradation and random shocks for similar systems.