Suppose X λ1 , . . . , X λn is a set of non-negative random variables with X λi having the distribution function G(λ i t), λ i > 0 for i = 1, . . . , n, and I p1 , . . . , I pn are independent Bernoulli random variables, independent of the X λi 's, with E(I pi ) = p i , i = 1, . . . , n. Let Y i = I pi X λi , for i = 1, . . . , n. It is of interest to note that in actuarial science, Y i corresponds to the claim amount in a portfolio of risks. In this paper, under certain conditions, by using the concept of vector majorization and related orders, we discuss stochastic comparison between the smallest claim amount in the sense of the usual stochastic and hazard rate orders. We also obtain the usual stochastic order between the largest claim amounts when the matrix of parameters (h( p), λ) changes to another matrix in a mathematical sense. We then apply the results for three special cases of the scale model: generalized gamma, Marshall-Olkin extended exponential and exponentiated Weibull distributions with possibly different scale parameters to illustrate the established results.

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Subway train operation is a complex, sociotechnical system that involves a variety of cognitively demanding tasks. The train operators are responsible for continuously monitoring the surrounding environment, maintaining awareness, processing information, and making decisions under risk. The resulting mental strain on operators can negatively affect their performance and the interaction of the human-machine system. The objective of this study was to evaluate if physiological, subjective, and performance measures could identify the level of mental workloads arising from routine and nonroutine operations in the subway system. A total of 11 subway train operators underwent different driving scenarios in a high-fidelity simulator. The simulated tasks were divided into two categories: routine operations (preparing to drive and driving between stations without interruptions or emergencies) and nonroutine operation (responding to a tunnel fire, dealing with a high density of passengers, encountering a passenger/technician on the track, and responding to train failure). The mental workload was monitored and evaluated in these tasks using an electrocardiogram, subjective self-rating scales, and driving performance. Both heart rate variability and performance measures (including reaction time and error rate) detected mental workload variations in the different operations. On the other hand, the subjective ratings (including NASA-TLX) assessed the overall mental workload associated with a task, without explaining the mental demand variations within the task over time. Subway train drivers experienced different levels of mental workload during routine and nonroutine driving conditions.

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