Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to...Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to the NBU(2) property of t he interarrival times. Secondly, the NBU(2) class of life distributions is prove d to be closed under the formation of series systems. Finally, it was also shown that the NBU(2) class is closed under convolution operation.展开更多
Assume an unreliable workstation performing jobs with a random service time, namely, it occasionally breaks down because of unexpected interruptions. As an interruption really occurs, the station is instantaneously re...Assume an unreliable workstation performing jobs with a random service time, namely, it occasionally breaks down because of unexpected interruptions. As an interruption really occurs, the station is instantaneously repaired and the uncompleted job is restarted again from the beginning till a job is completed without being interrupted. The total service time is shown to be NBU if and only if the total time it takes to finish each job with interruptions is stochastically larger than that without them, irrespective of when and how the breakdowns occur. As an application, a nonparametric procedure is developed to test for the strict NBU property of the service time. Finally, some numerical simulations are presented as well.展开更多
Istanbul author Orha n Pamuk once wrote that his hometow n Is immured in a sense of huzun,or melanchaly-a word denoting hopeless depression in English,while taking on fierce profundity in Turkish.Built on mil-iennia o...Istanbul author Orha n Pamuk once wrote that his hometow n Is immured in a sense of huzun,or melanchaly-a word denoting hopeless depression in English,while taking on fierce profundity in Turkish.Built on mil-iennia of history,the city and its citizens look forward while shadows of Constantinopb and the crumbled Ottoman Empire darken every comer.展开更多
文摘Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to the NBU(2) property of t he interarrival times. Secondly, the NBU(2) class of life distributions is prove d to be closed under the formation of series systems. Finally, it was also shown that the NBU(2) class is closed under convolution operation.
基金Supported by National Natural Science Foundation of China under Grant No. 10201010TY 10126014.
文摘Assume an unreliable workstation performing jobs with a random service time, namely, it occasionally breaks down because of unexpected interruptions. As an interruption really occurs, the station is instantaneously repaired and the uncompleted job is restarted again from the beginning till a job is completed without being interrupted. The total service time is shown to be NBU if and only if the total time it takes to finish each job with interruptions is stochastically larger than that without them, irrespective of when and how the breakdowns occur. As an application, a nonparametric procedure is developed to test for the strict NBU property of the service time. Finally, some numerical simulations are presented as well.
文摘Istanbul author Orha n Pamuk once wrote that his hometow n Is immured in a sense of huzun,or melanchaly-a word denoting hopeless depression in English,while taking on fierce profundity in Turkish.Built on mil-iennia of history,the city and its citizens look forward while shadows of Constantinopb and the crumbled Ottoman Empire darken every comer.
