مقايسه تصادفي چولگي سيستم هاي موازي در مدل پارتو

Stochastic Comparison of the Skewness of Parallel Systems in Pareto Model

ﭼﮑﯿﺪه: در اﻳﻦ ﻣﻘﺎﻟﻪ ﺑﻪ ﻣﻘﺎﯾﺴﻪ ﺗﺼﺎدﻓﯽ ﻃﻮل ﻋﻤﺮ ﺳﯿﺴﺘﻢ ﻫﺎي ﻣﻮازي ﺑﺎ ﻣﺆﻟﻔﻪ ﻫﺎي ﻏﯿﺮ ﻫﻤﮕﻦ از ﺗﻮزﯾﻊ ﭘﺎرﺗﻮ ﺑﺮ ﺣﺴﺐ ﺗﺮﺗﯿﺐ ﺗﺼﺎدﻓﯽ ﺳﺘﺎره و ﺗﺮﺗﯿﺐ ﺗﺼﺎدﻓﯽ ﻣﺤﺪب ﭘﺮداﺧﺘﻪ ﻣﯽ ﺷﻮد. ﺛﺎﺑﺖ ﺧﻮاﻫﺪ ﺷﺪ ﮐﻪ ﻃﻮل ﻋﻤﺮ ﯾﮏ ﺳﯿﺴﺘﻢ ﻣﻮازي ﺑﺎ ﻣﺆﻟﻔﻪ ﻫﺎي ﻣﺴﺘﻘﻞ ﻏﯿﺮ ﻫﻤﮕﻦ از ﻣﺪل ﭘﺎرﺗﻮ ﺑﺮ ﺣﺴﺐ ﺗﺮﺗﯿﺐ ﺗﺼﺎدﻓﯽ ﻣﺤﺪب،ﻫﻤﯿﺸﻪ ﮐﻤﺘﺮ از ﻃﻮل ﻋﻤﺮ ﯾﮏ ﺳﯿﺴﺘﻢ ﻣﻮازي دﯾﮕﺮ ﺑﺎ ﻣﺆﻟﻔﻪ ﻫﺎي ﻣﺴﺘﻘﻞ ﻫﻤﮕﻦ از ﻣﺪل ﭘﺎرﺗﻮ اﺳﺖ. ﻫﻤﭽﻨﯿﻦ ﺗﺤﺖ ﯾﮏ ﺷﺮط ﮐﻠﯽ روي ﭘﺎﻣﺘﺮﻫﺎي ﻣﻘﯿﺎس ﻧﺘﯿﺠﻪ اي در ارﺗﺒﺎط ﺑﺎ ﺗﺮﺗﯿﺐ ﺗﺼﺎدﻓﯽ ﺳﺘﺎره اﺛﺒﺎت ﻣﯽ ﺷﻮد.

In this paper, we further investigate stochastic comparisons of the lifetime of parallel systems with heterogeneous independent Pareto components in term of the star order and convex order. It will be proved that the lifetime of a parallel system with heterogeneous independent components from Pareto model is always smaller than from the lifetime of another parallel system with homogeneous independent components from Pareto model in the sense of convex order. Also, under a general condition on the scale parameters, it is proved a result involving with star order.