TY - JOUR T1 - Optimization Problem in Series Systems with Random Number of Components from the Family of Power Series Distributions TT - مسئله بهینه‌سازی در سیستم‌های سری با تعداد مؤلفه‌های تصادفی از خانواده توزیع‌های سری توانی JF - JSS JO - JSS VL - 15 IS - 2 UR - http://jss.irstat.ir/article-1-718-en.html Y1 - 2022 SP - 481 EP - 504 KW - Optimization KW - Geometric Distribution KW - Series System KW - Total Time on Test KW - Weibull Distribution. N2 - In this paper, the lifetime model based on series systems with a random number of components from the family of power series distributions has been considered. First, some basic theoretical results have been obtained, which have been used to optimize the number of components in series systems. The average lifetime of the system, the cost function, and the total time on test have been used as an objective function in optimization. The issue has been investigated in detail when the lifetimes of system components have Weibull distribution, and the number of components has geometric, logarithmic, or zero-truncated Poisson distributions. The results have been given analytically and numerically. Finally, a real data set has been used to illustrate the obtained results. M3 10.52547/jss.15.2.481 ER -