航空复杂产品项目活动时间混合分布估算模型的改进

Improved Mixture Densities for the Activity Time Estimation in Aviation Complex Product Project

航空复杂产品开发项目具有复杂性、随机性、多目标性的特点,并且产品本身小批量、多品种的生产模式使得无法大量积累历史数据。因此,航空复杂产品项目活动时间存在高度的不确定性。如何能够更加合理、准确的描述其项目活动时间,对优化航空复杂产品的研制过程、缩短研制周期以及降低研制成本具有重大的意义。本文在Hahn基于PERT所建立的Beta Rectangular混合分布模型的基础上,保留其期望值的表达式,对其方差表达式进行改进。按照Malcolm、José等人的思想,将最可能值m与Beta分布的众数相对应,并且考虑其对方差的影响。仅保留PERT的一个假设,使方差的推导更多地依照于Beta分布而不是较多的近似。仿真结果表明,改进后的混合分布模型不但更具柔性,而且可以更加科学准确地描述航空复杂产品调度中高度不确定的任务持续时间状况。

The aviation complex product project is usually characterized as complex, stochastic and multi-objective work, and in addition, the small output and variety production model makes it impossible to cumulate nu- merous statistical data. So, the activity time of aviation complex product project is highly uncertain. How to accurately and precisely estimate the activity time is significant to optimizing process, shortening periods and cutting cost in the aviation complex product project. This paper prefers the expectation to variance of Hahn＇ s Beta Rectangular mixture densities based on PERT. We improve his variance formula by, as was suggesfed by Mal- colm and Jos6 et al, aligning the most likely value m with the mode of Beta distribution as well as considering how the value m affects the variance. Since only one of the PERT assumptions is necessarily retained and the e- licitation of the variance is more straightforward from the Beta density rather than under more assumptions, the improved mixture model is not only more flexible in application but also more accurate to address the problem of highly uncertain task duration in the aviation complex product project. The results under data simulation have proved this.