网络计划中时间均值的方差问题

“运筹学”权威教材中关键工序作业时间均值的方差公式推导错误．一般数理统计中的样本是直接抽取的简单随机样本,即样本所包含的个体之间是相互独立的．文章所针对的教材都用直接样本先计算出间接样本,再用间接样本计算样本均值及其方差．这样的间接样本是统计相关的,可是上述教材在计算样本方差和样本均值的方差时,又用了随机样本的方差公式,所以结果是错误的．文中推导的结果竟是原公式的3倍。

Variance Questions of Average Value Time in Network Plan

There are some errors in variance formula deduction about average time values of critical procedure, in some authoritative "operation research" textbooks. Samples in general mathematic and physical statistics are simple, which are selected randomly and directly. That means the units in these samples are independent and have nothing to do with each other. These indirect samples are first calculated based on the direct ones in some textbooks, and then the sample averages and its variance are calculated based on the indirect samples. These indirect samples have some statistical relationship with each other, but when calculating sample variance and average variance, the variance formula of random samples are used, so a wrong result is deduced. The result deduced here is as 3 times as the one deduced by the previous formula.