This function performs the Second Moment Method (SMM) analysis to estimate the total mean, variance, and standard deviation of a project based on individual task means, variances, and an optional correlation matrix.
Value
The function returns a list of the total mean, variance, and standard deviation for the project.
Examples
# Set the mean vector, variance vector, and correlation matrix for a toy project.
mean <- c(10, 15, 20)
var <- c(4, 9, 16)
cor_mat <- matrix(c(
1, 0.5, 0.3,
0.5, 1, 0.4,
0.3, 0.4, 1
), nrow = 3, byrow = TRUE)
# Use the Second Moment Method to estimate the results for the project.
result <- smm(mean, var, cor_mat)
print(result)
#> Second Moment Method Results:
#> ------------------------------
#> Total Mean: 45
#> Total Variance: 49.4
#> Total Standard Deviation: 7.028513
# Without correlation matrix (independent tasks)
result <- smm(mean, var)
print(result)
#> Second Moment Method Results:
#> ------------------------------
#> Total Mean: 45
#> Total Variance: 29
#> Total Standard Deviation: 5.385165
# When certain tasks are discrete and others are continuous, the SMM can still
# be applied as long as the variance values accurately reflect the variability of each task.
discrete_mean <- c(5, 10)
discrete_var <- c(0, 0)
continuous_mean <- c(15, 20)
continuous_var <- c(4, 5)
mean <- c(discrete_mean, continuous_mean)
var <- c(discrete_var, continuous_var)
cor_mat <- matrix(c(
1, 0, 0.2, 0.3,
0, 1, 0.1, 0.2,
0.2, 0.1, 1, 0.4,
0.3, 0.2, 0.4,
1
), nrow = 4, byrow = TRUE)
result <- smm(mean, var, cor_mat)
print(result)
#> Second Moment Method Results:
#> ------------------------------
#> Total Mean: 50
#> Total Variance: 12.57771
#> Total Standard Deviation: 3.546507