Note that because of statistical convergence, the more details that are included in the cost estimate, the more accurate the cost estimate becomes. This is simply because mathematically, the more detail that is present in the estimate, the more accuracy there will be. In a detailed estimate we have individual estimates for each of the details. It is reasonable and statistically accurate to say that some of the estimates will be overestimates and others will be underestimates. When these estimates are added together, the overestimates and the underestimates will tend to cancel each other out. This, in turn, makes the overall cost summary more accurate.
Suppose we have an estimate that we are doing for a new product. It is estimated that the most likely cost for the project will be $63,000. Based on this estimate, we have determined that the standard deviation of the estimate is $1,250. If we were interested in an estimate that had a range of values such that the actual cost would be more than the minimum and less than the maximum, it would be reasonable to use + or - two standard deviations from the most likely value. In this case it would be $63,000 +$2,500 and -$2,500 and the range of values would be $65,500 to $60,500. If this project were being bid competitively or if the product we were making had a very narrow price range, we would probably want to have more accurate estimates.
To do this and take advantage of the convergence of the standard deviation, we could break the product into five subassemblies. Once the subassemblies were identified, we could estimate the cost of each by estimating the optimistic, pessimistic, and most likely values. We could then calculate the expected value of each subassembly and its standard deviation. To get the overall revised estimate of the cost of the whole product, we then sum the standard deviations by first squaring them, then adding them together, and then taking the square root of the total.
Suppose we have an estimate that we are doing for a new product. It is estimated that the most likely cost for the project will be $63,000. Based on this estimate, we have determined that the standard deviation of the estimate is $1,250. If we were interested in an estimate that had a range of values such that the actual cost would be more than the minimum and less than the maximum, it would be reasonable to use + or - two standard deviations from the most likely value. In this case it would be $63,000 +$2,500 and -$2,500 and the range of values would be $65,500 to $60,500. If this project were being bid competitively or if the product we were making had a very narrow price range, we would probably want to have more accurate estimates.
To do this and take advantage of the convergence of the standard deviation, we could break the product into five subassemblies. Once the subassemblies were identified, we could estimate the cost of each by estimating the optimistic, pessimistic, and most likely values. We could then calculate the expected value of each subassembly and its standard deviation. To get the overall revised estimate of the cost of the whole product, we then sum the standard deviations by first squaring them, then adding them together, and then taking the square root of the total.