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What is Statistical Cost Estimating?

Statistical cost estimating is a method of using statistics to determine the range of values of a cost estimate and the probability that the actual cost will occur between the two values in the range. This is the same technique that is discussed in the PERT method that is discussed in Time Management under "What is the PERT method?" The PERT technique is used to estimate the project duration. Here it is applied to estimating cost. The calculations are exactly the same here as they are in the PERT technique.
Most of the time in cost estimating we are satisfied with an estimated range of values that has a 95 percent probability of having the actual cost of the estimated item falling within the range. This is the range of values that is the expected value of cost plus two standard deviations and minus two standard deviations.

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In the PERT technique discussed in Time Management, we attempt to determine the probability of the project’s being completed between a pair of dates. The range of dates is the expected completion date of the project plus or minus two standard deviations calculated using the equations above. While the dates are approximations based on using a normal distribution, a skewed probability distribution such as the beta distribution (see SKEWED PROBABILITY DISTRIBUTION) would be more correct, but the results are accurate enough for schedule estimates. These same assumptions are equally valid for cost estimating.

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 as shown in EXAMPLE: INCREASING DETAIL OF AN ESTIMATE. 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.

An estimate is broken down into five subestimates (figures in thousands), Complete estimate has total cost of $63,000 with $640 std dev.

Now we still have an expected value of $63,000, but the standard deviation is $640. To get the 95 percent range of values as we did earlier, we take the $63,000 and + or − two standard deviations but now use $640 instead of $1,250. This gives us $63,000 + $1,280 − $1,280, or a range of values of $64,280 to $61,720. Simply decomposing the project into five components has had a significant increase in the accuracy of our estimate.

The interesting thing about estimating using this technique is that it tells you when you have done enough estimating work and what you must do to improve the estimate to where it will serve your current needs. Many times people spend too much work in producing an estimate that is too accurate for the purpose. This is a waste of effort.

By the use of this technique we begin our project with order of magnitude estimates that have a relatively low accuracy required (−25 percent to +75 percent). As we progress closer to making a commitment, we will want to increase the accuracy of our estimates to a 95 percent probability of having the actual cost come between the range of values that is estimated. To do this all that needs to be done is to look at the value of the largest subcomponent in the previous estimate and break that component down into sub-subcomponents and independently estimate the cost of each of those components. By doing this we will reduce the magnitude of the standard deviation of the total and thereby improve the overall accuracy of the total estimate. If the range of values and the probability of the actual cost being within them is good enough for this estimate, then we can stop work. If the range of values or the probability is not good enough, then we look for the next large component of cost and break it down into subgroups and recalculate our estimate. The standard deviation magnitude will become smaller and the range of values for a given probability will also become smaller.