# On the theory behind the Successive Principle

## The application area

The Principle is applied to issues such as estimates, budget proposals, schedules, resource plans, current value analyses or sales analyses. It generates a numerical total result which is calculated on the basis of a number of uncertain input parameters.

## The Principle

The Principle is based on the Bayesian theory of statistics which recognises and provides rules for dealing with subjective uncertainty. It focuses on the causes of the many elements of uncertainty, singling them out for explicit treatment. This helps to avoid having to work with correlation coefficients and other difficult statistical concepts. This is a great bonus in terms of practical application without sacrificing appreciably the intrinsic accuracy of the method. The procedure is amplified below.

## Sources of uncertainty

By way of introduction, the task and all its potential general sources of uncertainty are identified. It is vital to the quality of the result to identify all factors of any significance, including the very subjective and perhaps even the ‘uncomfortable’. Once the identified factors have been organised into discrete statistical items or factors, a suitable, clear reference basis of assumptions is chosen, which comprises inter alia a fixed, calculative definition and qualification of all the items, factors or activities.

## Calculation structure

A work breakdown structure can then be built up as a series of discrete, specific items, factors and/or activities. This process not only allows all sources of uncertainty to be shown separately in the result, but also helps to eliminate the need for correlation coefficients.

In order to minimise further the effect of any remaining correlation, the conditional uncertainty is consistently used, i.e. the local uncertainty, on the precondition that all other aspects are in their normal state. This means that for the first time we have a statistical procedure which is both user-friendly and sufficiently accurate.

Two types of items/factors/activities are worked on: (1) one set which typically represents physical and other well-defined aspects (hereinafter called ‘items’), and (2) another set which represents universal sources of uncertainty (hereinafter called ‘correction factors’ or simply ‘factors’). In the time and resources schedules, ‘items’ refer to activities.

## Calculations

The local conditional mean value, m, and related standard deviation, s, are determined for all items and factors. In the interests of the quality of the results, group estimates are typically used, coupled with systematic estimating techniques (see the literature). The subsequent statistical calculations are based on the so-called triple estimate, combining extreme outlying values and a most probable value.

The mean value of the result is simply calculated using the local mean values as a conventional deterministic figure. The related total uncertainty is derived from the calculated local sources of uncertainty in the manner set out below.

For each local source of uncertainty, its conditional effect on the uncertainty of the total is calculated. The corresponding uncertainty (the squares of s, s x s, called the variance) of the total is very close to the sum of all these squared standard deviations or variances. They therefore produce a valuable priority figure as they show how critical the individual local uncertainty is to the overall end result. They are normally given as a percentage of the corresponding sum total.

## The natural laws of uncertainty

According to the natural laws of statistics, the many incidental minor errors of judgement on the whole cancel each other out in the end result (in the same way as 200 tosses of heads or tails result astonishingly reliably in approximately 50% heads and 50% tails). The mean figure is typically slightly higher than the most probable value, commensurate with the fact that the skewness in the triple estimate mostly tends to turn upwards. The mean figures are essential, as they have to be used to calculate the results. The same natural laws also dictate that in the majority of cases the results show a fairly normal, and therefore symmetrical, distribution.

For more detailed information on the theory and the calculations, see the literature on the subject in the section, Further information Dr. Steen Lichtenberg

1930 - 2019 †
On the theory behind the Successive Principle
The principle is based on Bayesian statistical theory, psychology behind expert evaluations plus a consistent top down principle.