This page is designed for help with the RI TOI Estimation page. Help is also available for the Costs page and the Post-Survey Analysis page.
Remedial investigations (RI) are conducted at Department of Defense (DoD) sites to identify regions with munitions and explosives of concern (MEC). This module in VSP allows for the estimation of the rate (or count) of unacceptable items, referred to as Targets of Interest (TOI), (e.g. UXO, MEC, etc.) on a site and shows that this rate (or count) is no more than some pre-specified limit.
This design assumes that a transect survey will be performed and determines the survey area required and the location of randomly placed transects needed to confidently demonstrate that the rate (or count) of interest is no more than a pre-specified limit.
The assumptions associated with the formula for computing the number of transects are:
the distribution of the true number of unacceptable items given a sampling area follows a Binomial\((n,p)\) distribution, where \(n =\) true number of unacceptable items and \(p = \) proportion of site area that is surveyed,
the transect survey locations will be selected randomly and the size of transects is known,
prior to surveying, the likelihood of a transect containing TOI is equivalent across all possible transects,
the method used for inspection of anomalies (often digging and visual inspection) will reliably identify TOI.
no unacceptable items are found during surveying. If unacceptable items are found, the design conclusions presented are not valid and other analyses are needed (see post-survey analysis tab).
\( A \) |
is the area (user specified) of the site. |
\( N \) |
is the true (unknown) number of unacceptable items on the site. |
\( N_1 \) |
is the maximum count of unacceptable items (user specified). If a rate, \(r_1\), is specified, \(N_1=A*r_1\). |
\( p \) |
is the proportion of the site to be surveyed. |
\(k\) |
is the number of unacceptable items discovered during surveying (assumed to be 0). |
\( (1 - \alpha)\times 100\% \) |
is the desired confidence (user specified) that the true rate (or count) of unacceptable itmes is no more than the specified threshold. |
Given that \(N\) unacceptable items are present on the site, the probability of observing \(k\) unacceptable items when surveying \(p \times 100\% \) of the site is assumed to follow a binomial distribution:
\begin{equation} P(N; p) = \left(\begin{array}{c}N\\ k \end{array}\right) p^k (1 - p)^{N-k}. \end{equation}
Using Equation (1), the probability of the true number of unacceptable items on the site being no more than \(N_1\), given that no unacceptable items are discovered (\(k = 0\)), during surveying is:
\begin{equation}P(N \leq N_1 \mid k = 0) = \sum_{N=0}^{N_1} (1 - p)^N = 1 - (1 - p)^{N_1}\end{equation}
Setting Equation (2) equal to the desired level of confidence gives the proportion of the site that must be sampled:
\begin{equation} p = 1 - \alpha^{1/N_1} \end{equation}
and the required sample area, \(S\), is given by \(S = A*p\). If a desired rate of unacceptable items, \(r_1\), is provided (rather than a desired count) calculations are done using the above equations and \(N_1 = A*r_1\). The number of transects necessary will depend on the pre-specified transect dimension and can be calculated by dividing the total sample area by the dimension of one transect.
To provide as much spatial coverage as possible, survey transects should be as small as can be practically implemented.