Nuclear material accounting (NMA) is the only safeguards system whose benefits are routinely quantified. Process monitoring (PM) is another safeguards system that is increasingly used, and one challenge is how to quantify its benefit. This paper considers PM in the role of enabling frequent NMA, which is referred to as near-real-time accounting (NRTA). We quantify NRTA benefits using period-driven and data-driven testing. Period-driven testing makes a decision to alarm or not at fixed periods. Data-driven testing decides as the data arrives whether to alarm or continue testing. The difference between period-driven and datad-riven viewpoints is illustrated by using one-year and two-year periods. For both one-year and two-year periods, period-driven NMA using once-per-year cumulative material unaccounted for (CUMUF) testing is compared to more frequent Shewhart and joint sequential cusum testing using either MUF or standardized, independently transformed MUF (SITMUF) data. We show that the data-driven viewpoint is appropriate for NRTA and that it can be used to compare safeguards effectiveness. In addition to providing period-driven and data-driven viewpoints, new features include assessing the impact of uncertainty in the estimated covariance matrix of the MUF sequence and the impact of both random and systematic measurement errors.

One challenge in modern safeguards at declared facilities that process special nuclear material (SNM) is how to quantify the benefit of process monitoring (PM) [

Because PM can have several roles, it is necessary to consider the quantitative benefits of each possible role. For example, PM can have a “front-line” role in monitoring for indicators of facility misuse, such as a shift in nitric acid concentration to direct excess Pu to a waste stream from a separations area in an aqueous reprocessing facility [

Traditionally, nuclear material accounting (NMA) consists of relatively infrequent material balance closures (such as once per year), with the material balance (MB) defined as

Toward the goal of quantifying the benefits of PM data, this paper revisits statistical methods for NMA and for frequent NMA, called, near-real-time accounting (NRTA). Both NMA and NRTA have been discussed in two main literature reviews, Speed and Culpin [

NRTA is made possible by PM in the support role of enabling frequent material balance closures. The statistical methods include Shewhart charts based on multiple material balances during a year on MB data (the International Atomic Energy Agency refers to the MB sequence as the material unaccounted for, MUF, sequence), SITMUF (standardized independent transformed MUF) data, and a once-per-year balance based on the MUF data, known as CUMUF. The SITMUF sequence is a transform of the MUF sequence

As is customary in safeguards, entries in

We also consider joint cumulative sum or cusum (also known as Page's test) methods [

We revisit NRTA as a quantitative component of safeguards at declared facilities to monitor for SNM loss using both period-driven and data-driven testing. A period-driven approach makes a statistical decision to alarm or not at the end of each fixed period. A data-driven approach (also known as sequential testing) does not use a set decision period but instead decides as the data arrives whether to alarm or continue testing.

The difference between period-driven and data-driven viewpoints is illustrated simply by using both one-year and two-year periods, with sequential testing using a two-year truncation period serving as a surrogate for data-driven testing. For both one-year and two-year periods, conventional (period-driven) NMA using a once-per-year cumulative MUF (CUMUF, cumulative material unaccounted for) testing is compared to Shewhart and joint sequential cusum testing using either MUF or SITMUF (standardized, independently transformed MUF) data.

In addition to providing period-driven and data-driven viewpoints, new features include assessing the impact of uncertainty in the estimated covariance matrix of the MUF sequence and the impact of both random and systematic measurement errors.

There is interest in comparing pyroreprocessing to aqueous (and comparing several variations of aqueous) reprocessing with regard to proliferation resistance [

The paper is organized as follows. Section

Avenhaus and Jaech [

Avenhaus and Jaech [

In period-driven (annual) testing, Burr et al. [

In response to the “worst-case” loss scenario given previously from Avenhaus and Jaech [

Avenhaus and Jaech [

We consider the following setup motivated by Avenhaus and Jaech [

48, 36, 24, 12, 6, 4, 1 balances per year,

MUF covariance matrix

Avenhaus and Jaech [

and for

We let

The methods we consider are

MUF for

SITMUF for

CUMUF—one balance per year so

MUF Shewhart—multiple balances—alarm if any

SITMUF Shewhart—multiple balances—alarm if any

MUF joint cusum—two cusum streams, one for abrupt

SITMUF joint cusum—two cusum streams, one for abrupt

Our approach: critical values are found exactly or by simulation (

Our performance criteria are as follows.

For protracted threat, AP over one year.

For abrupt threat, timeliness AP, AP within 30 days; 90 and 60 days for

For protracted threat (same loss per balance), AP and expected loss. The AP is over the entire year and expected loss EL is computed as

where

From Figure

AP for protracted threat,

From Figure

AP for protracted threat,

For the (

We emphasize that what is new here is that we have identified different covariance matrices than considered previously where the SITMUF version does not dominate (have uniformly higher APs than) the MUF version and the joint cusum versions do not dominate CUMUF in terms of the AP.

For CUMUF, the expected loss

Expected loss for protracted threat,

For (

For (

From Figure

Timeliness AP for abrupt threat,

For (

For (

From Figure

AP for optimal protracted threat for CUMUF,

Here we consider the SITMUF joint cusum method performance as

AP for protracted threat using SITMUF joint cusum for

Expected loss for protracted threat using SITMUF joint cusum for

Timeliness AP for abrupt threat using SITMUF joint cusum for

From Figure

From Figures

From Figure

Jones [

As mentioned in Section

As a convenient way to introduce measurement error in the MUF covariance matrix

To study robustness to estimation error in

Similarly, for the SITMUF joint cusum, the critical values we used were based on the true MUF covariance matrix, and the FAP increases on average from 0.05 to 0.055 and the 0.05 and 0.95 quantiles across 1000 realizations of the estimated

These findings for the SITMUF cusum or joint cusum suggest robustness to 15% estimation error in

We find that the estimated APs are robust by being nearly the same as in the situation of having zero error in

In a real facility,

Regarding a possible performance advantage of SITMUF over MUF, this section shows that on average across random loss scenarios, the AP for SITMUF-based testing is the same as the AP for MUF-based testing. Note that because the SITMUF sequence

Burr and Hamada [

Burr and Hamada [

We also used a genetic algorithm (GA) to find scenarios which maximizes the MUF versus SITMUF difference. We considered 8 cases defined by

To contrast period-driven (make a statistical decision to alarm or not once per year, e.g.,) from data-driven testing (make a statistical decision to alarm or not on the fly, as data arrives), we can mimic data-driven testing by comparing a two-year study with truncated sequential testing to a one-year period-driven study.

We consider five covariance matrices for two years. These correspond to (1) no cleanout, no systematic measurement error, and the other four have systematic measurement error with (2) no cleanout, with measurement calibration, (3) no cleanout, without measurement calibration, (4) with cleanout, with measurement calibration, (5) with cleanout, with measurement calibration.

Avenhaus and Jaech [

The scenarios in the remainder of this section have systematic measurement error.

In the remaining sections we consider both random and systematic error components for

We have the

We have the

For

For

For

For

We have the same covariances for balances within the same year as given in the preceding scenario. The Appendix gives what has to be added for years 1 and 2 which applies to all pairs of years.

The FAP is set at

First we compare the APs from

AP for protracted threat using SITMUF joint cusum for

The APs for loss over two years of

Next we compare SITMUF joint cusum with CUMUF for

AP for protracted threat using SITMUF joint cusum versus CUMUF for

We have considered process monitoring in the support role of enabling NRTA. In most facilities, frequent balance closure is made possible by process monitoring to aid in estimating in-process inventory. We have evaluated options for NRTA, extending results from the safeguards literature by presenting both data-driven and period-driven views, including the effects of systematic measurement errors in several distinct covariance matrices

Our main summary points are the following.

In evaluating NRTA data, data-driven (sequential) testing is more appropriate than period-driven testing. However, the Neyman-Pearson lemma for fixed-period testing is convenient (as shown by [

For system studies such as those presented in Sections

In sequential testing, there is no analogue to the classic Neyman-Pearson lemma to identify the best test. However a joint cusum test as in Jones [

Our numerical study of robustness to estimation error in

Our inclusion of systematic errors in the measurements that are involved in estimating

We concur with Avenhaus and Jaech [

There are other possible roles for PM in safeguards, so future work will quantify the benefit of PM in possible roles other than enabling NRTA.

This appendix gives what has to be added to Section

The authors acknowledge support from the National Nuclear Security Administration Office of Nuclear Nonproliferation Research and Development (NA-22) and Nuclear Energy (NE) programs.

_{2}fuel in a pilot-scale reactor