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X%/Y% Tolerance Interval Approach to Determine Sample Sizes And PNWD-3099 WTP-RPT-013 X%/Y% Tolerance Interval Approach to Determine Sample Sizes and Demonstrate IHLW or ILAW Produced Over a Waste Type is Compliant with Chemical Durability Specifications Greg F. Piepel Scott K. Cooley August 2002 Prepared for Bechtel National, Inc. Under Contract Number 24590-101-TSA-W000-0004 PNWD-3099 WTP-RPT-013 X%/Y% Tolerance Interval Approach to Determine Sample Sizes and Demonstrate IHLW or ILAW Produced Over a Waste Type is Compliant with Chemical Durability Specifications Greg F. Piepel Scott K. Cooley August 2002 Prepared for Bechtel National, Inc. under Contract Number 24590-101-TSA-W000-0004 Battelle, Pacific Northwest Division Richland, Washington 99352 Completeness of Testing This report describes the results of work and testing specified by Subtask 3 of Test Specification 24590-WTP-TSP-RT-01-002 and Test Plan 24590-WTP-TP-RT-01-003 (PNWD number TP-RPP- WTP-097). The work and any associated testing followed the quality assurance requirements outlined in the Test Specification/ Plan. The descriptions provided in this test report are an accurate account of both the conduct of the work and the data collected. Test plan results are reported. Also reported are any unusual or anomalous occurrences that are different from expected results. The test results and this report have been reviewed and verified. Approved: _____________________________________ _________________ Gordon H. Beeman, Manager Date WTP R&T Support Project Approved for RPP-WTP Project Use: _____________________________________ _________________ G. Todd Wright, Manager Date Research and Technology Summary The River Protection Project—Waste Treatment Plant (RPP-WTP) will produce immobilized high-level waste (IHLW) and immobilized low-activity waste (ILAW) from Hanford tank wastes. The IHLW and ILAW must comply with specifications established in the contract governing the vitrification work (BNI 2001). IHLW must also comply with specifications in the Waste Acceptance Product Specifications (WAPS) developed by the Department of Energy (DOE 1996). The RPP-WTP Project strategies for complying with applicable IHLW and ILAW specifications are presented in the Waste Compliance Plan (WCP) (CHG 2001a) and the Products and Secondary Wastes Plan (PSWP) (CHG 2001b). Many of the RPP-WTP Project compliance strategies are statistical in nature, because sources of variation and uncertainty will be quantified and accounted for in demonstrating compliance with the specifications. The RPP-WTP Project compliance strategies for IHLW and ILAW have both process control and reporting aspects. Process control aspects of the compliance strategies focus on making and controlling each process batch so it will yield compliant IHLW or ILAW. The reporting aspects of the compliance strategies focus on reporting and demonstrating IHLW or ILAW produced from a given HLW or LAW waste type (see Definitions, as well as additional discussions in the WCP and PSWP) is compliant. Thus, process control addresses each batch, whereas reporting addresses the glass produced over the course of a given waste type. This report presents and illustrates the details of a statistical approach for one aspect of the reporting compliance strategies, namely demonstrating that IHLW or ILAW produced over the course of a HLW or LAW waste type is compliant with chemical durability specifications. These specifications involve three chemical durability tests, namely the Product Consistency Test (PCT) for IHLW and ILAW, the Vapor Hydration Test (VHT) for ILAW, and the Toxicity Characteristic Leaching Procedure (TCLP) for IHLW and ILAW. The statistical approaches for process control aspects of the IHLW and ILAW compliance strategies, as well as the reporting aspects not considered in this report, will be addressed in future reports. This report develops and illustrates statistical X%/Y% upper tolerance interval (X%/Y% UTI) formulas and related methods for calculating sample sizes (see Definitions) for use in demonstrating IHLW or ILAW produced from a given waste type is compliant with chemical durability specifications. In this report, an X%/Y% UTI has the general form X%/Y% UTI =µ+ kσ , (S.1) where µ is an estimate of the mean release rate for glass produced from a waste type, σ is an estimate of the variation of release rates for glass produced from a waste type, and k is an X%/Y% UTI multiplier. An X%/Y% UTI provides for stating with X% confidence that at least Y% of the IHLW or ILAW produced from a HLW or LAW waste type satisfies a chemical durability specification limit (e.g., an upper limit on the PCT boron release). Rather than selecting X and Y then calculating an X%/Y% UTI, the proposed approach is to calculate the values of X and Y that yield an X%/Y% UTI equal to a chemical durability specification limit. The resulting calculated X and Y values are thus the levels of compliance achieved over a waste iii type. The RPP-WTP Project will have to select minimally acceptable values of X and Y; however, it is envisioned that values of X and Y greater than 95, 99, or even higher will be achieved. The X%/Y% UTI formulas in this report were developed in a general manner to be applicable for demonstrating compliance with PCT, VHT, or TCLP specifications for either IHLW or ILAW produced from a given HLW or LAW waste type. The X%/Y% UTI approach directly addresses existing RPP-WTP Project reporting compliance strategies for PCT (IHLW and ILAW) and VHT (ILAW) as described in the WCP (CHG 2001a) and PSWP (CHG 2001b). The compliance strategy is still being developed for specifications involving TCLP, so it is not clear at this time whether an X%/Y% UTI approach will be needed. If so, the X%/Y% UTI formulas in this report will apply for TCLP as well as PCT and VHT. Although the X%/Y% UTI formulas are generally applicable for PCT, VHT, or TCLP, X%/Y% UTI calculations must be performed in the release rate (or transformed release rate) units used in the model to predict PCT, VHT, or TCLP release rate as a function of glass composition. Calculations of X%/Y% UTIs in this report assume the natural logarithm of release rate is modeled, which is the case for preliminary PCT and TCLP models developed at the Vitreous State Laboratory (Gan and Pegg 2001a, Gan and Pegg 2001b). X%/Y% UTI calculations for release models using other transformations (e.g., VHT or other PCT or TCLP models) can be performed in the future as the release models are developed further. X%/Y% UTI formulas are developed and presented in this report for the general situation in which: • samples (glass samples or vitrified process samples) are collected at n > 1 times over the course of a waste type, m ≥ 1 samples are collected at each time, and r ≥ 1 chemical analyses are performed on each sample • the resulting analyzed glass compositions (possibly adjusted and renormalized to address biases and reduce imprecision) are substituted into release-composition models to obtain predicted release rates(a) • the resulting N = n⋅m⋅r predicted release rates are then used to calculate the X%/Y% UTI. In addition to variation in release rates due to variation in glass composition over a waste type, the predicted release rates will be subject to sampling, analytical, and model prediction uncertainties. These three uncertainties are referred to as nuisance uncertainties, because they inflate the source of variation of interest (variation in true release rates over a waste type). The nuisance uncertainties inflate the magnitudes of X%/Y% UTIs, so methods to reduce and adjust for nuisance uncertainties were investigated. A no-adjustment method was also investigated for (a) If release rates are mathematically transformed to develop release-composition models, the predicted values will be in the transformed units. For example, PCT models often relate the natural logarithm of release (in g/m2) to glass composition, so that predicted values have units of ln(g/m2). In such a case, an X%/Y% UTI would also be calculated in the transformed ln(g/m2) units. However, the inverse transformation can always be applied to obtain predicted values or the X%/Y% UTI in the original units. iv comparison purposes. The following specific approaches were investigated: • No reduction or adjustment for nuisance uncertainties (m = 1, r = 1) • Reduction (by averaging) but no adjustment for nuisance uncertainties (m > 1 and/or r > 1) • Reduction (by averaging) and adjustment for nuisance uncertainties (m > 1 and/or r > 1) • Reduction (if m > 1 and/or r > 1) and adjustment for nuisance uncertainties, as well as removing (subtracting) the reduced sampling and/or analytical uncertainties using one of two removal methods. The first removal method subtracts estimates of sampling and analytical uncertainties obtained from production data, whereas the second method subtracts estimates obtained during qualification activities. However, the removal methods were found not to reduce X%/Y% UTIs. Hence, the work focused on the approaches in the first three bullets above. The magnitude of an X%/Y% UTI depends on the mean predicted release rate (or transformed release rate) over glass produced from an HLW or LAW waste type ( µ in (S.1)), as well as the UTI half-width (UTIHW) that accounts for the sources of variation and uncertainty (kσ in (S.1)). The UTIHW depends on many input parameters, including: • values of n, m, and r • magnitude of the variation in release rates over a waste type, expressed in release rate (a) σ units ( ˆ g ) • magnitudes of sampling and analytical uncertainties, expressed in release rate (a) σ σ units ( ˆ s and ˆa ) • degrees of freedom associated with a release-composition model (dfm) • magnitude of the average model prediction uncertainty for a given sampling time, expressed (a) σ in release rate units ( ˆ m ) • values of X (percent confidence) and Y (percent of glass from a waste type in compliance) • the reduction and adjustment methods used.
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