JMP Helps Describe nth Order Degradation Models for the US Army Prepared by: Kevin Singer U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT & ENGINEERING CENTER

The US Military has a clear need for energetic products Background The US Military has a clear need for energetic products These can range from explosives, to propellants, to pyrotechnics In an effort to reduce cost and, more importantly, maintain operational readiness, the military buys these products in large quantities and maintains a stockpile. Any products containing energetic materials must demonstrate that they can be stockpiled for long periods of time while still remaining effective, reliable, and safe. In order to accomplish this stabilizers are mixed into the energetics to ensure that it does not degrade. Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc. *All data has been anonymized and normalized for this presentation

Accelerated Life Testing Demonstrating the ‘life’ of an energetic often times involves conducting an accelerating aging test This entails exposing a sample to varying conditions over a specified duration and measuring a certain characteristic Conditions are set beyond use conditions but not so far so as to introduce new failure modes. In the case of chemical degradation an Arrhenius model is typically specified i.e. temperature is varied and concentration readings are taken over time Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc.

Chemical Kinetics Model Order Rate Law Integrated Rate Law JMP Specified Model 1st − 𝑑 𝐶 𝑑t =𝑘 𝐶 𝐶 = 𝐶 𝑜 𝑒 −𝑘𝑡 nth − 𝑑 𝐶 𝑑t =𝑘 𝐶 𝑛 1 𝐶 𝑛−1 = 1 𝐶 0 𝑛−1 + 𝑛−1 𝑘𝑡 Nonlinear Modelling with User Input Formula Necessary Where; n is the reaction order [C] is the reactant concentration, mol E a , activation energy, kJ/(mol • K) k is the rate constant, 1 M 𝑛−1 ∙sec And k=A 𝑒 E a R∙T E a , activation energy, kj mol R is the universal gas constant, kj mol∙K T is temperature, K A is the pre-exponential factor, 1 M 𝑛−1 ∙sec Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc.

Initial slope of the curves increases with temperature. Data In military grade energetics, a common metric associated with its remaining life is Remaining Effective Stabilizer (RES) This is measured by sampling the billet at various times throughout the duration of the conditioning Initial slope of the curves increases with temperature. This is in agreement with an Arrhenius model Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc.

However, JMP has trouble solving for parameters that are roots. Nonlinear Model The algebra for the integrated rate law equation for an nth order reaction when solved for RES concentration works out to the formula below. However, JMP has trouble solving for parameters that are roots. Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc.

JMP customer service helped me identify this issue. Nonlinear Model JMP customer service helped me identify this issue. Simple solution: replace root with a fraction exponent Thanks Duane Hayes from JMP Technical Support! Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc.

Nonlinear Fit Platform RES column is the concentration data Integrated Rate Formula column is input by the user (shown in previous slide) Set parameters in Nonlinear Fit Platform RES0 is the initial concentration and remains locked n can be reasonably guessed as an integer from 1 to 4* A can be reasonably guessed on the order of 10-5 to 10-7* Ea can be reasonably guessed between - -10 and -20* Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc. *This is based on the orders of magnitude commonly seen for these parameters

results A model was developed estimating the parameters with a 95% profile likelihood confidence bound Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc.

Set a degradation standard 0.05 for example Life Estimation Set a degradation standard 0.05 for example Utilize profiler to estimate shelf life as at a proposed storage temperature 25oC (298K) Life assuming room temperature storage is approximately 112.2 years. Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc.

Check on Process Simulate data using integrated rate formula in excel with known parameters Import into JMP Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc.

Very useful for modelling chemical kinetics Conclusions Nonlinear fit platform accurately predicts root parameters when input properly Very useful for modelling chemical kinetics Estimate useful life of degrading components JMP technical support is extremely helpful! Treaty based engagements are NATO Activities or overarching treaties with countries for R&D. Project Based engagements are specific and we leverage numerous programs for engagement such as Grants, Project Agreements, Loans, etc. Competency Based engagements such as in Energetics, or Precision, etc. Country Based engagements would be where the U.S. President declares that the U.S. will be more involved, such as with India. FMS leads to opportunities for sales, or technical services, such as QA monitoring of a contractor for quality, or Inspection criteria, etc.