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Probability of brittle failure

A methodology was developed for collecting statistically representative data for crack initiation and arrest from small number of test specimens. An epoxy (based on bisphenol A diglycidyl ether and polyglycol extended diglycyl ether and cured with diethylene triamine) is selected as a model material. A compact tension specimen with displacement controlled loading is used to observe multiple crack initiation and arrests. The energy release rate at crack initiation is significantly higher than that at a crack arrest, as has been observed elsewhere. The difference between these energy release rates is found to depend on specimen size (scale effect), and is quantitatively related to the fracture surface morphology. The scale effect, similar to that in statistical strength theory, is usually attributed to the statistics of defects which control the fracture process. Triangular shaped ripples (deltoids) are formed on the fracture surface during the slow subcritical crack growth, prior to the smooth mirror-like surface characteristic of fast cracks. The deltoids are complementary on the two crack faces which excludes any inelastic deformation from consideration. Presence of defects is also suggested by the observed scale effect. However, there are no defects at the deltoid apexes detectable down to the 0.1 micron level.

Kim, A.↗

Improving Thermal Model Prediction Through Statistical Analysis of Irradiation and Post-Irradiation Data from AGR Experiments

As part of the High Temperature Reactors (HTR) R&D program, a series of irradiation tests, designated as Advanced Gas-cooled Reactor (AGR), have been defined to support development and qualification of fuel design, fabrication process, and fuel performance under normal operation and accident conditions. The AGR tests employ fuel compacts placed in a graphite cylinder shrouded by a steel capsule and instrumented with thermocouples (TC) embedded in graphite blocks enabling temperature control. While not possible to obtain by direct measurements in the tests, crucial fuel conditions (e.g., temperature, neutron fast fluence, and burnup) are calculated using core physics and thermal modeling codes. This paper is focused on AGR test fuel temperature predicted by the ABAQUS code's finite element-based thermal models. The work follows up on a previous study, in which several statistical analysis methods were adapted, implemented in the NGNP Data Management and Analysis System (NDMAS), and applied for qualification of AGR-1 thermocouple data. Abnormal trends in measured data revealed by the statistical analysis are traced to either measuring instrument deterioration or physical mechanisms in capsules that may have shifted the system thermal response. The main thrust of this work is to exploit the variety of data obtained in irradiation and post-irradiation examination (PIE) for assessment of modeling assumptions. As an example, the uneven reduction of the control gas gap in Capsule 5 found in the capsule metrology measurements in PIE helps identify mechanisms other than TC drift causing the decrease in TC readings. This suggests a more physics-based modification of the thermal model that leads to a better fit with experimental data, thus reducing model uncertainty and increasing confidence in the calculated fuel temperatures of the AGR-1 test.

99 GENERAL AND MISCELLANEOUS↗

Estimated Accuracy of Three Common Trajectory Statistical Methods

Three well-known trajectory statistical methods (TSMs), namely concentration field (CF), concentration weighted trajectory (CWT), and potential source contribution function (PSCF) methods were tested using known sources and artificially generated data sets to determine the ability of TSMs to reproduce spatial distribution of the sources. In the works by other authors, the accuracy of the trajectory statistical methods was estimated for particular species and at specified receptor locations. We have obtained a more general statistical estimation of the accuracy of source reconstruction and have found optimum conditions to reconstruct source distributions of atmospheric trace substances. Only virtual pollutants of the primary type were considered. In real world experiments, TSMs are intended for application to a priori unknown sources. Therefore, the accuracy of TSMs has to be tested with all possible spatial distributions of sources. An ensemble of geographical distributions of virtual sources was generated. Spearman s rank order correlation coefficient between spatial distributions of the known virtual and the reconstructed sources was taken to be a quantitative measure of the accuracy. Statistical estimates of the mean correlation coefficient and a range of the most probable values of correlation coefficients were obtained. All the TSMs that were considered here showed similar close results. The maximum of the ratio of the mean correlation to the width of the correlation interval containing the most probable correlation values determines the optimum conditions for reconstruction. An optimal geographical domain roughly coincides with the area supplying most of the substance to the receptor. The optimal domain s size is dependent on the substance decay time. Under optimum reconstruction conditions, the mean correlation coefficients can reach 0.70 0.75. The boundaries of the interval with the most probable correlation values are 0.6 0.9 for the decay time of 240 h and 0.5 0.95 for the decay time of 12 h. The best results of source reconstruction can be expected for the trace substances with a decay time on the order of several days. Although the methods considered in this paper do not guarantee high accuracy they are computationally simple and fast. Using the TSMs in optimum conditions and taking into account the range of uncertainties, one can obtain a first hint on potential source areas.

Kabashnikov, Vitaliy P.↗

Evaluation of a commercial automatic treatment planning system for prostate cancers

Recent developments in Radiation Oncology treatment planning have led to the development of software packages that facilitate automated intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT) planning. Such solutions include site-specific modules, plan library methods, and algorithm-based methods. In this study, the plan quality for prostate cancer generated by the Auto-Planning module of the Pinnacle{sup 3} radiation therapy treatment planning system (v9.10, Fitchburg, WI) is retrospectively evaluated. The Auto-Planning module of Pinnacle{sup 3} uses a progressive optimization algorithm. Twenty-three prostate cancer cases, which had previously been planned and treated without lymph node irradiation, were replanned using the Auto-Planning module. Dose distributions were statistically compared with those of manual planning by the paired t-test at 5% significance level. Auto-Planning was performed without any manual intervention. Planning target volume (PTV) dose and dose to rectum were comparable between Auto-Planning and manual planning. The former, however, significantly reduced the dose to the bladder and femurs. Regression analysis was performed to examine the correlation between volume overlap between bladder and PTV divided by the total bladder volume and resultant V70. The findings showed that manual planning typically exhibits a logistic way for dose constraint, whereas Auto-Planning shows a more linear tendency. By calculating the Akaike information criterion (AIC) to validate the statistical model, a reduction of interoperator variation in Auto-Planning was shown. We showed that, for prostate cancer, the Auto-Planning module provided plans that are better than or comparable with those of manual planning. By comparing our results with those previously reported for head and neck cancer treatment, we recommend the homogeneous plan quality generated by the Auto-Planning module, which exhibits less dependence on anatomic complexity.

61 RADIATION PROTECTION AND DOSIMETRY↗

Use of Minute-by-Minute Cardiovascular Measurements During Tilt Tests to Strengthen Inference on the Effect of Long-Duration Space Flight on Orthostatic Hypotension

Typical methodology for evaluating the effects of spaceflight on orthostatic hypotension (OH) has been survival analysis of tolerance times from 80 head-up tilt tests. However when scheduled test durations are short, there may not be enough failures to allow survival analysis to adequately estimate and compare the effects of flight phase (e.g. pre-flight, number of days post-flight), flight duration, and their interaction, as well as interactions with effects of interventions or countermeasures. The problem is exacerbated in the presence of a repeated measures design, in which subjects participate in tilt tests during various flight phases. Here we show how it is possible to dramatically improve the efficiency of statistical inference in this setting by making use of the additional information contained in minute-by-minute observations of cardiovascular parameters thought to be reflective of progression towards presyncope during tilt testing. Methods: We retrospectively examined operational tilt test (OTT; 10 -min 80 head-up tilt) data from 20 International Space Station (ISS) and 66 Shuttle astronauts 10 d before launch (L-10), on landing day (R+0) and during recovery (R+1, R+3, R+6-10) depending on the level of participation. Data from 5 ISS astronauts tested on R+0 or R+1 who used non-standard countermeasures were excluded. In addition to OTT survival time, 8 cardiovascular parameters (CP: heart rate, systolic, diastolic, and mean arterial blood pressure, pulse pressure, stroke volume, cardiac output, and total peripheral resistance) that might be predictive of progression towards presyncope were measured every minute of each OTT. Statistical analysis was predicated on a two ]stage model of causation. In the first stage, flight duration and time from landing affect the astronauts' degree of OH, which is manifested in the time trends and variation of the above CPs during OTTs. In the second stage, the behavior of these parameters directly affects OTT survival time. Actual analysis proceeded in the opposite direction. First we identified those CPs or linear combinations that best predicted OTT survival regardless of what spaceflight conditions led to OTT completion or presyncope. From these, we calculated a summary statistic (one per OTT) that best predicted survival. We then used mixed ]model regression analysis to relate changes in the summary statistic to flight phase and duration. Inference on the effects of phase, duration, and their interaction on OH follows directly from this second analysis. Results: A linear combination (W) of diastolic blood pressure (DBP) and stroke volume (SV) was found to be the best predictor of OTT survival using the complete data set of minute-by-minute observations of CPs for each OTT. Furthermore, the log-transformed standard deviation of W (Z = log SW) was found to be a strong predictor of survival in the reduced data set consisting of one observation per OTT. In other words, this measure of variability of W during an OTT was the best indicator of whether or not the subject could complete the 10-min test, with higher variability (i.e. higher values of Z) being associated with greater probability of failure. In the mixed-model regression analysis where Z was now treated as a outcome with flight phase and duration groups (ISS and STS) as predictors, we found that there was a significantly more variability in W (higher values of Z) for both groups at R+0, but with no evidence of an interaction until R+3, when the ISS group still had inflated variability, but not the STS group. Conclusions: Variability of the cardiovascular index W recovers more slowly after long-compared to short-duration spaceflight. Since high variability of W has also been shown to be predictive of OTT failure, a primary manifestation of OH, a logical conclusion is that recovery from OH also is slower after long-duration compared to short-duration spaceflights.

Feiveson, Alan H.↗

On Geomagnetism and Paleomagnetism

A statistical description of Earth's broad scale, core-source magnetic field has been developed and tested. The description features an expected, or mean, spatial magnetic power spectrum that is neither "flat" nor "while" at any depth, but is akin to spectra advanced by Stevenson and McLeod. This multipole spectrum describes the magnetic energy range; it is not steep enough for Gubbins' magnetic dissipation range. Natural variations of core multipole powers about their mean values are to be expected over geologic time and are described via trial probability distribution functions that neither require nor prohibit magnetic isotropy. The description is thus applicable to core-source dipole and low degree non-dipole fields despite axial dipole anisotropy. The description is combined with main field models of modem satellite and surface geomagnetic measurements to make testable predictions of: (1) the radius of Earth's core, (2) mean paleomagnetic field intensity, and (3) the mean rates and durations of both dipole power excursions and durable axial dipole reversals. The predicted core radius is 0.7% above the 3480 km seismologic value. The predicted root mean square paleointensity (35.6 mu T) and mean Virtual Axial Dipole Moment (about 6.2 lx 1022 Am(exp 2)) are within the range of various mean paleointensity estimates. The predicted mean rate of dipole power excursions, as defined by an absolute dipole moment <20% of the 1980 value, is 9.04/Myr and 14% less than obtained by analysis of a 4 Myr paleointensity record. The predicted mean rate of durable axial dipole reversals (2.26/Myr) is 2.3% more than established by the polarity time-scale for the past 84 Myr. The predicted mean duration of axial dipole reversals (5533 yr) is indistinguishable from an observational value. The accuracy of these predictions demonstrates the power and utility of the description, which is thought to merit further development and testing. It is suggested that strong stable stratification of Earth's uppermost outer core leads to a geologically long interval of no dipole reversals and a very nearly axisymmetric field outside the core. Statistical descriptions of other planetary magnetic fields are outlined.

Voorhies, Coerte V.↗

Predicting Operator Execution Times Using CogTool

Researchers and developers of NextGen systems can use predictive human performance modeling tools as an initial approach to obtain skilled user performance times analytically, before system testing with users. This paper describes the CogTool models for a two pilot crew executing two different types of a datalink clearance acceptance tasks, and on two different simulation platforms. The CogTool time estimates for accepting and executing Required Time of Arrival and Interval Management clearances were compared to empirical data observed in video tapes and registered in simulation files. Results indicate no statistically significant difference between empirical data and the CogTool predictions. A population comparison test found no significant differences between the CogTool estimates and the empirical execution times for any of the four test conditions. We discuss modeling caveats and considerations for applying CogTool to crew performance modeling in advanced cockpit environments.

Santiago-Espada, Yamira↗

Repeatability of Cryogenic Multilayer Insulation

Due to the variety of requirements across aerospace platforms, and one off projects, the repeatability of cryogenic multilayer insulation has never been fully established. The objective of this test program is to provide a more basic understanding of the thermal performance repeatability of MLI systems that are applicable to large scale tanks. There are several different types of repeatability that can be accounted for: these include repeatability between multiple identical blankets, repeatability of installation of the same blanket, and repeatability of a test apparatus. The focus of the work in this report is on the first two types of repeatability. Statistically, repeatability can mean many different things. In simplest form, it refers to the range of performance that a population exhibits and the average of the population. However, as more and more identical components are made (i.e. the population of concern grows), the simple range morphs into a standard deviation from an average performance. Initial repeatability testing on MLI blankets has been completed at Florida State University. Repeatability of five GRC provided coupons with 25 layers was shown to be +/- 8.4% whereas repeatability of repeatedly installing a single coupon was shown to be +/- 8.0%. A second group of 10 coupons have been fabricated by Yetispace and tested by Florida State University, through the first 4 tests, the repeatability has been shown to be +/- 15-25%. Based on detailed statistical analysis, the data has been shown to be statistically significant.

multilayer insulation↗

Ensemble Kalman filters for dynamical systems with unresolved turbulence

Ensemble Kalman filters are developed for turbulent dynamical systems where the forecast model does not resolve all the active scales of motion. Coarse-resolution models are intended to predict the large-scale part of the true dynamics, but observations invariably include contributions from both the resolved large scales and the unresolved small scales. The error due to the contribution of unresolved scales to the observations, called ‘representation’ or ‘representativeness’ error, is often included as part of the observation error, in addition to the raw measurement error, when estimating the large-scale part of the system. It is here shown how stochastic superparameterization (a multiscale method for subgridscale parameterization) can be used to provide estimates of the statistics of the unresolved scales. In addition, a new framework is developed wherein small-scale statistics can be used to estimate both the resolved and unresolved components of the solution. The one-dimensional test problem from dispersive wave turbulence used here is computationally tractable yet is particularly difficult for filtering because of the non-Gaussian extreme event statistics and substantial small scale turbulence: a shallow energy spectrum proportional to k{sup −5/6} (where k is the wavenumber) results in two-thirds of the climatological variance being carried by the unresolved small scales. Because the unresolved scales contain so much energy, filters that ignore the representation error fail utterly to provide meaningful estimates of the system state. Inclusion of a time-independent climatological estimate of the representation error in a standard framework leads to inaccurate estimates of the large-scale part of the signal; accurate estimates of the large scales are only achieved by using stochastic superparameterization to provide evolving, large-scale dependent predictions of the small-scale statistics. Again, because the unresolved scales contain so much energy, even an accurate estimate of the large-scale part of the system does not provide an accurate estimate of the true state. By providing simultaneous estimates of both the large- and small-scale parts of the solution, the new framework is able to provide accurate estimates of the true system state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evaluation of SLAR and thematic mapper MSS data for forest cover mapping using computer-aided analysis techniques

A set of training statistics for the 30 meter resolution simulated thematic mapper MSS data was generated based on land use/land cover classes. In addition to this supervised data set, a nonsupervised multicluster block of training statistics is being defined in order to compare the classification results and evaluate the effect of the different training selection methods on classification performance. Two test data sets, defined using a stratified sampling procedure incorporating a grid system with dimensions of 50 lines by 50 columns, and another set based on an analyst supervised set of test fields were used to evaluate the classifications of the TMS data. The supervised training data set generated training statistics, and a per point Gaussian maximum likelihood classification of the 1979 TMS data was obtained. The August 1980 MSS data was radiometrically adjusted. The SAR data was redigitized and the SAR imagery was qualitatively analyzed.

Hoffer, R. M.↗

Constraining the local variance of H {sub 0} from directional analyses

We evaluate the local variance of the Hubble Constant H {sub 0} with low-z Type Ia Supernovae (SNe). Our analyses are performed using a hemispherical comparison method in order to test whether taking the bulk flow motion into account can reconcile the measurement of the Hubble Constant H {sub 0} from standard candles ( H {sub 0} = 73.8±2.4 km s{sup -1} Mpc {sup -1}) with that of the Planck's Cosmic Microwave Background data ( H {sub 0} = 67.8 ± 0.9km s{sup -1} Mpc{sup -1}). We obtain that H {sub 0} ranges from 68.9±0.5 km s{sup -1} Mpc{sup -1} to 71.2±0.7 km s{sup -1} Mpc{sup -1} through the celestial sphere (1 σ uncertainty), implying a Hubble Constant maximal variance of δ H {sub 0} = (2.30±0.86) km s{sup -1} Mpc{sup -1} towards the ( l,b ) = (315°,27°) direction. Interestingly, this result agrees with the bulk flow direction estimates found in the literature, as well as previous evaluations of the H {sub 0} variance due to the presence of nearby inhomogeneities. We assess the statistical significance of this result with different prescriptions of Monte Carlo simulations, obtaining moderate statistical significance, i.e., 68.7% confidence level (CL) for such variance. Furthermore, we test the hypothesis of a higher H {sub 0} value in the presence of a bulk flow velocity dipole, finding some evidence for this result which, however, cannot be claimed to be significant due to the current large uncertainty in the SNe distance modulus. Then, we conclude that the tension between different H {sub 0} determinations can plausibly be caused to the bulk flow motion of the local Universe, even though the current incompleteness of the SNe data set, both in terms of celestial coverage and distance uncertainties, does not allow a high statistical significance for these results or a definitive conclusion about this issue.

79 ASTRONOMY AND ASTROPHYSICS↗

RAY-RAMSES: a code for ray tracing on the fly in N-body simulations

We present a ray tracing code to compute integrated cosmological observables on the fly in AMR N-body simulations. Unlike conventional ray tracing techniques, our code takes full advantage of the time and spatial resolution attained by the N-body simulation by computing the integrals along the line of sight on a cell-by-cell basis through the AMR simulation grid. Moroever, since it runs on the fly in the N-body run, our code can produce maps of the desired observables without storing large (or any) amounts of data for post-processing. We implemented our routines in the RAMSES N-body code and tested the implementation using an example of weak lensing simulation. We analyse basic statistics of lensing convergence maps and find good agreement with semi-analytical methods. The ray tracing methodology presented here can be used in several cosmological analysis such as Sunyaev-Zel'dovich and integrated Sachs-Wolfe effect studies as well as modified gravity. Our code can also be used in cross-checks of the more conventional methods, which can be important in tests of theory systematics in preparation for upcoming large scale structure surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Flight investigation of a four-dimensional terminal area guidance system for STOL aircraft

A series of flight tests and fast-time simulations were conducted, using the augmentor wing jet STOL research aircraft and the STOLAND 4D-RNAV system to add to the growing data base of 4D-RNAV system performance capabilities. To obtain statistically meaningful data a limited amount of flight data were supplemented by a statistically significant amount of data obtained from fast-time simulation. The results of these tests are reported. Included are comparisons of the 4D-RNAV estimated winds with actual winds encountered in flight, as well as data on along-track navigation and guidance errors, and time-of-arrival errors at the final approach waypoint. In addition, a slight improvement of the STOLAND 4D-RNAV system is proposed and demonstrated, using the fast-time simulation.

Neuman, F.↗

Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d.—quantum lattice systems and more

Quantum Stein’s lemma is a cornerstone of quantum statistics and concerns the problem of correctly identifying a quantum state, given the knowledge that it is one of two specific states (ρ or σ). It was originally derived in the asymptotic i.i.d. setting, in which arbitrarily many (say, n) identical copies of the state (ρ{sup ⊗n} or σ{sup ⊗n}) are considered to be available. In this setting, the lemma states that, for any given upper bound on the probability α{sub n} of erroneously inferring the state to be σ, the probability β{sub n} of erroneously inferring the state to be ρ decays exponentially in n, with the rate of decay converging to the relative entropy of the two states. The second order asymptotics for quantum hypothesis testing, which establishes the speed of convergence of this rate of decay to its limiting value, was derived in the i.i.d. setting independently by Tomamichel and Hayashi, and Li. We extend this result to settings beyond i.i.d. Examples of these include Gibbs states of quantum spin systems (with finite-range, translation-invariant interactions) at high temperatures, and quasi-free states of fermionic lattice gases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Upsampling Monte Carlo Reactor Simulation Tallies in Depleted Sodium-Cooled Fast Reactor Assemblies Using a Convolutional Neural Network

The computational demand of neutron Monte Carlo transport simulations can increase rapidly with the spatial and energy resolution of tallied physical quantities. Convolutional neural networks have been used to increase the resolution of Monte Carlo simulations of light water reactor assemblies while preserving accuracy with negligible additional computational cost. Here, we show that a convolutional neural network can also be used to upsample tally results from Monte Carlo simulations of sodium-cooled fast reactor assemblies, thereby extending the applicability beyond thermal systems. The convolutional neural network model is trained using neutron flux tallies from 300 procedurally generated nuclear reactor assemblies simulated using OpenMC. Validation and test datasets included 16 simulations of procedurally generated assemblies, and a realistic simulation of a European sodium-cooled fast reactor assembly was included in the test dataset. We show the residuals between the high-resolution flux tallies predicted by the neural network and high-resolution Monte Carlo tallies on relative and absolute bases. The network can upsample tallies from simulations of fast reactor assemblies with diverse and heterogeneous materials and geometries by a factor of two in each spatial and energy dimension. The network’s predictions are within the statistical uncertainty of the Monte Carlo tallies in almost all cases. This includes test assemblies for which burnup values and geometric parameters were well outside the ranges of those in assemblies used to train the network.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

SU-F-T-362: Quantification and Modelling of the Ionization Chamber Simulation Effective Points On Monaco Treatment Planning System

Purpose: Because of statistical noise in Monte Carlo dose calculations, effective point doses may not be accurate. Volume spheres are useful for evaluating dose in Monte Carlo plans, which have an inherent statistical uncertainty.We use a user-defined sphere volume instead of a point, take sphere sampling around effective point make the dose statistics to decrease the stochastic errors. Methods: Direct dose measurements were made using a 0.125cc Semiflex ion chamber (IC) 31010 isocentrically placed in the center of a homogeneous Cylindric sliced RW3 phantom (PTW, Germany).In the scanned CT phantom series the sensitive volume length of the IC (6.5mm) were delineated and defined the isocenter as the simulation effective points. All beams were simulated in Monaco in accordance to the measured model. In our simulation using 2mm voxels calculation grid spacing and choose calculate dose to medium and request the relative standard deviation ≤0.5%. Taking three different assigned IC over densities (air electron density(ED) as 0.01g/cm3 default CT scanned ED and Esophageal lumen ED 0.21g/cm3) were tested at different sampling sphere radius (2.5, 2, 1.5 and 1 mm) statistics dose were compared with the measured does. Results: The results show that in the Monaco TPS for the IC using Esophageal lumen ED 0.21g/cm3 and sampling sphere radius 1.5mm the statistical value is the best accordance with the measured value, the absolute average percentage deviation is 0.49%. And when the IC using air electron density(ED) as 0.01g/cm3 and default CT scanned EDthe recommented statistical sampling sphere radius is 2.5mm, the percentage deviation are 0.61% and 0.70%, respectivly. Conclusion: In Monaco treatment planning system for the ionization chamber 31010 recommend air cavity using ED 0.21g/cm3 and sampling 1.5mm sphere volume instead of a point dose to decrease the stochastic errors. Funding Support No.C201505006.

60 APPLIED LIFE SCIENCES↗

Data-driven Alignment of the Tracker for the Mu2e Experiment

An alignment of the Mu2e Tracker is investigated using the Mu2e Offline Software and Millepede-II. Simulated misalignments of Tracker planes were inserted between Monte-Carlo event generation and before reconstruction using randomly generated $(x,y,z)$-translations and rotations of the rigid-body planes in the detector model. Cosmic ray muons, with no magnetic field present in the Detector Solenoid, will follow a straight-line trajectory. A maximum-likelihood fit is used to reconstruct a track and determine its parameters. Tracks traversing at least four planes, with ten registered straw hits, and a maximum time residual of $20$ ns are selected to be used in an alignment sample. The cuts were chosen to discard tracks with low information content, such as those with high levels of multiple scattering or those with low numbers of measurements contributing to a single track fit. Millepede-II produces the resulting alignment constants according to a simultaneous least-squares fit of the alignment parameters and the track parameters for all input tracks. The improved alignment constants are used to repeat the process and recover an increased number of suitable tracks, further improving the estimate of the alignment constants in subsequent iterations. A performance study of the process was conducted on a misaligned Tracker in the case of translation-only, and translation plus rotational misalignments. In both cases, the correct alignment constants were recovered to within statistical error after three global fit iterations. Additionally, a continuous integration system was developed for the \texttt{Mu2e/Offline} GitHub repository, introducing a convenient automated testing process for all proposed changes (``pull requests"). The tests developed included a full build of the software, followed by tests of the validation routines, geometry overlap checking, and multi-threading mode. Additionally, code quality checks and low-statistics physics comparison checks a re also available.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Lessons from NASA

Particular requirements related to the design and the operation of spacecraft have forced NASA to take a reliability approach that differs somewhat from that used in many other applications. NASA has found that some of the traditional tools of reliability engineering, such as life testing, reliability demonstration testing, maintainability analysis, and direct failure analysis, are impractical for spacecraft. In place of a statistical approach, the space agency uses an engineering approach to mission reliability. Reliability is to be obtained with the aid of three different approaches, including the application of effective design principles, the control and screening of all parts, and the testing of the entire spacecraft or its prototype for predicted capabilities. Attention is given to failure-mode analysis, the enhancement of Voyager reliability by autonomous operation, the redundancy in Shuttle design, the weeding out of bad hardware, and the preference for off-the-shelf devices.

Williams, W. C.↗