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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2009

Developing an Empirical Model for Estimating the Probability of Electrical Short Circuits from Tin Whiskers

To comply with lead-free legislation, many manufacturers have converted from tin-lead to pure tin finishes of electronic components. However, pure tin finishes have a greater propensity to grow tin whiskers than tin-lead finishes. Since tin whiskers present an electrical short circuit hazard in electronic components, simulations have been developed to quantify the risk of said short circuits occurring. Existing risk simulations make the assumption that when a free tin whisker has bridged two adjacent exposed electrical conductors, the result is an electrical short circuit. This conservative assumption is made because shorting is a random event that had an unknown probability associated with it. Note however that due to contact resistance electrical shorts may not occur at lower voltage levels. In our first article we developed an empirical probability model for tin whisker shorting. In this paper, we develop a more comprehensive empirical model using a refined experiment with a larger sample size, in which we studied the effect of varying voltage on the breakdown of the contact resistance which leads to a short circuit. From the resulting data we estimated the probability distribution of an electrical short, as a function of voltage. In addition, the unexpected polycrystalline structure seen in the focused ion beam (FIB) cross section in the first experiment was confirmed in this experiment using transmission electron microscopy (TEM). The FIB was also used to cross section two card guides to facilitate the measurement of the grain size of each card guide's tin plating to determine its finish.

Courey, Karim J.↗
NASA NTRS1988

A method for modeling bias in a person's estimates of likelihoods of events

It is of practical importance in decision situations involving risk to train individuals to transform uncertainties into subjective probability estimates that are both accurate and unbiased. We have found that in decision situations involving risk, people often introduce subjective bias in their estimation of the likelihoods of events depending on whether the possible outcomes are perceived as being good or bad. Until now, however, the successful measurement of individual differences in the magnitude of such biases has not been attempted. In this paper we illustrate a modification of a procedure originally outlined by Davidson, Suppes, and Siegel (3) to allow for a quantitatively-based methodology for simultaneously estimating an individual's subjective utility and subjective probability functions. The procedure is now an interactive computer-based algorithm, DSS, that allows for the measurement of biases in probability estimation by obtaining independent measures of two subjective probability functions (S+ and S-) for winning (i.e., good outcomes) and for losing (i.e., bad outcomes) respectively for each individual, and for different experimental conditions within individuals. The algorithm and some recent empirical data are described.

Nygren, Thomas E.↗
NASA NTRS1989

PRIME: A bottom-up approach to probabilistic rule development

PRIME is a system to be used by an intelligent machine to allow it to operate in an abstract but uncertain (or stochastic) environment. It maintains a model of the effects of the machine's actions in the form of a rule base, which is induced from experience. This bottom-up approach to rule development allows the model to adapt to changes in the environment. Each rule consists of a condition under which the rule is active, an action, the effect of the action on the environment, and an estimate of the probability of this effect occurring. The effect probabilities are used to model the uncertainty in the environment, permitting multiple possible effects for a single action under a particular set of conditions. The objective of the intelligent machine is to satisfy user-specified goals with maximum probability of success. PRIME fulfills this requirement in two ways: it continuously updates the rule base with the most recent information, to ensure the validity of the model; and it generates plans which have the maximum probability of achieving the goals, based on the probability estimates in the rule base. PRIME is composed of three main processes: exploration, generalization, and planning. In exploration, the machine executes various randomly chosen actions, observes the effects on the environment, and updates the rule base accordingly. This process is used to develop the rule base in simulation, as well as to supplement the current knowledge during normal operation. Generalization is the procedure used to induce general rules from experience, which is encoded in the form of specific rules. These general rules extend the machine's knowledge to situations which have not been encountered yet, thereby increasing the capability of the machine to plan effectively. Planning is the process of constructing an optimal sequence of actions to satisfy a goal, using the rule base to predict the effects of these actions and to determine the probability of success of the plan. The rule representation and many other data structures were specifically chosen to maximize the efficiency of these processes. A simulated environment was designed to test the performance of PRIME. The results of experimentation were largely negative. The main problem was that the domain coverage of the rules was inadequate for the number of rules stored in the rule base, due to redundancies in general rules and numerous rules covering ineffective actions. It was determined that a more efficient generalization, and some form of goal-directed exploration, are necessary in order to solve most of the current deficiencies in PRIME.

Miller, Scott A.↗
NASA NTRS1982

A model of human decision making in multiple process monitoring situations

Human decision making in multiple process monitoring situations is considered. It is proposed that human decision making in many multiple process monitoring situations can be modeled in terms of the human's detection of process related events and his allocation of attention among processes once he feels event have occurred. A mathematical model of human event detection and attention allocation performance in multiple process monitoring situations is developed. An assumption made in developing the model is that, in attempting to detect events, the human generates estimates of the probabilities that events have occurred. An elementary pattern recognition technique, discriminant analysis, is used to model the human's generation of these probability estimates. The performance of the model is compared to that of four subjects in a multiple process monitoring situation requiring allocation of attention among processes.

Greenstein, J. S.↗
NASA NTRS2018

Synthesizing a New Launch Vehicle Failure Probability Based on Historical Flight Data

New launch vehicles have historically had significantly higher failure rates in early flights than what has been predicted using Probabilistic Risk Assessment - PRA. This is because PRAs typically model a mature vehicle where a significant portion of the early failure probability contributors have been eliminated due to testing and improvements after actual field operation. To capture a more accurate early flight failure probability estimate, this paper develops a method that estimates ascent failure probability starting with the first flight based on historical launch vehicle records. With new launch vehicles being developed, such as the Space Launch System - SLS, a PRA model must be extended to cover early flight failure probability contributions that are either not covered in the mature-vehicle PRA or are underestimated. These failure probability contributions include design errors, quality control deficiencies, installation errors, and environmental impacts. There are also failure dependencies due to systemic errors that still exist due to limited entire-system testing.

Cross, Robert B.↗
NASA NTRS1974

Nonparametric maximum likelihood estimation of probability densities by penalty function methods

When it is known a priori exactly to which finite dimensional manifold the probability density function gives rise to a set of samples, the parametric maximum likelihood estimation procedure leads to poor estimates and is unstable; while the nonparametric maximum likelihood procedure is undefined. A very general theory of maximum penalized likelihood estimation which should avoid many of these difficulties is presented. It is demonstrated that each reproducing kernel Hilbert space leads, in a very natural way, to a maximum penalized likelihood estimator and that a well-known class of reproducing kernel Hilbert spaces gives polynomial splines as the nonparametric maximum penalized likelihood estimates.

Demontricher, G. F.↗
NASA NTRS2005

ESTIMATING THE BENEFIT OF TRMM TROPICAL CYCLONE DATA IN SAVING LIVES

The Tropical Rainfall Measuring Mission (TRMM) is a joint NASA/JAXA research mission launched in late 1997 to improve our knowledge of tropical rainfall processes and climatology (Kummerow et ai., 2000; Adler et ai., 2003). In addition to being a highly successful research mission, its data are available in real time and operational weather agencies in the U.S. and internationally are using TRMM data and images to monitor and forecast hazardous weather (tropical cyclones, floods, etc.). For example, in 2004 TRMM data were used 669 times for determining tropical cyclone location fixes (National Research Council, 2004). TRMM flies at a relatively low altitude, 400 km, and requires orbit adjustment maneuvers to maintain altitude against the small drag of the atmosphere. There is enough fuel used for these maneuvers remaining on TRMM for the satellite to continue flying until 2011-12. However, most of the remaining fuel may be used to perform a controlled re-entry of the satellite into the Pacific Ocean. The fuel threshold for this operation will be reached in the summer of 2005, although the maneuver would actually occur in late 2006 or 2007. The full science mission would end in 2005 under the controlled re-entry option. This re-entry option is related to the estimated probability of injury (1/5,000) that might occur during an uncontrolled re-entry of the satellite. If the estimated probability of injury exceeds 1/10,000 a satellite is a candidate for a possible controlled re-entry. In the TRMM case the NASA Safety Office examined the related issues and concluded that, although TRMM exceeded the formal threshold, the use of TRMM data in the monitoring and forecasting of hazardous weather gave a public safety benefit that compensated for TRMM slightly exceeding the orbital debris threshold (Martin, 2002). This conclusion was based in part on results of an independent panel during a workshop on benefits of TRMM data in concluded that the benefit of TRMM data in saving lives through its use in operational forecasting could not be quantified. The objective of this paper is to describe a possible technique to estimate the number of lives saved per year and apply it to the TRMM case and the use of its data in monitoring and forecasting tropical cyclones.

Adler, Robert F.↗
NASA NTRS2003

Structural Reliability Using Probability Density Estimation Methods Within NESSUS

A reliability analysis studies a mathematical model of a physical system taking into account uncertainties of design variables and common results are estimations of a response density, which also implies estimations of its parameters. Some common density parameters include the mean value, the standard deviation, and specific percentile(s) of the response, which are measures of central tendency, variation, and probability regions, respectively. Reliability analyses are important since the results can lead to different designs by calculating the probability of observing safe responses in each of the proposed designs. All of this is done at the expense of added computational time as compared to a single deterministic analysis which will result in one value of the response out of many that make up the density of the response. Sampling methods, such as monte carlo (MC) and latin hypercube sampling (LHS), can be used to perform reliability analyses and can compute nonlinear response density parameters even if the response is dependent on many random variables. Hence, both methods are very robust; however, they are computationally expensive to use in the estimation of the response density parameters. Both methods are 2 of 13 stochastic methods that are contained within the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) program. NESSUS is a probabilistic finite element analysis (FEA) program that was developed through funding from NASA Glenn Research Center (GRC). It has the additional capability of being linked to other analysis programs; therefore, probabilistic fluid dynamics, fracture mechanics, and heat transfer are only a few of what is possible with this software. The LHS method is the newest addition to the stochastic methods within NESSUS. Part of this work was to enhance NESSUS with the LHS method. The new LHS module is complete, has been successfully integrated with NESSUS, and been used to study four different test cases that have been proposed by the Society of Automotive Engineers (SAE). The test cases compare different probabilistic methods within NESSUS because it is important that a user can have confidence that estimates of stochastic parameters of a response will be within an acceptable error limit. For each response, the mean, standard deviation, and 0.99 percentile, are repeatedly estimated which allows confidence statements to be made for each parameter estimated, and for each method. Thus, the ability of several stochastic methods to efficiently and accurately estimate density parameters is compared using four valid test cases. While all of the reliability methods used performed quite well, for the new LHS module within NESSUS it was found that it had a lower estimation error than MC when they were used to estimate the mean, standard deviation, and 0.99 percentile of the four different stochastic responses. Also, LHS required a smaller amount of calculations to obtain low error answers with a high amount of confidence than MC. It can therefore be stated that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ and the newest LHS module is a valuable new enhancement of the program.

Chamis, Chrisos C.↗
NASA NTRS2004

Probability Distribution Estimated From the Minimum, Maximum, and Most Likely Values: Applied to Turbine Inlet Temperature Uncertainty

Modern engineering design practices are tending more toward the treatment of design parameters as random variables as opposed to fixed, or deterministic, values. The probabilistic design approach attempts to account for the uncertainty in design parameters by representing them as a distribution of values rather than as a single value. The motivations for this effort include preventing excessive overdesign as well as assessing and assuring reliability, both of which are important for aerospace applications. However, the determination of the probability distribution is a fundamental problem in reliability analysis. A random variable is often defined by the parameters of the theoretical distribution function that gives the best fit to experimental data. In many cases the distribution must be assumed from very limited information or data. Often the types of information that are available or reasonably estimated are the minimum, maximum, and most likely values of the design parameter. For these situations the beta distribution model is very convenient because the parameters that define the distribution can be easily determined from these three pieces of information. Widely used in the field of operations research, the beta model is very flexible and is also useful for estimating the mean and standard deviation of a random variable given only the aforementioned three values. However, an assumption is required to determine the four parameters of the beta distribution from only these three pieces of information (some of the more common distributions, like the normal, lognormal, gamma, and Weibull distributions, have two or three parameters). The conventional method assumes that the standard deviation is a certain fraction of the range. The beta parameters are then determined by solving a set of equations simultaneously. A new method developed in-house at the NASA Glenn Research Center assumes a value for one of the beta shape parameters based on an analogy with the normal distribution (ref.1). This new approach allows for a very simple and direct algebraic solution without restricting the standard deviation. The beta parameters obtained by the new method are comparable to the conventional method (and identical when the distribution is symmetrical). However, the proposed method generally produces a less peaked distribution with a slightly larger standard deviation (up to 7 percent) than the conventional method in cases where the distribution is asymmetric or skewed. The beta distribution model has now been implemented into the Fast Probability Integration (FPI) module used in the NESSUS computer code for probabilistic analyses of structures (ref. 2).

Holland, Frederic A., Jr.↗
NASA NTRS1999

Analysis and Assessment of Peak Lightning Current Probabilities at the NASA Kennedy Space Center

This technical memorandum presents a summary by the Electromagnetics and Aerospace Environments Branch at the Marshall Space Flight Center of lightning characteristics and lightning criteria for the protection of aerospace vehicles. Probability estimates are included for certain lightning strikes (peak currents of 200, 100, and 50 kA) applicable to the National Aeronautics and Space Administration Space Shuttle at the Kennedy Space Center, Florida, during rollout, on-pad, and boost/launch phases. Results of an extensive literature search to compile information on this subject are presented in order to answer key questions posed by the Space Shuttle Program Office at the Johnson Space Center concerning peak lightning current probabilities if a vehicle is hit by a lightning cloud-to-ground stroke. Vehicle-triggered lightning probability estimates for the aforementioned peak currents are still being worked. Section 4.5, however, does provide some insight on estimating these same peaks.

Johnson, D. L.↗
NASA NTRS2010

A Method to Estimate the Probability That Any Individual Lightning Stroke Contacted the Surface Within Any Radius of Any Point

A technique has been developed to calculate the probability that any nearby lightning stroke is within any radius of any point of interest. In practice, this provides the probability that a nearby lightning stroke was within a key distance of a facility, rather than the error ellipses centered on the stroke. This process takes the current bivariate Gaussian distribution of probability density provided by the current lightning location error ellipse for the most likely location of a lightning stroke and integrates it to get the probability that the stroke is inside any specified radius. This new facility-centric technique will be much more useful to the space launch customers and may supersede the lightning error ellipse approach discussed in [5], [6].

Huddleston, Lisa L.↗
NASA NTRS2009

An Empirical Model for Estimating the Probability of Electrical Short Circuits from Tin Whiskers

In this experiment, an empirical model to quantify the probability of occurrence of an electrical short circuit from tin whiskers as a function of voltage was developed. This empirical model can be used to improve existing risk simulation models. FIB and TEM images of a tin whisker confirm the rare polycrystalline structure on one of the three whiskers studied. FIB cross-section of the card guides verified that the tin finish was bright tin.

Courey, Karim↗