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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

An Impedance-Based Complexity Metric for Unmanned Aircraft System Traffic Scenario Classification

This paper introduces an impedance-based metric to capture the complexity of a given unmanned aircraft system traffic scenario. The metric accounts for both the number of aircraft and the traffic flow pattern. The work presented here extends an earlier approach that introduced another scenario complexity metric based on the number of potential conflicts weighted by the conflict resolution cost associated. Complexity measurements for randomly-generated scenarios were produced through high-fidelity fast-time simulations and treated as baseline. Then the impedance based metric was evaluated, for the same scenarios, without the need for an actual flight simulation and a conflict resolution method. The results show that the impedance-based metric has a strong correlation to the baseline data and performs marginally better than the weighted conflict-based complexity metric introduced in the earlier work. The metric computation generates impedance maps which are useful for identifying high complexity regions in a scenario, where flight plan changes might be necessitated. This metric can therefore be used, in conjunction with other complexity metrics, to inform adequate traffic management strategies and classify a traffic scenario as acceptable, unacceptable or acceptable with changes made to flight plans that pass through the high complexity regions. The metric can also be used as a guidance metric for strategic conflict management methods.

Complexity↗
NASA NTRSDate not supplied

The System Complexity Metric (SCM) Predicts System Costs and Failure Rates

A complex system has many parts and interactions and so is difficult to understand. Systems with higher complexity generally have higher costs and failure rates. A System Complexity Metric (SCM) is defined to be the sum of the number of nodes, N, in the system block diagram plus the number of one-way interactions, I, between the nodes. SCM = N + I. SCMs are easily determined by direct inspection of high level block diagrams of life support systems. System cost was found to be directly proportional to SCM. The system MTBF (Mean Time Before Failure) is the inverse of the system failure rate. MTBF = 1/f. The system MTBF was found to be proportional to SCM^(-2.2) for estimated preflight MTBFs. As is typical for systems that are not extensively tested and redesigned to eliminate unexpected failure modes, the life support flight failure rates were about ten times higher than the preflight estimates and the MTBFs one-tenth the preflight estimates. The system MTBF was found to be proportional to SCM^(-2.6) for observed flight MTBFs.

System compleity↗
NASA NTRS1994

The development and application of composite complexity models and a relative complexity metric in a software maintenance environment

A great deal of effort is now being devoted to the study, analysis, prediction, and minimization of software maintenance expected cost, long before software is delivered to users or customers. It has been estimated that, on the average, the effort spent on software maintenance is as costly as the effort spent on all other software costs. Software design methods should be the starting point to aid in alleviating the problems of software maintenance complexity and high costs. Two aspects of maintenance deserve attention: (1) protocols for locating and rectifying defects, and for ensuring that noe new defects are introduced in the development phase of the software process; and (2) protocols for modification, enhancement, and upgrading. This article focuses primarily on the second aspect, the development of protocols to help increase the quality and reduce the costs associated with modifications, enhancements, and upgrades of existing software. This study developed parsimonious models and a relative complexity metric for complexity measurement of software that were used to rank the modules in the system relative to one another. Some success was achieved in using the models and the relative metric to identify maintenance-prone modules.

Hops, J. M.↗
NASA NTRSDate not supplied

Applying the System Complexity Metric (SCM)

A fundamental cause of difficulty in larger engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, so that there is no obvious mental model that correctly predicts its behavior. Higher complexity is usually associated with higher cost and higher failure rate. Complexity is indicated by a system having more and diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and often the emergence of unanticipated failure modes. Identifying and removing these signs of complexity should reduce complexity and improve performance. Here we limit complexity measurement to the number of components and their interactions. A System Complexity Metric (SCM) is defined as equal to the sum of the number of parts in a system, N, plus the sum of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of system block diagrams. Previous work found that life support system cost was directly proportional to SCM and that failure rate increased faster than SCM squared. SCM can be used to compare systems or to guide their redesign to reduce cost and failure rate. Carbon dioxide removal systems will be analyzed using SCM, cost, and failure rate.

Harry W Jones↗
NASA NTRSDate not supplied

Using the System Complexity Metric (SCM) to Compare CO2 Removal Systems

A fundamental cause of difficulty in large engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, where there is no obvious mental model that correctly predicts its behavior. Higher system complexity is usually associated with higher cost and higher failure rate. Complexity is perceived if a system has many diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and unanticipated failure modes. Identifying and removing these signs of complexity should improve performance and reduce the cost and failure rate. Complexity can be directly measured by the number of components and their interactions. The System Complexity Metric (SCM) is defined as the sum of the number of parts in a system, N, plus the number of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of the system block diagram. SCM can be used to compare systems and to guide their redesign to reduce cost and failure rate. Carbon dioxide removal systems are analyzed using SCM, cost, and failure rate. As in previous work, cost is directly proportional to SCM and that failure rate increases as a power of SCM for large differences in SCM. The SCM ranking of carbon dioxide removal systems is the same as their ranking in detailed analysis and practice.

Harry W. Jones↗
NASA NTRSDate not supplied

Using the System Complexity Metric (SCM) to Compare CO2 Reduction Systems

A fundamental cause of difficulty in large engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, where there is no obvious mental model that correctly predicts its behavior. Higher system complexity is usually associated with higher cost and higher failure rate. Complexity is perceived if a system has many diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and unanticipated failure modes. Identifying and removing these signs of complexity should improve performance and reduce the cost and failure rate. Complexity can be directly measured by the number of components and their interactions. The System Complexity Metric (SCM) is defined as the sum of the number of parts in a system, N, plus the number of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of the system block diagram. SCM can be used to compare systems and to guide their redesign to reduce cost and failure rate. Carbon dioxide reduction systems are analyzed using SCM, cost, and failure rate. As in previous work, cost is directly proportional to SCM and that failure rate increases as a power of SCM for large differences in SCM. The SCM ranking of carbon dioxide reduction systems is the same as their ranking in detailed analysis and practice.

Harry W. Jones↗
NASA NTRS2009

A Complexity Metric for Automated Separation

A metric is proposed to characterize airspace complexity with respect to an automated separation assurance function. The Maneuver Option metric is a function of the number of conflict-free trajectory change options the automated separation assurance function is able to identify for each aircraft in the airspace at a given time. By aggregating the metric for all aircraft in a region of airspace, a measure of the instantaneous complexity of the airspace is produced. A six-hour simulation of Fort Worth Center air traffic was conducted to assess the metric. Results showed aircraft were twice as likely to be constrained in the vertical dimension than the horizontal one. By application of this metric, situations found to be most complex were those where level overflights and descending arrivals passed through or merged into an arrival stream. The metric identified high complexity regions that correlate well with current air traffic control operations. The Maneuver Option metric did not correlate with traffic count alone, a result consistent with complexity metrics for human-controlled airspace.

Aweiss, Arwa↗
NASA NTRS2018

Uncertainty in Heart Rate Complexity Metrics Caused by R-Peak Perturbations

Heart rate complexity (HRC) is a proven metric for gaining insight into human stress and physiological deterioration. To calculate HRC, the detection of the exact instance of when the heart beats, the R-peak, is necessary. Electrocardiogram (ECG) signals can often be corrupted by environmental noise (e.g., from electromagnetic interference, movement artifacts), which can potentially alter the HRC measurement, producing erroneous inputs which feed into decision support models. Current literature has only investigated how HRC is affected by noise when R-peak detection errors occur (false positives and false negatives). However, the numerical methods used to calculate HRC are also sensitive to the specific location of the fiducial point of the R-peak. This raises many questions regarding how this fiducial point is altered by noise, the resulting impact on the measured HRC, and how we can account for noisy HRC measures as inputs into our decision models. This work uses Monte Carlo simulations to systematically add white and pink noise at different permutations of signal-to-noise ratios (SNRs), time segments, sampling rates, and HRC measurements to characterize the influence of noise on the HRC measure by altering the fiducial point of the R-peak. Using the generated information from these simulations provides improved decision processes for system design which address key concerns such as permutation entropy being a more precise, reliable, less biased, and more sensitive measurement for HRC than sample and approximate entropy.

Napoli, Nicholas J.↗
NASA NTRSDate not supplied

The System Complexity Metric (SCM) Explains Systems Design and is Correlated with Cost and Failure Rate

The human short term memory span and working capacity is limited to three to five items, especially if they are organized complex “chunks” of information. The impression of complexity occurs when a system is simply difficult to understand, where there is no apparent pattern to predict its behavior. Hierarchical systems design can reduce perceived complexity and increase the amount of information that can be managed. The SCM was developed to measure complexity and help compare proposed overall system architectures before detailed design information is available. The SCM is defined as the sum of the number of major nodes, N, in the system block diagram plus the number of one-way interactions, I, between the nodes. SCM = N + I. SCM’s are easily determined by direct inspection of high-level block diagrams of life support systems. Axiomatic design develops a hierarchy of subsystem requirements and designs together in a top-down, back-and-forth process. A coupling matrix is used to control the relationships between the subsystem functions and design concepts. Axiomatic design can improve system design by decoupling requirements and designs. Axiomatic design was applied to the planning of a closed life support system, similar to that used on the International Space Station. A materially open as opposed to a closed system design was created by removing the interconnections required to close the system. The open system had the same number of designed subsystems as the closed system, but it had many fewer interconnections and its SCM was lower by about half. The costs were estimated and the MTBF (Mean Time Before Failure) tabulated for open and closed space life support systems. The estimated costs were linearly proportional to SCM for the wide variations of SCM in life support, but small differences may not be significant. The flight and preflight MTBF’s both declined exponentially with increasing MTBF, faster than MTBF-2, even though the preflight estimated MTBF’s were about ten times higher than the flight MTBF’s.

System Complexity Metric (SCM)↗
NASA NTRS1991

A Dynamic Testing Complexity Metric

This paper introduces a dynamic metric that is based on the estimated ability of a program to withstand the effects of injected "semantic mutants" during execution by computing the same function as if the semantic mutants had not been injected. Semantic mutants include: (1) syntactic mutants injected into an executing program and (2) randomly selected values injected into an executing program's internal states. The metric is a function of a program, the method used for injecting these two types of mutants, and the program's input distribution; this metric is found through dynamic executions of the program. A program's ability to withstand the effects of injected semantic mutants by computing the same function when executed is then used as a tool for predicting the difficulty that will be incurred during random testing to reveal the existence of faults, i.e., the metric suggests the likelihood that a program will expose the existence of faults during random testing assuming faults were to exist. If the metric is applied to a module rather than to a program, the metric can be used to guide the allocation of testing resources among a program's modules. In this manner the metric acts as a white-box testing tool for determining where to concentrate testing resources. Index Terms: Revealing ability, random testing, input distribution, program, fault, failure.

Voas, Jeffrey↗