Claude Skills by ashfordeOU

Use when designing or reviewing an F Prime topology, checking opcode and port-type consistency, or generating the component scaffold manifest. Model and validate a NASA JPL F Prime (F´) flight software component architecture: define components as active, queued or passive, attach typed input and output ports plus serial interfaces, register commands with unique opcodes, declare telemetry channels and severity-flagged events, connect producer outputs to consumer inputs across a topology, sched...

Use when you must decide the offline schedulability of an avionics flight software task set under the dual-criticality execution-time model: each task carries the C_LO and C_HI execution-time estimates with C_HI at least C_LO, run the lo-criticality-mode fixed-point response-time iteration over the C_LO estimates for every task, then run the hi-criticality-mode amc-rtb fixed point after the criticality-mode change, with higher-priority LO tasks charged at C_LO and higher-priority HI tasks cha...

Use when you must decide the offline schedulability of a periodic hard-real-time task set: compute the processor utilization of (C, T) tasks with implicit deadlines, apply the Liu-Layland utilization bound for rate-monotonic fixed-priority scheduling, run the exact iterative response-time analysis task by task, and test earliest-deadline-first feasibility with the full-utilization condition. Produces the utilization, the RM bound verdict, the exact response times with an RM feasibility verdic...

Use when you must account for shared-resource blocking in a fixed-priority avionics task set: assign each protected resource its priority ceiling from the tasks that lock it, compute the worst-case blocking time each task can suffer from lower-priority tasks under the priority ceiling protocol, and run the response-time analysis with the blocking term to decide schedulability. Produces the per-resource ceiling map, the per-task worst-case blocking times, the response times with blocking, and ...

Use when you must decide the offline schedulability of an avionics flight software task set under the dual-criticality execution-time model scheduled by edf-vd virtual-deadline scheduling: each task carries the C_LO and C_HI execution-time estimates with C_HI at least C_LO and the implicit-deadline period T, sum the per-mode demand contributions of the LO and HI tasks, derive the common virtual-deadline factor x for the HI tasks, and check the lo-criticality-mode and the hi-criticality-mode d...

Use when scoping an IMA platform, planning module acceptance, or laying out development assurance steps for an integrated modular avionics system. Plan the integrated modular avionics (IMA) platform architecture in the spirit of DO-297: identify the IMA modules, application partitions, and shared resources, allocate applications to partitions with CPU, memory, and I/O budgets, and check the allocation for resource contention against integrity and availability requirements. Produce the module ...

Use when sizing an ARINC 653 partition schedule, writing the partition configuration table, or reviewing inter-partition communication ports against frame, period, and latency budgets for certification. Compute and validate ARINC 653 integrated modular avionics (IMA) partition configurations: check partition schedule feasibility by summing the partition durations within the major frame and verifying that each partition receives its period slot, build the partition configuration table from fra...

Use when you must assess an ADS-B Out installation and ADS-B In reception geometry against the DO-260B-style performance categories: map the navigation integrity category (NIC) to its containment radius, map the navigation accuracy category for position (NACp) to its 95-percent accuracy bound, map the source integrity level (SIL) to its per-flight-hour probability bound, select the NIC and NACp category whose bound covers a required containment or accuracy value, and compute the 1090 MHz exte...

Use when you must compute airborne weather radar operating-point quantities for convective weather avoidance: convert radar reflectivity factor Z to rainfall rate and back with the Marshall-Palmer Z-R relation, estimate the antenna elevation tilt that scans a storm cell top from own altitude and slant range, derive the flat-earth ground range to the cell, check a tilt setting against ground clutter return geometry, and rate echo intensity into standard levels from the reflectivity. Produces t...

Use when you must evaluate a TCAS II resolution advisory for an own aircraft against a single intruder from measured range and altitude state: select the sensitivity level from the own altitude band, compute the modified tau closing time with the DMOD term, apply the horizontal threat test and the altitude test against the tau and ALIM thresholds, and choose the climb or descend advisory sense from the intruder position. Produces the sensitivity level, the modified tau, the threat verdict and...

Use when a task concerns the skill delivery layer, the standard atmosphere, engineering documentation, or numerical analysis: guide the router to the cross-cutting pack. SEP-2640 skill-delivery, skill-evaluation, skill-authoring cover SKILL.md conformance, quality, authoring; isa-atmosphere, unit-conversion, and temperature-conversion cover atmosphere and units; engineering-margins and engineering-report cover margins and reports; tolerance-stackup assembly tolerancing and position-tolerance-...

Use when you must assess an aeronautical engineering data source before relying on it as the engineering reference in a calculation or report: classify the authoritative data type (atmospheric model, aerodynamic database, materials properties, standard part library, regulatory data), check the publisher, edition, and review status, and score source credibility from regulatory, industry, vendor, or community origin. Produces a source registry entry, an approved or review-required verdict, and ...

Use when you must compute the margin of safety for a structural element and state it in an engineering report: compare the allowable load against the applied load, express the stress margin as a unitless decimal or a percent, and produce the pass/fail verdict on the limit basis or ultimate basis. Produces the margin of safety, the margin percent, the limit margin, and the one-line report sentence with consistent units in newtons. Trigger: margin of safety, engineering report, allowable load, ...

Use when you must draft or review an engineering report and verify its structure: the required sections (abstract, introduction, method, results, discussion, conclusion, references), abstract length against the recommended 150 to 300 word range, completeness of the deliverable, units and uncertainty statements for every reported value, traceability of results to requirements, review gates, and version control. Produces missing-section lists, abstract-length pass or fail, units-statement pass ...

Use when an aerospace engineer or agent must decide whether an item, data set, or task is export controlled under ITAR or EAR: it produces an export control assessment, screens restricted topics for red flags (turbine blade alloys, gas turbine engines, guidance systems for missiles, propulsion, sensors, avionics, spacecraft), and returns a verdict class (defense article, dual-use, public domain, not controlled) with handling guidance including deemed export checks for foreign collaborators. T...

Use when you must design a digital Butterworth IIR bandpass or bandstop filter from its two band-edge frequencies, sample rate, and order by the z-domain LP-to-BP / LP-to-BS digital frequency transformation: map a digital Butterworth prototype into the band so both edges land at exactly -3.0103 dB on the magnitude response, then filter a sampled signal. Produces the bandpass or bandstop coefficient vectors, substitution parameters, center frequency, band-edge gain checks, filtered output, and...

Use when you must test whether observed counts fit a stated categorical model: the chi-square goodness-of-fit statistic as the sum of the squared observed-minus-expected gaps over expected counts, the degrees of freedom k minus 1 minus estimated parameters, and the one-tailed p-value from the chi-square survival function via its own regularized lower incomplete gamma, returning the reject or fail-to-reject verdict at a stated significance level. Produces the statistic, degrees of freedom, p-v...

Use when you must compute complex-number algebra with the Python standard library: form a complex value from rectangular or polar coordinates, add, subtract, multiply and divide complex values, take the conjugate, modulus and argument, raise a complex value to an integer power by De Moivre's formula, generate the n-th roots of unity, and convert between rectangular, polar and Euler exponential forms, verifying identities such as z times its conjugate equals the squared modulus and e to the i ...

Use when you must estimate a confidence interval for a sample statistic: the Student t interval for a sample mean, the pooled or Welch-Satterthwaite interval for a difference of means, and the chi-square interval for the variance and standard deviation of a measured or production batch, each at a stated confidence level. Quantiles come from in-leaf inversion: the two-sided t quantile by bisection on the regularized incomplete beta relation and the chi-square quantile by lower incomplete gamma...

Use when you must verify that a CFD or structural mesh sequence has converged: compute the observed order of accuracy from the finest, medium, and coarse solutions, apply Richardson extrapolation to estimate the exact solution, and report the grid convergence index (GCI) with the 1.25 safety factor. Produces the observed order, the extrapolated value, the GCI, and a monotone converged, oscillatory, or diverging verdict that gate whether the discretization error is acceptable for the assessmen...

Use when you must compute the cross-correlation or autocorrelation of sampled signal sequences to quantify channel similarity and time delay: evaluate the raw cross-correlation over the full lag range with zero padding, normalize it to a correlation coefficient in [-1, 1] from the zero-lag energies, estimate the delay between channels from the peak lag, apply the biased or unbiased convention, and verify the even symmetry of the autocorrelation. Produces the correlation sequence, the peak lag...

Use when you must summarize a sample of engineering measurements with descriptive statistics: compute the arithmetic mean, median, data range, sample and population variance and standard deviation, the quartiles and interquartile range by linear interpolation, the five-number summary, the coefficient of variation, and flag outliers with the 1.5-IQR rule. Produces the location, spread, and outlier report that gates a first look at any measured data set; pure Python stdlib, deterministic, no di...

Use when you must compute the coefficients of a digital Butterworth IIR lowpass or highpass frequency-selective filter from a cutoff frequency, sample rate, and order: prewarp the analog cutoff, map the normalized Butterworth poles through the bilinear transform, build the b and a coefficients with unity DC or Nyquist gain, evaluate the magnitude response in dB at any frequency, and apply the filter to a sampled signal with the direct-form difference equation. Produces the coefficient vectors...

Use when the task is an eigen-decomposition: spectral analysis, dominant eigenvalue, modal frequencies, covariance or stiffness matrix diagonalization, stability of a linear system, or verifying a pair with the residual A v minus lambda v, and numpy or other numerical libraries are unavailable. Compute eigenvalues and eigenvectors of square matrices with only the Python standard library: the power iteration returns the dominant eigenvalue-eigenvector pair of a general square matrix, deflation...

Use when you must test an observed count against a hypothesized proportion: compute the exact binomial tail probability of k or fewer successes in n trials under a null proportion p zero, form the two-sided p-value by doubling the one-sided tail mass capped at one with an optional mid-p variant and a continuity-corrected normal cross-check, and decide the verdict against a significance level. Produces the exact p-value, the lower and upper tail masses, the observed direction, and the small-co...

Use when you must compute the frequency content of a sampled signal with the discrete Fourier transform or the radix-2 fast Fourier transform: apply the DFT definition for small N, use the Cooley-Tukey decomposition when N is a power of two, extract the magnitude and phase spectrum, and recover the time series with the inverse FFT. Produces the complex spectrum, the magnitude, phase, and power spectra, and the reconstructed signal with Parseval energy checks that gate spectral analysis of sam...

Use when you must compute numerical derivatives of a function or of tabulated data with finite difference formulas: choose between the forward, backward, and central difference stencils, size the step h, compute the second derivative with the centered three point stencil, and differentiate evenly spaced tabulated data with one sided differences at the boundaries. Produces the first and second derivative estimates and the tabulated derivative values that gate the differentiation step. Trigger:...

Use when you must design a linear-phase finite-impulse-response highpass, bandpass, or bandstop filter by the windowed-sinc method with spectral inversion and cosine frequency translation of a lowpass prototype: build the windowed prototype at the cutoff, the half bandwidth for bands, form the highpass as the windowed unit sample minus the prototype, the bandpass as twice the prototype times the center cosine, and the bandstop as spectral inversion of the translated bandpass, under the rectan...

Use when you must design a linear-phase finite-impulse-response lowpass filter with the windowed-sinc method: build the ideal lowpass impulse response from the cutoff frequency and the sample rate, apply a selected window (rectangular, Hann, Hamming, or Blackman), normalize the coefficient vector to unity DC gain, evaluate the magnitude response in dB at any frequency as the real cosine sum of the symmetric tap set, return the group delay of the taps, and filter a sampled signal by direct con...

Use when you must test a 2x2 contingency table with small expected counts: run the exact Fisher test under the fixed-margin null, compute the hypergeometric probability of the observed table, enumerate every table with the same margins, sum the one-tailed and two-tailed exact p-values, compute the odds ratio with the Haldane-Anscombe zero-cell correction, and return the small-expected-count verdict that recommends the exact test over the large-sample approximation. Produces p_obs, p_one_tail,...

Use when you must test a normal sample for a single outlier: compute the sample mean and standard deviation, form the Grubbs G statistic as the largest absolute deviation from the mean divided by the sample standard deviation, compare it against the two-sided 0.05 critical value for the sample size from an embedded reference table with linear interpolation between listed sizes, and report the outlier verdict with the flagged value. Produces the G statistic, the critical value, the reject or n...

Use when you must run significance tests on aerospace engineering data: the one-sample and two-sample Student t tests (pooled and Welch), the paired t test, the two-variance F test, the chi-square test of independence, and the one-way ANOVA F test, computing each statistic, its degrees of freedom, and its p-value from the incomplete beta and gamma functions and returning the reject-null or fail-to-reject verdict at a stated significance level. Produces the statistic, df, p-value, and verdict ...

Use when you must compute the information content of a symbol distribution: the Shannon entropy in bits per symbol of a measured count distribution or probability mass function, the binary entropy function of a two-symbol source, the uniform-distribution entropy bound log2 of the symbol count, and the minimum source-coding bit rate as entropy times symbol rate. Produces the entropy, the uniform bound, the redundancy verdict against it, and the minimum bit rate that gates data-channel and quan...

Use when you must estimate a value between the tabulated points of an aerospace data table: interpolate linearly between two adjacent data points, perform piecewise linear interpolation over a whole table, build a natural cubic spline through the data points and evaluate it at an intermediate abscissa, extend beyond the table ends with the boundary behavior, and validate that the table is sorted and well formed before the lookup. Produces the interpolated value, the spline coefficients, and t...

Use when you must compare three or more independent groups without the normality assumption: run the Kruskal-Wallis test by merging all observations, assigning average ranks for ties, computing the H statistic, applying the ties correction denominator, evaluating the p-value from the chi-square survival function with k minus 1 degrees of freedom, and returning the verdict at the chosen significance level. Produces H, the ties-corrected H, degrees of freedom, p-value, per-group rank sums and t...

Use when you must fit a straight line to paired measurements by ordinary least squares: compute the slope and intercept of the best fit, the residual standard deviation, and the coefficient of determination, and predict the response at a new input. Produces the fit coefficients, the goodness of fit, and the residual scatter that gate whether the linear model is adequate for the analysis. Trigger: least squares, linear regression, best fit line, slope, intercept, residual standard deviation, c...

Use when the task is a direct-method dense matrix problem: a linear system solve, a determinant evaluation, a matrix inverse, a singular-matrix check, or a residual verification of a solution, and numpy or other numerical libraries are unavailable. Compute and verify dense square-matrix operations with only the Python standard library: solve the linear system Ax=b by Gaussian elimination with partial pivoting, compute the determinant, invert the matrix, and detect singularity. Produces the so...

Use when you must estimate the distribution of an output quantity by Monte Carlo sampling: draw seeded pseudo-random samples from a uniform input range, compute the sample mean and the sample standard deviation, extract percentile confidence intervals, and bin the draws into a histogram. Produces the sample statistics, the confidence interval, and the histogram counts that gate the sampling study. Trigger: monte carlo sampling, random seed, sample size, percentile, confidence interval, histog...

Use when you must fit a multiple linear regression model: solve the normal equations for the partial-regression-coefficient vector from two or more predictors, compute each coefficient-standard-error with the two-sided p-value of its t statistic, the overall regression-f-test p-value, R-squared and adjusted-r-squared, and the variance-inflation-factor multicollinearity-check for every predictor, then predict the response at a new design point. Produces the coefficient vector, diagnostic table...

Use when you must integrate a function numerically: select the composite trapezoid rule, the composite Simpson rule, or Gauss-Legendre quadrature for the integrand, compute the integral estimate, and estimate the error with Richardson extrapolation of the trapezoid rule. Produces the integral estimate, the chosen method with its justification, and the error estimate that gate quantitative analysis of smooth, endpoint-singular, and high-degree integrands. Trigger: numerical integration, trapez...

Use when a task asks for an ODE solver, differential-equation time marching, an initial-value problem, a decay or response trajectory, or an error-versus-exact comparison. Solve first-order ordinary differential equations numerically with explicit Euler, Heun's method (RK2), and classical RK4: step the initial-value problem forward from y(t0), tabulate the solution, compare it against a closed-form reference, and check step-size convergence of the global error. Produces the solution table, th...

Use when you must minimize a scalar or multivariate design objective numerically: bracket a smooth one-variable objective and locate the minimum with golden-section search, or apply Newton's method on the derivative; run gradient descent with an Armijo backtracking line search or the derivative-free Nelder-Mead simplex for multivariate problems, and report the converged minimizer, the objective value, and the iteration count at a specified tolerance. Produces the unconstrained minimum, the co...

Use when you must compute a confidence interval for a Poisson rate from a count over an exposure: estimate the rate lambda_hat = k / T, form the exact Garwood interval from in-leaf chi-square quantiles with lower bound chi2(2k, alpha/2)/(2T) and upper bound chi2(2k+2, 1-alpha/2)/(2T), and report the normal approximation as the large-count cross-check. Produces the rate estimate, the exact lower and upper bounds per exposure unit, the approximation bounds, and the containment verdict that gate...

Use when you must determine the sample size or the statistical power of a planned comparison: compute the minimum sample size per group for a two-sample pooled z-based comparison at a significance level, target power and effect size, with the one-sample and one-sample-proportion variants, round up to whole groups, and evaluate the achieved power at the rounded sample size. Produces the per-group sample size, the total sample size and the achieved power that gate qualification-test planning an...

Use when you must estimate the power spectral density of a stochastic signal: Welch averaged periodogram estimation with a Hann window, overlapping segments (default 50 percent), and one-sided density scaling in units squared per hertz. Produces the PSD array and its frequency axis, the equivalent noise bandwidth, the integrated total power, and a peak summary for random-vibration and noise surveys of measured acceleration or response time histories. Trigger: power spectral density, welch per...

Use when you must fit and characterize a standard probability distribution for aerospace engineering data analysis: estimate the normal, lognormal, exponential, and Weibull distribution parameters from a univariate sample, evaluate the pdf, cdf, quantile, reliability, and hazard functions, score the fit with the chi-square and Kolmogorov-Smirnov goodness-of-fit statistics, and report percentiles plus reliability at a target time. Produces the fitted parameter dict, the fit-quality verdict, an...

Use when you must estimate a confidence interval for a binomial proportion: compute the Wilson score interval and its continuity-corrected variant, compute the exact Clopper-Pearson interval by inverting the binomial tail through an in-leaf regularized incomplete beta, and compute the confidence interval for the difference of two proportions from attribute data at a stated confidence level. Produces the lower and upper bounds by each method, the interval width, and the method recommendation t...

Use when you must compute single-step quaternion algebra with the Python standard library: form the Hamilton quaternion product, take the conjugate, norm, and inverse, normalize to a unit quaternion, rotate a 3-vector by a quaternion with the stated conjugate rotation convention, build a quaternion from an axis and angle or from yaw-pitch-roll angles with the ZYX convention, convert between quaternion and direction cosine matrix, and interpolate between two unit quaternions with spherical lin...

Use when you must compare two samples without relying on the normality assumption: run the Wilcoxon rank-sum test (Mann-Whitney U) on two independent samples, the Wilcoxon signed-rank test and the sign test on paired measurements, using average ranks for ties, exact rank sums, the normal approximation z with the 0.5 continuity correction toward zero, the two-sided p-value from the standard normal CDF, and the reject or accept verdict at a chosen alpha. Produces the test statistic, z, p-value ...

Use when a task asks for a root finder, zero finding, nonlinear equation solving, compressible flow Mach number solution, or implicit performance equation inversion in aerospace analysis. Determine the root of a nonlinear scalar equation f(x) = 0 numerically with the bisection method, Newton-Raphson, the secant method, or fixed-point iteration: bracket the root or supply an initial guess, apply the iteration, and produce the root to a specified tolerance under function tolerance, step toleran...