On Estimating Reliability of a Stress – Strength Model in Case of Rayleigh Pareto Distribution

The stress – strength model is one of the models that are used to compute reliability. In this paper, we derived mathematical formulas for the reliability of the stress – strength model that follows Rayleigh Pareto (Rayl. – Par) distribution. Here, the model has a single component, where strength Y is subjected to a stress X, represented by moment, reliability function, restricted behavior, and ordering statistics. Some estimation methods were used, which are the maximum likelihood, ordinary least squares, and two shrinkage methods, in addition to a newly suggested method for weighting the contraction. The performance of these estimates was studied empirically by using simulation experimentation that could give more varieties for different-sized samples for stress and strength. The most interesting finding indicates the superiority of the proposed shrinkage estimation method.

Concordance: In-flight Calibration of X-Ray Telescopes without Absolute References

We describe a process for cross-calibrating the effective areas of X-ray telescopes that observe common targets. The targets are not assumed to be “standard candles” in the classic sense, in that we assume that the source fluxes have well-defined, but a priori unknown values. Using a technique developed by Chen et al. that involves a statistical method called shrinkage estimation, we determine effective area correction factors for each instrument that bring estimated fluxes into the best agreement, consistent with prior knowledge of their effective areas. We expand the technique to allow unique priors on systematic uncertainties in effective areas for each X-ray astronomy instrument and to allow correlations between effective areas in different energy bands. We demonstrate the method with several data sets from various X-ray telescopes.