I. MATHEMATICAL MODELS The mixture Weibull distribution produced from the combination has five or more parameters. These are; the shape parameters, scale parameters, location parameters, in addition to the mixing parameter (w). This type of distribution is even more useful because multiple causes of failure can be simultaneously modelled. Different values of the mixing parameter were used to ob...

Key elements of the 36 MJ Atlas capacitor bank have been evaluated for individual probabilities of failure. These have been combined to estimate system reliability which is to be greater than 95% on each experimental shot. This analysis utilizes Weibull or Weibull-like distributions with increasing probability of failure with the number of shots. For transmission line insulation, a minimum thic...

In this research we investigate how the Weibull distribution is suited as an alternative to common approaches in the stochastic modeling of machine downtimes and times between failures. We present an algorithm that automatically calculates Weibull parameters from machine data based on the SEMI E10 standard. We also discuss the question whether sampling shop-floor data should not only include fi...

By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the extrapolation is quite limited generally in comparison with a heavy tailed distribution. In view of t...

Lower bounds are typically used to evaluate the performance of heuristics for solving combinatorial minimization problems. In the absence of tight analytical lower bounds, optimal objective-function values may be estimated statistically. In this paper, extreme value theory is used to construct confidence-interval estimates of the minimum makespan achievable when scheduling nonsimilar groups of ...

Different functions, each in the form of a modified Weibull cumulative distribution function (cdf), were joined together to form a segmented cdfto approximate diameter distributions in forest stands. Estimates of five percentile points (the 0th, 25th, 50th, 75th, and 100th percentiles) were used to determine a segmented cdf. The segmented cdf and the Weibull distribution were fit to diameter da...

The Weibull distribution is widely used to analyze the cumulative loss of performance, i.e., breakdown, of a complex system in systems engineering. We found for the first time that the difference curve of two Weibull distribution functions almost identically fitted the isovolumically contracting left ventricular (LV) pressure-time curve [P( t)] in all 345 beats (3 beats at each of 5 volumes in ...

Error-rate performance is studied for selection combining (SC) with arbitrary number of diversity branches over generalized correlated Weibull fading channels. Using a transformation of cumulative distribution function of average branch signal-to-noise ratio (SNR), we present the exact error-rate expressions for coherent and noncoherent modulations in infinite series forms. In particular, we de...