Rayleigh Distribution
Characteristic life is the only parameter required for the Rayleigh distribution. The Rayleigh distribution can be viewed as a special case of the Weibull distribution where the shape factor (β) is known to equal 2 (WeiBayes Beta=2).
The Rayleigh distribution is an important distribution in its own right, finding application not only in reliability problems but also in noise problems associated with communication systems. A single-parameter distribution similar to the exponential distribution, the Rayleigh distribution can be used to describe the root mean square (RMS) value of error sources. The Rayleigh distribution is recommended if the failure rate increases linearly with time.
Calculations
The probability density function, f(t), and the survival function, that is reliability, 
, with respect to time t, follows for computing Rayleigh distributions. A Rayleigh distribution is a special case of the Weibull distribution with β = 2 and
, with respect to time t, follows for computing Rayleigh distributions. A Rayleigh distribution is a special case of the Weibull distribution with β = 2 and
. The equation for computing Rayleigh distributions is:
Where t ≥ 0 and σ > 0.
In this case, σ is the scale (characteristic life) parameter of the distribution.
 | If a location parameter exists, see Location Parameter for additional calculation information. |