Constant Time

Unreliability or Unavailability (F)

The reliability of the component is described in terms of unreliability or unavailability (F) in terms of an unchanging number of hours (default) or minutes. The constant time distribution is the default for maintenance tasks in the RBD module. For more information, see Constant Time Distribution.

Exponential

Failure rate (λ) or MTBF (1 / λ)

The reliability of the component is described in terms of the failure rate (λ) or MTBF (1 / λ). This distribution is recommended when the failure rate is constant over time. It is the default for failure distributions. The exponential distribution can be viewed as a special case of the Weibull distribution, where the shape factor (β) is known to equal 1 (WeiBayes Beta=1). For more information, see Exponential Distribution.

Gamma

Theta (θ) and Alpha (α)

The gamma distribution was developed during the early stages of statistical development as the sampling distribution of several statistics. It has several applications in reliability engineering. It can be used to model the failure characteristics of standby systems. The Exponential, Erlang, and Chi-Square distributions are special cases of the gamma distribution. For more information, see Gamma Distribution.

Gumbel- (Lower) and Gumbel+ (Higher)

Probability density function, f (t), and survival function, which is reliability with respect to time t:

The reliability of the component is described in terms of the probability density function, f (t), and survival function, which is reliability with respect to time t:

Gumbel distributions are available only in the ALT and Weibull modules. They are used to model extreme values. For more information, see Gumbel Distributions.

Log-logistic

Mean (μ) and Standard Deviation (σ)

The reliability of the component is described in terms of the mean (μ) and standard deviation (σ). This distribution is also called the Fisk distribution. For more information, see Log-logistic Distribution.

Logistic

Mean (μ) and Standard Deviation (σ)

The reliability of the component is described in terms of the mean (μ) and standard deviation (σ). This distribution.receives its name from its cumulative distribution function (CDF), which is an instance of the family of logistic functions. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). It is used in growth models and in health and social sciences. It also has applications in reliability modeling. For more information, see Logistic Distribution.

Lognormal

Mean (μ) and Standard Deviation (σ)

The reliability of the component is described in terms of the mean (μ) and standard deviation (σ) for the underlying normal distribution. This distribution is recommended when the time-to-failure results from the multiplication of effects. For example, in the case of progressive deterioration, a crack forms due to stress, and the stress increases as the crack grows. For more information, see Lognormal Distribution.

Normal

Mean (μ) and Standard Deviation (σ)

The reliability of the component is described in terms of the mean (μ) and standard deviation (σ). This distribution is recommended when failure times can be expressed as the summation of some other random variables. For more information, see .Normal Distribution

Rayleigh

Characteristic Life (η)

The reliability of the component is described in terms of the characteristic life (η). This 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 recommended when the failure rate increases linearly with time. For more information, see Rayleigh Distribution.

Time Independent

Unreliability or Unavailability (F)

The reliability of the component is described in terms of a specified value for unreliability or unavailability. This distribution is available for modeling failure times but not repair times. It is recommended if the failure rate is assumed to remain constant rather than to vary over time. For more information, see Time Independent Distribution.

Uniform

Lower Bound (α) and Upper Bound (β)

The reliability of the component is described in terms of the lower bound (α) and upper bound (β). This distribution is recommended if the random variable can exist only in a linear range of α to β and the probability of occurrence is directly proportional to the interval length. For more information, see .Uniform Distribution

WeiBayes

Characteristic Life (η)

The reliability of the component is described in terms of the characteristic life (η). The WeiBayes distribution can be viewed as a special case of the Weibull distribution, where some known shape factor (β) can be specified (WeiBayes Beta=2). For more information, see WeiBayes Distribution.

Weibull

Characteristic Life (η), Shape Factor (β), and possibly Location (t 0)

The reliability of the component is described in terms of the characteristic life (η), shape factor (β), and possibly an optional location parameter (t0). This distribution is recommended when the failure rate decreases over time (burn-in period) or increases over time (wear-out period). For more information, see Weibull Distribution.