In many cases, it is valuable to fit a distribution that represents the system's times-to-failure. This can be useful when the system is part of a larger assembly and may be used for repeated calculations or in calculations for other systems. In cases such as this, it can be useful to characterize the system's behavior by fitting a distribution to the overall system and calculating parameters for this distribution. (Note: This is particularly useful in system simulation since it significantly reduces simulation time.) This is equivalent to fitting a single distribution to describe RS(t). In essence, it is like reducing the entire system to a component in order to simplify calculations.
For the system in Figure 5.2:
To compute
an approximate reliability function for this system, 
,
one would compute n pairs
of reliability and time values and then fit a single distribution to the
data, or:
A single distribution, RA(t), that approximates RS(t) can now be computed from these pairs using life data analysis methods. If using the Weibull++ software, one would enter the values as free form data.
Compute a single Weibull distribution approximation for the system in Time-Dependent System Reliability (Analytical) Example 2.
The system in the previous example, shown in Figure 5.5, can be approximated by use of a 2-parameter Weibull distribution with β = 2.02109 and η = 1123.51. In BlockSim, this is accomplished by representing the entire system as a block and going to the Subdiagram tab of the Block Properties window and selecting the "Represent Diagram as Distribution" option (Figure 5.12). (Note: Detailed descriptions of this functionality and its use can be found in the BlockSim User's Guide.)
Figure 5.12: Representing a system with a distribution.
Figure 5.13: Distribution Settings window.
Upon clicking the Distribution Settings button, the Distribution Settings window will appear (Figure 5.13).
In this window, you can select a distribution to represent the data. BlockSim will then generate a number of system failure times based on the system's reliability function. The system's reliability function can be used to solve for a time value associated with that unreliability value. The distribution of the generated time values can then be fitted to a probability distribution function.
Consider a value of F(t) = 0.11. Using the system's reliability equation and solving for time, the corresponding time-to-failure for a 0.11 unreliability can be calculated. For the system of Example 2, the time for a 0.11 unreliability is 389.786 hours.
Once enough points have been generated, the selected distribution will be fitted to this data set and the distribution's parameters will be returned. In addition, if ReliaSoft's Weibull++ 6 or later is installed, the generated data can be viewed/analyzed using a Weibull++ instance, as shown in Figure 5.14.
Figure 5.14: Using Weibull++ to calculate system distribution parameters.
It is recommended that the analyst examine the fit to ascertain the applicability of the approximation.
See Also:
Time-Dependent System Reliability (Analytical)
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