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Reliability Basics | |||||||

## Component Reliability Importance in System Reliability Analysis
Once the reliability of a system has been determined, engineers are often faced with the task of identifying the component(s) that cause the most problems to the system in order to prioritize improvements in the design and channel resources and efforts of system improvement to the areas that will have the most impact on the system's performance. In simple systems such as a series system, it is easy to identify the weak components. In more complex systems, however, this becomes quite a difficult task. Identifying the weakest component is an exercise that is based on understanding both the reliability of each component and the roles the components play reliability-wise in the system, which is determined by their location in the reliability block diagram (RBD). For complex systems, the analyst needs a mathematical approach that will provide the means of identifying and quantifying the importance of each component in the system. (Note: the cost of improving the reliability of the component is not considered. Cost of improvement is covered in the Reliability Allocation section of the online Life Data Analysis Reference.) In this article, BlockSim is used to generate plots that assist in understanding the reliability importance of each component in the analyzed system.
Using reliability importance measures is one method of identifying the
relative importance of each component in a system with respect to the
overall reliability of the system. The reliability importance,
i
in a system of
n components is given by
Leemis [1].
Where: -
*R*is the system reliability_{s} -
*R*is the component reliability_{i}
The value of the reliability importance given by Eqn. (1) depends on both the reliability of a component and its corresponding position in the system. It can be observed that for a simple series system the rate of increase of the system reliability is greatest when the least reliable component is improved.
Let us consider a simple example of three static blocks in series.
The blocks have the following reliability values.
By
increasing the reliability of a component
The same conclusion can be drawn by using Eqn. (1) and obtaining the reliability importance in terms of a value for each component. Using BlockSim, the reliability importance values for these components can be calculated with Eqn. (1). Using the plot option and selecting the "Static Reliability Importance" plot type, the plot shown next can be obtained. Note that the time input required to create this plot is irrelevant for this example because the components are static.
The values in the y-axis of the above plot are derived using Eqn. (1). The reliability equation for this series system is given by:
Taking the partial derivative of Eqn. (2) with respect to
Thus, the reliability importance of Component # 1 is
The
same concept can be extended to time-dependent (time varying reliability)
components. That is, if
In
turn, this can be viewed as either a static plot (at a given time) or as
time varying plot, as illustrated in the next figures. Specifically, Figures
3, 4 and 5 present the analysis for three components configured
reliability-wise in series following a Weibull distribution with η_{2} = 2,000 and
η_{3}
= 3,000. Figure 3 shows a bar chart of
while Figure 4 shows the
in BlockSim's "tableau chart" format. In this chart, the area of the square
is , thus bigger
areas indicate more importance. Lastly, Figure 5 shows the
(t)
vs. time.
The above analysis can be applied to complex systems. Let us consider the following system's RBD.
The next table shows the components' reliability distribution models.
Figure 6 illustrates (
Leemis, L.M., | |||||||

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