Duty Cycle

Components of a system may not operate continuously during a system's mission, or may be subjected to loads greater or lesser than the rated loads during system operation. To model this, a factor called the Duty Cycle (dc) is used. The duty cycle may also be used to account for changes in environmental stress, such as temperature changes, that may effect the operation of a component. The duty cycle is a positive value, with a default value of 1 representing continuous operation at rated load, and any values other than 1 representing other load values with respect to the rated load value (or total operating time). (Note:The value of dc depends on the Life-Stress relationship (LSR) of the component. If a linear LSR can be assumed, dc is simply the ratio of the load on the component (V2) to the rated load (V1) ( i.e. dc= (V2/V1). For an inverse power LSR, dc= (V2/V1)n.) A duty cycle value higher than 1 indicates a load in excess of the rated value. A duty cycle value lower than 1 indicates that the component is operating at a load lower than the rated load or not operating continuously during the system's mission. For instance, a duty cycle of 0.5 may be used for a component that operates only half of the time during the system's mission.

The reliability metrics for a component with a duty cycle are calculated as follows. Let dc represent the duty cycle during a particular mission of the component, t represent the mission time and t' represent the accumulated age. Then:

The reliability equation for the component is:

The component pdf is:

The failure rate of the component is:

Time-Dependent System Reliability (Analytical) Example 4

Consider a computer system with three components: a processor, a hard drive and a CD drive in series as shown next. Assume that all three components follow a Weibull failure distribution with the parameters β1 = 1.5 and η 1 = 5000 for the processor, β2 = 2.5 and η 2 = 3000 for the hard drive and β3 = 2 and η 3 = 4000 for the CD drive. Determine the reliability of the computer system after one year (365 days) of operation, assuming that the CD drive is used only 30% of the time.

Solution to Time-Dependent System Reliability (Analytical) Example 4

The reliability of the processor after 365 days of operation is given by:

The reliability of the hard drive after 365 days of operation is given by:

The reliability of the CD drive after 365 days of operation (taking into account the 30% operation using a duty cycle of 0.3) is given by:

Thus the reliability of the computer system after 365 days of operation is:

This result can be obtained in BlockSim as shown in Figure 5.15.

Figure 5.15: Using Weibull++ to calculate system distribution parameters.

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