Reliability Growth Analysis and Plots
During the first phases of a product's development, the estimate of the product's final reliability is called the reliability goal. However, the first prototypes produced will almost certainly contain design, manufacturing and/or engineering deficiencies that prevent the product from reaching that goal. In order to identify and correct these deficiencies, prototypes are usually subjected to a rigorous testing program and appropriate corrective actions are implemented to improve the design. This structured process of finding reliability problems and monitoring the increase of the product's reliability through successive phases is called reliability growth.
Until now, the software available for analyzing reliability growth data has been fairly limited. However, ReliaSoft is currently working in cooperation with Dr. Larry Crow, the premier expert in the field of reliability growth, to develop the next generation of reliability growth analysis software, RGA 6. This article presents a brief overview of the capabilities of RGA 6 (scheduled for release in Fall 2003) and an introduction to some of the results and plots that are available for your reliability growth and related analyses.
Analysis Results and Plots
Figure 1: Expected Number of Failures vs. Time
Figure 2: Instantaneous MTBF vs. Time
RGA 6’s QCP also provides point estimates for these metrics given time. In addition, you can generate charts and results for the cumulative MTBF and similar output for instantaneous and cumulative failure rates.
A variety of charts and results are available to support this effort. For example, Figure 3 shows the Growth Potential MTBF plot, which presents the reliability achieved during the test, the reliability that is projected after the implementation of delayed fixes and the maximum achievable reliability, given the current management strategy. If you determine that you will not meet your reliability goal, then you can re-evaluate your failure modes and change some A modes to B modes. In other words, you can decide to correct more failure modes. While doing projections, the assumption is that Beta is equal to one. Figure 4 shows one of several methods to check whether this assumption is valid, the Beta Bounds plot, which displays the confidence bounds on Beta at different confidence levels and demonstrates how these compare to the line where Beta equals one.
Figure 3: Growth Potential MTBF plot
Figure 4: Beta Bounds plot to confirm assumption
RGA also provides pie charts and bar charts for this type of analysis. For example, the bar chart in Figure 5 displays the actual (current) failure rate with the predicted failure rate for all the B modes in the analysis. The chart can also be generated for each individual failure mode. In these charts, the red bar (left) represents the actual failure rate and the green bar (right) represents the failure rate after the fixes have been implemented. From the chart in Figure 5, you can see how each failure mode is contributing to the failure rate of the system. In addition, you can also see how the failure rate for each failure mode is decreasing after the implementation of the fix.
Figure 5: Before and after failure rates for B modes
Figure 6 displays a pie chart of failure modes with categories to represent the steps taken to address the modes: "Type A" will not be addressed. "Type B-Unseen" have not yet appeared in testing but are estimated from the analysis. "Type B-Remain" are failure modes that remain in the system since the corrective actions were not 100% effective and "Type B-Removed" are failure modes that have been removed through corrective actions and their effectiveness. For example, according to this pie chart, almost 29% of the failure modes have not even been observed yet through testing.
Figure 6: Failure modes pie chart
In RGA 6's repairable systems interface, you can enter a start and end time for each system, along with any failure data that you may have for the system. You also have the ability to remove individual systems from consideration in a particular analysis if, for example, the data is not representative of the rest of the population. You can then analyze the data to combine each of these individual systems into a single "superposition" system. The parameters Beta and Lambda for that system, along with the results of the Laplace Trend Test and the Cramer Von Mises goodness-of-fit test, are also displayed for each system individually and for the combined "superposition" system.
Figure 7 displays one of the plots available for repairable systems analysis in RGA 6. This is the System Operation plot, which displays a timeline of the failures for each of the individual systems, along with the failures for the combined superposition system. You can also generate plots of reliability and unreliability vs. time for the extrapolated superposition system, as shown in Figure 8. Other plots, such as the Cumulative Number of Failures vs. Time plot with either linear or logarithmic axes, are also available.
Figure 7: Failures for individual, superposition systems
Figure 8: Reliability vs. Time for superposition system