Crow/AMSAA
(C/A) plots are log-log plots from the field of reliability for showing you’ve
made improvements and reduced failures. Its
show me, don’t tell me, technology for handling a variety of data. You’ll also see the name spelled as
Crow-AMSAA (C-A) plots.
Two plots are used with C/A analysis:
• The first plot is a simple cumulative
failures on the vertical Y-axis and cumulative time on the horizontal
X-axis. This plot always climbs from the
lower left hand corner of the plot towards the upper right hand corner as both
time and failures accumulate.
• The second plot is derived from the first plot by transforming the Y-axis
into cumulative MTBF by dividing the cumulative failures into the cumulative
time. The MTBF plot goes up and to the
right with improvements, or it goes down and to the
right with increasing failure rates.
Remember our task as reliability engineers is to put a flattening cusp on the cumulative failures versus
cumulative time trend line so that failures come more slowly. Deciding about the cusps is a subject for
engineering judgment.
C/A methodology does not have the strict data requirements demanded for Weibull plots. For example, Weibull plots require:
- Weibull age-to-failure data requires knowing the age from time = 0 where time commences, up to the age at failure, for a human example, this means knowing the date of birth and the date of death to get the age-to-failure, and
- Weibull plots require only a single failure mode for each Weibull plot (excluding mixture analysis techniques).
Weibull analysis provides a simple statistic for components which infers the mode of failure (b<1 for infant mortality, b>1 for wear out, and b≈1 for random failures). Weibull analysis also gives a single value for describing the characteristic value at failure (h) for the skewed distributions. These statistics provide important clues for corrective actions or coping with expected failures because you will know how the failures occur and when the failures are expected. Strict data requirements for Weibull plots provide very smart Weibull results but they carry heavy demands for data recording.
Whereas C/A plots provide good information as:
- C/A plots can tolerate an arbitrary starting point for accumulation of time as you are not forced to zero time,
- Mixed failure modes are acceptable for analysis which will provide a statistic to tell if failures are increasing (b>1), decreasing (b<1), or neither increasing/decreasing (b≈1). Mixed failure modes push the C-A analysis, and
- The visually simple method of extrapolation provides visual evidence of forecasts for future failures.
Data can be entered directly into WinSMITH Visual (WSV) or can be easily imported from Excel worksheets with a simple copy/past command. The data are about time and failure events. Consider the raw failure data shown in Figure 1.
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Sept. 1, 2001 is a red letter date representing the initiation of a fix to permanently avoid a failure mode by using improved maintenance methods.
Did
we get an improvement? How many failures
have we avoided?
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The C/A plot in Figure 2 shows a long term improvements (b<1) with a good curve fit. Do we have an improvement cusp at failure 6? The cusp is more visible on the MTBF plot in Figure 3. Figure 3 clearly shows improvements in the mean time between failures that is not so obvious in the trend line of Figure 2 although the statistic in Figure 2 (beta = 0.593) shows big improvements.
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Use good engineering judgment. Split the data from Figure 1 into old data and new data as shown in Figure 4. It seems to work better if you maintain a common data point in each set as the turning point.
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Put the two data sets into a new WinSMITH Visual plot as shown in Figure 5. Extrapolate
the old and new lines. Find the vertical
gap between new and old at 816 days. The
gap is clear in Figure 5. It shows 31
failures have been avoided (at 816 days: 45.9 old-14 new = 31 rounding down) with
the new procedure. Crow/AMSAA plots
provide strong, graphical, evidence for management that the new maintenance
methods are demonstrating improvements by reducing failures. Figure 5 uses the data to show you’ve made
improvements.
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When will the next failure occur? WSV forecasts the next failure on the new trend line as 133 days into the future at 949 cum days.
Some will be skeptical if the beta value for the new data set truly indicates improvement. WSV’s report option shows with 90% confidence, the new b=0.457 lies between 0.188 and 0.726 which gives solid evidence for decreasing failures as b<1 indicating future failures are coming more slowly.
Crow/AMSAA methods are simple tools with strong results using failure data from your maintenance records.
This page is described in terse format in WeibullNews Issue 18. Other Crow/AMSAA details are available at the November 2002 and January 2004 problems of the month. More details are available in The New Weibull Handbook about reliability growth plots.
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