Death Of Soldiers In Iraq During Gulf War II

The field of reliability is concerned with identifying, predicting, and preventing failures.  One way to make reliability obvious is to prepare Crow/AMSAA plots of cumulative failures versus cumulative time. 

Crow/AMSAA methodology is useful for mixed failure modes, which means the cause for the failures can be by many different reasons.  When improvements have occurred, a cusp will appear on the trend line signifying failures are coming more slowly (if improvements are being made).  Or the failures may be coming more quickly (if the situation deteriorates to a less favorable condition).

The interesting thing about Crow/AMSAA plots is stable processes give straight lines when plotted on log-log paper.  The straight line can be regressed using simple curve fit techniques to forecast future failures.  The slope (the beta value from the regression) of the Crow/AMSAA trend line is an important statistic as it tells if failures are increasing, decreasing, or floundering along with no deterioration or no improvement.

The website http://icasualties.org has been publishing fatality statistics during Gulf War II.  Obviously, deaths of soldiers represent failures.  War deaths have mixed modes of failures.  Crow/AMSAA plots should produce straight line plots on log-log paper and give a way to determine if:
            1) failures are reducing (b<1), deteriorating (b>1), or without changes (b≈1),
            2) a cusp has formed on the trend line signifying improvement or deterioration,
            3) predict future failures (deaths) of soldiers.

Here are the statistics from Icasualties (which I have accepted as “fact” although that is frequently a risky thing to do with data from the Internet).  Table 1 shows the May 28, 2007 Memorial Day score card.  Revisions to earlier data continues.

A Crow/AMSAA plot of the data in Figure 1 (including incomplete month of May ‘07) with a single trend line for USA Data.  The line slope shows casualties continue to increase:

Figure 1: Total USA Fatalities Are Accelerating (see beta =1.248)

Zooming in on the top right hand portion of the trendline we see:

Figure 2:  Recent USA Fatalities Expected For Balance Of 2007

Figure 2 shows the data fit the trend line and we forecast the failures for the remainder of the year:
                 Month          Cum Month     Cum Fatalities      Forecasted Fatalities
            May 2007à            52                    3454+                        104+
            June 2007à            53                    3537                           83
             July 2007à            54                    3621                            84
       August 2007à            55                    3704                            83
  September 2007à            56                    3789                            85
      October 2007à            57                    3873                            84
  November 2007à            58                    3958                            85
   December 2007à            59                    4043                            85

We need to see a cusp on the current data which causes the trend line to move horizontally to the right with no deaths over a long time interval!  The goodness of fit criteria for the USA casualties is poor (P-value < 10%) and is just outside a good fit line based on a typical regression line rather than the IEC 1164 curve fit criteria.  The equation for predicting future failures is: N(t)=l*tb.  You get l and b from the regression analysis of data show on Figure 2.  When the b value is > 1, failures (casualties) are coming more quickly, and when b value is < 1, failures are coming more slowly.

Please note, I’m not causing the forecasted fatalities (so don’t send hysterical Email!), I’m only predicting the outcome based on the data.  I’ll be happy to forecast fewer failures if I can see objective evidence of meaningful improvements—in short, show me the improvements don’t tell me about the good things that could or might happen.

We desperately need to put a cusp on the trend line to prevent the deaths of USA and UK soldiers (by the way, I don’t have a magic solution for how to accomplish this feat)!!!  Keep your eye peeled at this site for future data.  See if a cusp appears signifying reductions in deaths (failures).  How many more deaths of soldiers do I want to see?—the answer is ZERO, and how many more deaths will we have—the answer is too many.  Wars are dirty business to meet the objectives of peace.

Where can you learn more about Crow/AMSAA plots:

1)      The New Weibull Handbook by Dr. Robert B. Abernethy

2)      WinSMITH Visual software by Fulton Findings for making reliability growth plots

3)      Crow/AMSAA Reliability Growth Plots Problem Of The Month

4)      MIL-HDBK-189 Reliability Growth Management

5)      TR-652 AMSAA Reliability Growth Guide available for download from the November ‘02 Problem Of The Month

You can download a PDF copy of this by clicking here.

The bottom line:

Crow/AMSAA plots show cusps when failures decline to push the trend line to lower failure rates.  Likewise, a cusp forms when failures increase and the trend predicts more failures.  The main issue is to decrease failures.

Comments:

Refer to the caveats on the Problem Of The Month Page about the limitations of the following solution. Maybe you have a better idea on how to solve the problem. Maybe you find where I've screwed-up the solution and you can point out my errors as you check my calculations. E-mail your comments, criticism, and corrections to: Paul Barringer by     clicking here.   Return to top of page.

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Last revised 5/28/2007
© Barringer & Associates, Inc. 2004