## CorTech Training Red Wing MN |

In 1995, I prepared the following files to accomplish Task 1. As a student of engineering, you have the opportunity to duplicate the results in order to satisfy yourself that you have met self-imposed performance-based training objectives. - at a given time of exposure maximum pit depth depends on the amount of surface area inspected
- maximum pit depth for a given surface area increases relatively rapidly in the first few years of exposure and increases less rapidly at longer exposure times
QBasic programs linrgr.bas, wybrgr01.bas, and wybrgr02.bas were prepared to help you accomplish performance-based training objectives. The following code fragment is given to remind you to let QBasic know where you have placed data file Kay.dat.
CorTech Training prepared the following files for participants:
- Download the completely free self-extracting Weibull Trending Toolkit wtt01.exe from an archive.
- Use QBasic program makefile.bas to make data file aziz01.dat for the specimens exposed for one week. Convert pit depth units from microns to mils. Run program wrisk.exe, which is included it archive wtt02.exe.
- Study three-parameter Weibull analysis results.
- With the one year data in mind, select a graph upper limit of 20 mils. Study the resulting Weibull curves.
Task 8 is the third of four Tasks about pitting corrosion in aluminum alloys. The first experimental data set analyzed includes effects of time of exposure. I suggest you follow the Tasks meticulously. If you are a student, retiree, or particularly diligent working technician or engineer, try to repeat the steps taken to deduce curve fitting relations, tables, and graphs.
- Make data files aziz01.dat through aziz06.dat for the specimens exposed for six exposure times. Convert pit depth units from microns to mils. Run program wrisk.exe. Study three-parameter Weibull analysis results.
Task 9 is the last of four Tasks about pitting corrosion in aluminum alloys. The first experimental data set analyzed includes effects of time of exposure. I suggest you follow the Tasks meticulously. If you are a student, retiree, or particularly diligent working technician or engineer, try to repeat the steps taken to deduce curve fitting relations, tables, and graphs.
- Make data files aziz01.dat through aziz06.dat for the specimens exposed for six exposure times.
- Convert pit depth units from microns to mils.
- Run program wrisk.exe. Study three-parameter Weibull analysis results.
- Examine results in Task 8 in pairs. Average Weibull threshold parameter E for exposure times of one week and one month equals 3.49 mils. Average E for exposure times of six months and one year equals 13.0 mils. Average Weibull characteristic value V also increased with exposure time. The Weibull shape parameter K seems to have a random behavior. It is clear that some smoothing or grouping of Aziz's data must be used to generalize shape parameter behavior.
- Group Aziz's data for exposure times of one week and one month into data file task901.dat using MS-DOS Edit. Express the 19 values in units of mils.
- Group Aziz's data for the remaining four exposure times into a set of 39 maximum of depths, mils, in file task902.dat.
- Apply QBasic program SORT.BAS given in the Weibull Trending Toolkit to files task901.dat and task902.dat. SORT does just that, and creates two new files otask901.dat and otask902.dat.
- Apply Weibull Trending Toolkit program WRISK.EXE to files otask901 and otask902. Program sees the leading o's and calls the sorted files TASK901 and TASK902.
- Examine WRISK numerical results for files task901 and task902.
Include H. P. Godard's Industrial Water Pipeline Data - Examine H. P. Godard's industrial water pipeline data on p. 64 of the above reference. He measured maximum pit depth in each of 20 three foot long sections of AA 5052 pipe after 13 years exposure.
- The instructor was able to read 16 pit depths from Godard's graph. As a course participant, you may make data file task903.dat to store Godard's data.
- Apply program WRISK to file task903.
- Examine the following numerical results.
- Plot results of analyzing Godard's data. Choose a graph
upper limit of 80 mils.
Create Modeling Program DESIGN - Notice the Weibull shape parameter K values for files task901, task902, and task903 have much less variation than the K values for data files studied in Task 8.
- Average the three K values found here to obtain K = 2.75439.
- After some thought, decide to use E and V values for files task901 and task903 to model time dependence. Let E = A * T + B and V = C * T + D, where T is exposure time in years and A, B, C, and D are constants.
- The Weibull Trending Toolkit includes a program called WDESIGN. It uses an order statistic to estimate N probabilities. A user supplies trial Weibull exponent K, threshold E and an estimate of the median random variable. The program estimates N values of the variate and finds Weibull K, E, and V to match design sample and Weibull mean, standard deviation, and skewness, values.
- The instructor used WDESIGN as the basis for creating new program DESIGN.
- DESIGN has an exponent K which is independent of exposure time, and parameters E and V which are linearly dependent on time exposure. When a user runs DESIGN, she/he is prompted to input a file name, number of measurements N being modeled, and exposure time.
- DESIGN uses an order statistic base on N, the constant K, and calculated E and V to generate N design sample maximum pit depths.
- DESIGN matches sample and Weibull mean, standard deviation, and skewness values to find K, E, and V for the N design measurements.
Model Grouped Aziz Data for Three Week Exposure and Godard Data for 13 Year Exposure
Industrial Water Pipeline with 50 Year Design Life
The Weibull Trending Toolkit Program wrisk.exe is 1995 copyrighted property of: Glenn E. Bowie 2426 Hallquist Ave. Red Wing, MN 55066 (651) 388-2374 e-mail: glennbowie@hotmail.com Do not try to use WRISK.EXE to process a file with more than 1024 data values. WRISK.EXE runs on an IBM compatible PC with Microsoft Windows. Make sure you have VBRUN300.DLL in your C:\>WINDOWS\SYSTEM directory. The Weibull Trending Toolkit program WRISK.EXE has three curves instead of two. blue = Weibull probability density green = Weibull cumulative probability yellow = Weibull risk Weibull Probability Density, p p = k * ((x - e)/(v - e)^(k - 1) * Exp(-((x - e)/(v - e))^k/(v - e). Weibull Cumulative Probability, F F = 1 - Exp(-((x - e)/(v - e))^k) Let P = Exp(-((x - e)/(v - e))^k) Weibull Risk R = k * ((x - e)/(v - e))^(k - 1)/(v - e) You see that p = R * P, or R = p/P. The probability density and risk curves are scaled so you can see their shapes. When you are ready to study probability density and risk mag nitudes, you can use QBasic program RISK.BAS as a starting tool. I like to use to PCs side by side when studying Weibull risk. A good starting point is to examine file 6061.DAT using Edit. There are 102 fatigue lives in the file. The first two lives are 233 and 258. Count down to find the median life in the file equals 400. Examine the last entry in the file. The 102nd value in the file is 560. Run WRISK and choose file 6061. Use a graph upper limit = 800. There are 19 tics on the Y-axis. Each scale division is worth 40 life units. 20 x 40 = 800. From the summary screen, k = 3.61498 e = 195.1232 v = 420.0841 Median = 398.3941 Type QBasic risk, press enter on your second PC. RISK asks you for the Weibull shape parameter k, threshold parameter e, median, and production run size. Enter the above values for k, e, and median and 102 for production run size. RISK tells you characteristic value v = 420.0842. The value in the summary screen of WRISK is truncated rather than rounded. We accept that the two characteristic values are the same. RISK tells you the probability of survival at the first failure is 0.9903. The cumulative distribution curve, green, is a probability of failure curve. P = probability of survival F = probability of failure F = 1 - P. The height of the green curve is 1 - 0.9903 or 0.0097 at the first failure, according to RISK. RISK predicts the time to first failure = 257.6. Compare with actual first experimental value in 6061.DAT, 233. RISK tells us the probability density at time 257.6 equals 0.0005588. Calculate the risk at first failure: R = p/P = 0.0005588/0.9903 = 0.0005643. RISK tells us R = 0.0005643 at first failure. Work your way through second failure comparisons at your leisure. Move to the median. RISK predicts the median life equals 398.3941, and the experimental value is 400. WRISK shows the mean, median, and mode are close together for file 6061. RISK tells us the height of the probability density curve at the median equals 0.00616. And at time 538.956, the density drops back down to 0.000473. The difference in time units between the last failure and the threshold e equals 538.956 - 195.1232 = 343.8328. Multiply this difference by the density at the median to obtain 2.1192. Remember the area of a triangle equals 0.5 x base x height. We just estimated the area under the density curve to be 0.5 x 2.1192 = 1.0596. The area under a probability density curve equals 1.0. I used a clear, plastic scale divided in mm to find the height of the yellow risk curve at the mode and at 538 time units to be 19 and 79 mm. The height ratio equals 19/79 or 0.24. RISK predicts the ratio to be 0.0123/0.0487 = 0.25. Stare at the graph for file 6061. Use a scale to confirm that the cumula tive probability is at 0.5 of the maximum height, for this case. The probability of survival at the median = 0.5. RISK tells us risk R = 0.1232696 at the median. At the median, find R x P = 0.0616348. The density p at the median is then 0.0616348, as RISK told us already. It is important to practice looking at the curves when interpreting numerical results. Look at the probability density and cumulative probability curves for file 6061. Think of the probability density as the rate of change of the cumulative probability. The slope of the cumulative probability curve, the green one, is maximal at the mode. The probability density is maximal at the mode. Glenn E. Bowie Red Wing, MN September 1, 1995
The Weibull Trending Toolkit Program wdesign.exe is 1995 copyrighted property of: Glenn E. Bowie 2426 Hallquist Ave. Red Wing, MN 55066 (651) 388-2374 e-mail: glennbowie@hotmail.com It is important to remember that WDESIGN writes a data file and a results file each time it is used. When WDESIGN asks you for a file name, NEVER give it the same name as an experimental file such as 6061, 7075 and so on. It is a good practice to use the leading letter D in all file names you give WDESIGN. Avoid naming experimental data files with a leading D. Let me assume you have applied WRISK.EXE to study data file 6061 as outlined in the above note about WRISK. Run WDESIGN. Click the box "Enter N, k, e and Median". Be sure to enter a file name. This time enter D6061. Enter the following values: For N: 102 For k: 3.61498 For e: 195.1232 For Median: 398.3941 Compare the summary results and graph with the summary and graph you get when you apply WRISK to file 6061. Keep the median at 398.3941 and decrease k gradually. At each step, compare with WRISK and 6061 results. Finally, choose N: 102 k: 3.55 e: 194 Median: 398.3941 Apply WRISK to file D6061. You get the same results given by WDESIGN for the above parameters. Please do not apply WDESIGN for N > 1024. Please supply design threshold e values that are sufficiently large to keep resulting threshold values in the summary screen positive. Please be aware there is room for research. Please be aware as you practice using WDESIGN in relation to your database that you are thinking about possible application of WDESIGN concepts for preparation of production run specifications. ___________________________________________________________________ Design Practice At the DOS prompt, type QBasic risk. Run RISK.BAS. Enter shape parameter k equal to 1, threshold parameter 0 and median 300. See the characteristic value v = 432.8085. Enter run size 500. It is important to see that risk h(t) is constant from the first to the last failure. Here h(t) = 0.002310491. Now find 1/v. For k = 1 and e = 0, h(t) = 1/v. The failure rate is constant. Many reliability and risk analysts limit their work to the special case where the risk or failure rate is constant. Programs WTT01.EXE, WRISK.EXE, and WDESIGN.EXE do not apply to the special case where k = 1. In order to show you the difference between the constant risk case and one where k is slightly greater than 1.0, the following exercise was constructed. At the DOS prompt for directory wtt02, load Windows. C:\wtt02\win. Hopefully, you see the Program Manager high- lighted. Click File, then click Run. In the Run Window, enter on the command line: c:\wtt02\wrisk.exe. Click OK on the WRISK sign-on screen. Click "Match Sample Statistics". Enter file name 6061. Click "Plot Control Chart" and enter graph upper limit 800. You see the graph. Notice a portion of the summary screen is visible below the graph. Hopefully, you also can see the Program or File Manager word File. Click File. Click Run. Enter on the command line: c:\wtt02\wdesign.exe. Click OK on the WDESIGN sign-on screen. Click "Enter N, K, E, And Median". Enter file name delight. For N, 500. For K, 0.95. For E, 27.0. For Median, 300. Notice k = 1.032018, and e = 0.4963179. If you ever analyze material property data and obtain a k value as close to 1.0 as this, with e not negative, consider sending me a copy of your data. See UCL = 2743.9. Click "Plot Control Chart" and enter graph upper limit 3000. Examine the yellow RISK curve. It is a delight. I believe risk curves such as this one can represent many data sets which are now represented by a constant failure rate approach. In the lower left corner of the screen, click the small rectangular portion of WRISK summary screen. Click "Match Sample Statistics". Enter file name delight. WDESIGN generated file delight.dat. WRISK has now analyzed the file and obtained familiar results. Click "Plot Control Chart", and enter 3000. The graph is again a delight. Click the small rectangular portion of WDESIGN summary screen in the lower right corner of your display. Enter the following: design11 500 1.1 25 300 Study the summary values. Since UCL = 2042.8, choose graph upper limit 2500. Notice the risk curve. Click anywhere on the portion of WDESIGN summary screen visible below the graph. Enter: design12 500 1.2 25 300 Study the summary values. Choose graph upper limit 2000. Click WDESIGN summary screen at the bottom, enter: design13 500 1.3 25 300 Choose graph upper limit 2000. Proceed to generate file design14 with k = 1.4, design15 with k= 1.5, and so on until you have generated file design19 with k = 1.9. Choose graph upper limit 1000. It is time to generate a particular case. Enter file name drayly, with N = 500, k = 1.928, e = 7.9 and median = 300. Notice k = 1.999 and e = 0.01767976. Choose upper limit 1000. Describe the risk curve. In the special case where k = 2.0 and e = 0, the Weibull distribution becomes a Rayleigh distribution. For a Rayleigh distribution, the risk is a straight line. Generate files design20, design21 and so on until you have generated file design40. Examine the graphs with upper limit 1000 in each case. Watch changes in risk. Click the portion of WRISK summary screen at lower left and review files delight, design11 through design19, drayly, and design20 through design40. Examine skewness aand kurtosis values during your review. Decide for yourself what range of k yields probability density curves which might be considered to be symmetrical or pseudo-normal. Glenn E. Bowie Red Wing, MN September 1, 1995
Copyright Glenn E. Bowieİ, CorTech Training, Red Wing, MN 1996, 2000, 2001, 2003. All rights reserved. |