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Three Weibull Parameters by Correlation Optimisation

The caption is a mouthful. I am really telling you about a free Quickbasic program called Classwyb. Check to see if your pc with a Windows operating system has Quickbasic or Qbasic onboard. If not:

Go to Open folder MSLFILES. Scroll to find OLDDOS.EXE. Save OLDDOS.EXE in your hard disk downloads folder. Make a new directory called OLDDOS. OLDDOS.EXE is self-extracting. Extract its contents to directory OLDDOS. It is FORBIDDEN to extract OLDDOS.EXE to your root directory.

See Quickbasic as qb in OLDDOS. Make a desktop icon for qb.

I use as an online archive. See folders data and software. Visit them. Decide to make directory wtt with folders data and software on your hard disk.

Use your browser to open CLASSWYB.BAS in Save CLASSWYB.BAS as a text file in d:/wtt/software/ where d: or other disk address is on your pc. Use a text worthy program such as wordpad to examine the saved CLASSWYB file. Rename it as CLASSWYB.BAS. See data files Rao408.dat in folder data. Open Rao.dat with your browser, save as a text file, use text editor to make file Rao408.dat in d:/wtt/data/.

File Rao408.dat contains 10 computer times to repair for a mainframe computer system. The data are from page 408 of:

Reliability-Based Design, S. S. Rao, McGraw-Hill, 1992,
pp 1-569, ISBN 0-07-051192-6.

The book is out of print. Amazon states that it has limited availability. ReliabilityWeb mailing list members could ask McGraw-Hill to issue a new printing.

Start Quickbasic. Open file CLASSWYB.BAS. Run it. Enter 5 as an x axis upper limit. Enter file name d:/wtt/data/rao408. You see a comparison of two probabilities of meeting repair times, one based on an order statistic, and the other on calculation based on three Weibull parameters and the measured values of times to repair.

Program CLASSWYB.BAS finds three Weibull parameters: exponent k, characteristic value v, and threshhold value e. The reduced variate is defined as ratio (x -e)/(v - e), where x is the time based variable.

Using a 6061-T6 Aluminum Alloy Specimen Failure Data
as an Example Data Set

The data set consists of 102 failure times. It is 6061.dat in online folder "data". I added calculation of median life based on the three Weibull parameters. Use CLASSWYB.BAS to obtain the following graph:

In folder "software", find online program wdesign.exe. It is included in Program wdesign uses estimates of median life, threshhold value, and exponent k. You provide wdesign with a production run size N and it calculates N lives. I used N=102 and the median, threshhold and exponent from the above CLASSWYB.BAS graph. Program wdesign treated the N values as measured data and calculated "best" values of k, e, and v to match measured and Weibull calculated life values. The following results were obtained by wdesign:

Data generated by wdesign are in file 6061d.dat. You would expect that when CLASSWYB.BAS is used to analyze 6061d.dat a "perfect" fit should be obtained. Here is the graph produced by CLASWYB.BAS when analyzing 6061d.dat:

Analysis Of Data When Exponent k Is Less Than Or Equal To 2

The horizontal axis in CLASSWYB.BAS graphs is called the Reduced Variate. It is the ratio (x - e)/(v - e). When exponent k is greater than 2, you will most often find an axis upper limit equal to 2 to be satisfactory. For lower values of 2, an X-axis upper limit of 4 might be more suitable. In such cases, I use CLASSW~1.BAS to reduce the data.

In the period 1990-93, I provided training courses for maintenance supervisors and mechanics at Northern States Power (NSP) Prairie Island Training Center. I had access to a program package called WEIPLOT. It was provided to NSP by the Electric Power Training Center of the Electric Power Research Institute (EPRI). One of the data sets in the package was called Mletest.wbl. It contains 23 times to failure for a set of 23 test objects. My online data archive has the values in file Mletest.dat.

Here are the results of applying CLASSW~1.BAS to the data:

Three Parameter Analysis of Random Data, Perhaps Time Based

To give you an example, I used a random noise generator program to generate a sequence of 1024 random numbers. You might be experienced with narrow band spectrum analysis and measurement. It is common to perform spectral analysis on sets of 1024 values.

I am giving you, if you care to use it, a Quickbasic program called sort.bas. It is in archive folder The example data file is noise10.dat. It is archive /data/. Apply program sort to sort the data from smallest to largest values in file onoise10.dat.

Apply wtt01 to noise10.dat to obtain:

Now apply wtt01 to ordered data in file onoise10.dat. The Weibull cumulative probability curve and example data overlap.

In a predictive/preventive maintenance environment, you could log results of periodic Weibull analysis of vibration, acoustical noise, or other data. Changes in Weibull analysis results might track changes in machinery condition.

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