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Tests of Comparison

Stress-Strength Test Example

Steel rods with a diameter of 0.5 +/- 0.015 inches are to be used in an application where the load is purely tensile. Investigations of the application reveal that the load is not constant in magnitude. The following tables show the typical load values and the strength data for 50 specimens.

Table I: Typical Load Values (lbs)
10455 12372 16559 19703
16961 10595 10898 5814
17279 12849 11661 6795
7821 13017 11263 17934
6821 15426 14656 17703

 

Table II: Ultimate Tensile Strength Data of 50 specimens (psi)
103779 103633 103779 103633 103799
102906 102616 101162 107848 103488
104796 106831 102470 99563 102906
103197 102325 105232 105813 101017
100872 104651 103924 108430 104651
97383 105087 102325 106540 103197
101162 106399 105377 101744 105337
98110 100872 104796 101598 101744
104651 104360 106831 103799 106104
102906 101453 105087 100145 100726

 

The objective is to estimate the reliability of the steel rods against fractures.

Note: The data sets in this example use units that are not shipped with the software (inches, pounds, and pounds per square inch). If you have the  "Manage other repository settings" permission, you could add these units to the repository, define their conversion factors and have them available for use for any analysis performed within the database. For the purpose of this example, it is not necessary for the software to able to convert these units to some other units, so we will use the simpler approach of setting up all the units to be in hours.

Obtain the Stress Distribution

In this example, stress is defined as:

(S.1)

 

where F is the tensile load on the rod and d is the rod’s diameter. These variables are distributed. In order to obtain the stress data set, the distributions for these two variables need to be obtained first.

To use this information, create a new Weibull++ standard folio in the project. Rename the data sheet to "Diameter." On the control panel, choose the Normal distribution and the RRX parameter estimation method. Click the Calculate icon on the Main page of the control panel. In the input window, enter 0.5 for the mean and 0.005 for the standard deviation, as shown next.

Click OK. The data sheet will be empty but the parameters of the distribution will be visible in the Analysis Summary area of the control panel.

Click the Settings tab. In the Data Points area, enter 1,000 and then click OK to generate the stress data set. This creates a new folio in the project. Rename the new folio to "Stress Values."

Obtain the Strength Distribution

The parameters for the normal distribution of the tensile strength are mean = 103421.0800 psi and standard deviation = 2395.1061psi.

Calculate the Reliability

Finally, use the stress-strength folio to calculate the reliability of the steel rods. Add the folio to the project by choosing Insert > Tools > Stress-Strength.

Select the data sheets containing the stress and strength data, as shown next. Click OK.

The stress-strength test shows the following plot (with the scaling adjusted and an area of the plot shaded to show the region where the strength exceeds the stress).

The result on the control panel indicates that the reliability of the steel rods against fractures is estimated to be 96.2171%, as shown next.

 

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