Stress-Strength Parameter Uncertainty Example

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This example appears in the Life Data Analysis Reference book.


Assume that we are going to use stress-strength analysis to estimate the reliability of a component used in a vehicle. The stress is the usage mileage distribution and the strength is the miles-to-failure distribution of the component. The warranty is 1 year or 15,000 miles, whichever is earlier. The goal is to estimate the reliability of the component within the warranty period (1 year/15,000 miles).

The following table gives the data for the mileage distribution per year (stress):

Stress: Usage Mileage Distribution
10096 12405
10469 12527
10955 12536
11183 12595
11391 12657
11486 13777
11534 13862
11919 13971
12105 14032
12141 14138


The following table gives the data for the miles-to-failure distribution (strength):

Strength: Failure Mileage Distribution
13507 16125
13793 16320
13943 16327
14017 16349
14147 16406
14351 16501
14376 16611
14595 16625
14746 16670
14810 16749
14940 16793
14951 16862
15104 16930
15218 16948
15303 17024
15311 17041
15480 17263
15496 17347
15522 17430
15547 17805
15570 17884
15975 18549
16003 18575
16018 18813
16052 18944

Solution

First, estimate the stress and strength distributions using the given data. Enter the stress and strength data into two separate data sheets and analyze each data sheet using the lognormal distribution and MLE analysis method. The parameters of the stress distribution are estimated to be log-mean = 9.411844 and log-std = 0.098741.

The parameters of the strength distribution are estimated to be log-mean = 9.681503 and log-std = 0.083494.

Next, open the Stress-Strength tool and choose to compare the two data sheets. The following picture shows the pdf curves of the two data sets:

Since the warranty is 1 year/15,000 miles, all the vehicles with mileage larger than 15,000 should not be considered in the calculation. To do this, go to the Setup page of the control panel and select the Override auto-calculated limits check box. Set the value of the upper limit to 15,000 as shown next.

Recalculate the results. The estimated reliability for vehicles less than 15,000 miles per year is 98.84%. The associated confidence bounds are estimated from the variance of the distribution parameters. With larger samples for the stress and strength data, the width of the bounds will be narrower.

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