Using Stress/Strength Analysis to Reduce Sample Size

“An attribute stress test results in a pass/fail result. However, the unit is exposed to higher stresses than are typical under normal conditions. As a result, the stress test is expected to produce more failures than will occur under normal conditions. This allows the number of units tested to be reduced. Stress testing requires identifying the appropriate stressor, including time, temperature, force, humidity, and voltage. Examples of stress tests include dropping a product from a higher height, exposing a product to more cycles, and exposing a product to a wider range of operating conditions.

Published: Monday, October 16, 2023 – 12:03

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Oftentimes, due to several constraints such as material availability, resource constraints, and unforeseen circumstances, one may not be able to use the required sample sizes. I’m proposing here that we can use the stress/strength relationship to appropriately justify the use of a smaller sample size, while at the same time not compromising on the desired reliability/confidence level combination.

n = ln(1 – C)/ ln(R), where n is the sample size, ln is the natural logarithm, C is the confidence level, and R is reliability.


Using Stress/Strength Analysis to Reduce Sample Size

Practical suggestions for reducing sample sizes for attribute testing

Published Oct. 1, 2023, in Harish’s Notebook.


A common depiction of a stress/strength relationship is shown below for a product. We can see that as long as the stress distribution doesn’t overlap with the strength distribution, the product should function with no issues. The space between the two distributions is referred to as the margin of safety. Often, the product manufacturer defines the normal operating parameters based on this. The specifications for the product are also based on this, and some value of margin of safety is incorporated in the specifications.

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“Many test methods contained in standards are in fact stress tests designed to provide a safety margin. For example, the ASTM packaging standards provide for conditioning units by repeated temperature/humidity cycles and dropping of units from heights that are more extreme and at intervals that are more frequent than most products would typically see during shipping. As a result, it is common practice to test smaller sample sizes. The ASTM packaging conditioning tests are shown… to be five-times stress tests.”