Stress Strength Model: Definition

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A stress strength model compares the strength and stresses on a system; it is used primarily in reliability engineering but also in economics, psychology and medicine.

In a stress strength model both stresses and strength are considered as separate random variables. Stress experienced by a component is often represented by the random variables designated X; strength of the component is represented by Y. A situation in which X > Y is one in which the stresses are greater than the strengths, and the component fails. If Y > X, the strengths are greater than the stressors.

We can define reliability, then, as the probability a component will not fail: P( X < Y). This, R = P ( X < Y ), is the basic stress strength model, and refining it and applying it to real life analysis is the essence of stress strength analysis.

Applications of Stress Strength Models

In their landmark book on stress strength models, Kotz et. al details many examples of stress strength models in a survey of scientific literature. These include such applications as:

  • Reliability of Rocket Engines: When Y is the strength of a rocket chamber and X stands for the maximal chamber pressure which is generated when a solid propellent is ignited, P( X < Y ) is the probability that the engine will be fired successfully.
  • Earthquake Resistance: The strength stress model was used to study the risk an earthquake posed to a particular nuclear generator. With no concrete numbers to define the strength, the researcher took strength estimates from five experts and used the log-normal distribution as a model and a weighted least squares procedure to estimate the strength. A similar procedure was used for the stressor, and the conclusion P(ln X < ln Y) = 0.99978 was reached—a very reassuring number, if accurate
  • In a medical study, the reaction of leprosy patients to a medicine was modeled on a P( X < Y ) stress strength model. Initial condition (infiltration status) was taken as X, and Y the change in health after 48 weeks of treatment. The null hypothesis, that initial infiltration values did not affect outcomes, was strongly rejected after an analysis of the data.


Barbiero, Alessandro. “Inference on Reliability of Stress-Strength Models for Poisson Data,” Journal of Quality and Reliability Engineering, vol. 2013, Article ID 530530, 8 pages, 2013. doi:10.1155/2013/530530
Retrieved from on March 11, 2018
Johnson, R. A. 3 Stress-strength models for reliability. Handbook of StatisticsVolume 7, 1988, Pages 27-54.
Kotz, Lumelskii, and Pensky. The Stress-Strength Model and its Generalizations.

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