Tolerance interval "censored data"/"over detection limit"

[#1]

Hi

I am running a test on the yield strength of some material, but due to some limitations in the measurement setup, I can not run the test until the specimens break. I.e. for example I can only run the test up to an applied force of 1kN. This means I can not find the actual yield strength and its distribution, I only know that I have a number of samples, N, that can take over 1kN of force.

Is there method to estimate a tolerance interval for this type of data?

Your input is much appreciated.

[#2]

You have several challenges:

1. You cannot separate measurement error from the product variation

2. Since your data is truncated it will be difficult to get an estimate of central tendency or dispersion.

You could think about the test as a go/no-go (treat the response variable as nominal) and estimate probabilities of failure.  Can you apply a constant force (<1kN) and measure some other characteristic of the material (changes in material properties like elongation)?

[#3]

I am wondering if it is possible to treat this with a proportional hazards model, with the force strength treated as if it were the time variable.  In other words, rather than data censored by time to event, it would be analyzed as force applied to event.  In both cases, the data is censored in that some observations (perhaps many) will not have the event at the end point (either time or force applied).  I have no idea if this is a legitimate approach, but the situations seem analogous. 

[#4]

Thank you for the answer. I had the same considerations about the dispersion, but had not thought about your point 1. - Great input.

I had also wondered about changing it to a pass/fail test, with the downside that it would increase the required sample size. But with the challenges you mentioned, that may look like the most suitable option.

Unfortunately, there are no other metrics I can use, so basically, I only have pass/fail data.

[#5]

Along with what @statman suggested, check out this paper https://www.stat.cmu.edu/technometrics/90-00/vol-38-01/v3801050.pdf in which I believe that they have a similar situation. And they set up experiment at different voltage levels. In your case, you may want to set up tests at different stress levels. The paper uses non-parametric inference. Related parametric inference includes: logistic regression, probit analysis, etc.

Regarding what @dale_lehman suggested, proportional hazard might be related if you have other covariates. Otherwise, other techniques for analyzing time-to-event data can apply. Just use your stress variable in place of the time-to-event variable. The relationship between the one-shot experiment data and time-to-event data and their modeling can be found in this paper: Quantile POD for nondestructive evaluation with hit-miss data, by Yew-Meng Koh and William Q. Meeker. https://www.tandfonline.com/doi/abs/10.1080/09349847.2017.1374493?journalCode=urnd20