Survival Analysis not on Time to Failure, but Concentration to Failure

Shujinko — Fri, 09 Jun 2023 00:42:20 GMT

Hello, I am interested in using survival analysis to predict the probability of failure at certain concentrations of a factor. This is for consumer rejection of a product, modeled as a function of three variables (e.g. concentrations of three different ingredients). For one of the variables (Y), I am interested in knowing probability of rejection as a function of it and X and Z.

Note: In parallel I am also evaluating the nominal logistic platform, although I am exploring survival analysis because it seems like an interesting methodology.

Scoring

1. I have an ordinal score 1 - 9 in one column. This is the panelist response.

2. I have a category score of "Pass" or "Fail" based on the panelist response. If a response is > 5, then it gets a score of "Pass." Otherwise, "Fail."

3. I have the censor column of 1 or 0. I have coded it such that a Fail (e.g. consumer rejection) is a 0, whereas a Pass is a 1. I did this because if a consumer gave a "Pass" score, then I consider it not having a time to failure since it didn't technically fail.

Inputs

1. Factor X: continuous numerical concentration of an ingredient X. I expect the likelihood of failing to increase as the concentration goes up.

2. Factor Y: continuous numerical concentration of an ingredient Y. I expect the likelihood of failing to decrease as the concentration goes up.

3. Factor Z: continuous numerical concentration of an ingredient Z. I expect the likelihood of failing to increase as the concentration goes up.

Approach: using Factor Y (concentration) as "Time to Failure"

0. Analyze --> Reliability and Survival --> Fit Parametric Survival

1. I treated this like the VA Lung Cancer Set, where I set "Time to Failure" as Factor Y since I am interested in seeing how probability of failure changes as a function of Y. Note that I expect probability of failure to go down as Y goes up.

2. I put censor as the censor.

3. Location Effects: Factor X and Factor Y since I am interested in the model being able to model Failure Probability as a function of Factors X, Y, and Z.

Issues

1. Looking at the Distribution profiler, it shows that my Probability of failure actually increases as "Time" (aka Factor Y) goes up. This is the opposite of what I expect.

2. I also repeated the analysis where I put Factor X and Y as Factor effects, and Factor Z as "Time to Event." In this case, I do expect probability of failure to increase with an increase with Factor Z.. However, the distribution profiler still predicts that Factor Y increasing causes an increase in probability of failure. I don't think this is correct.

I suspect that I'm either setting up the survival analysis incorrectly, and/or I should just be using nominal logistic regression instead. However, I know that survival methodology has been used for finding concentration thresholds (e.g. probability of consumer rejecting product will be >50% if concentration of X is greater than some percent). For example, this paper here: "Determination of Consumer Acceptance Limits to Sensory Defects Using Survival Analysis".

Resources

1. I have attached an example data set (JMP table) to show my inputs.

2. I have attached an analysis showing where I put Factor Y as my Time to Event.

Re: Survival Analysis not on Time to Failure, but Concentration to Failure

peng_liu — Tue, 23 Nov 2021 19:52:04 GMT

What you setup here using 0 and 1, for Fail and Pass, means "Failure" and "Right Censored" in survival analysis. However the paper that you refers to does differently. Please read the formula (1), and there paragraph it is within, also the paragraph above it.

You might want to refer to this paper Quantile POD for nondestructive evaluation with hit--miss data to understand why it is so.

topic Re: Survival Analysis not on Time to Failure, but Concentration to Failure in Discussions

Survival Analysis not on Time to Failure, but Concentration to Failure

Re: Survival Analysis not on Time to Failure, but Concentration to Failure