I'm currently stuck with a problem, concerning how reliability of a process effects the variance of the process.

let me give you an example:

Lets assume there is a machine that produces a product X.

the machine and runs for 1000 hours. However, the machine has a breakdown and is therefore just producing for 900 hours. this results in a 90% reliability of the machine.

now If the reliability goes down, can we measure an impact on the variance?

someone told me to Use the weighted variance, where the weight is the largest value (USL) for a variable; then add the three weighted variances to get a total variance. You can assume a two-sided Taguchi Loss Function for total loss as a function of the total weighted variance. Use a ‘dummy-coefficient’ for the reliability effect on total weighted variance where variance goes up as reliability goes down.

does this make sense?

thank you so much!