Comparing failure rates between two processes

[#1]

Process A has 2 fails out of 1000 units and Process B has 4 fails out of 750 units. Point estimates of failure rate are 2/1000 = 0.002 and 4/750 = 0.005 for Process A and B, respectively. How can I use JMP to prove statistical significance of failure rate difference? How do I setup the data table for that? How to put confidence interval around those failure rate estimates to check if intervals are overlapping or not?

[#2 · Accepted solution]

Hi @cfs_analyst :  See the attached to get you started. I've included two analyses. One comparing them, the other looking at each process individually  Be careful, overlap (or not) of individual intervals does not define statistical significance; they have to overlap "enough" to be not statistically significant, so the comparison script (Fit Y by X...) is the right one to make the comparison. There you will see the 95% confidence interval on the difference.  It includes zero, therefore no statistically significant difference at alpha = 0.05. 

[#3]

You can also use a contingency table to analyze your data and test for a difference in proportions. I entered your data this way for convenience:

Select Analyze > Fit Y by X, enter Outcome in Y role, Process in X role, and Count in Freq role.

[#4]

Indeed @Mark_Bailey  and @cfs_analyst ! That is what I used to create my analyses in my response above (I inadvertently neglected to say that).

[#5]

Thank you @Mark_Bailey & @MRB3855 for the statistical significance analysis method!

@MRB3855, for putting a confidence band around the failure rate (0.002 Vs 0.005), I can use the lower and upper CI of Level=1 in the distribution platform?

[#6]

Hi @cfs_analyst  . Yes, you’d use the lower and upper CL for Level =1;  I used 1 as a failure and 0 as non- failure. I could have used Pass and Fail or some other desired descriptors as @Mark_Bailey  did.