The problem statement is I want to be able to compare 2 populations' survival and give a confidence interval around the point estimate. JMP can plot a simultaneous or pairwise confidence interval around any given population, but cannot give a confidence interval around the difference. Therefore, I suggest to everyone in my company to use R or python to do survival analysis, because the point of comparing survival is to quantify the difference, and the uncertainty in the difference.
RMST is one way to compare survival across 2 populations and derive confidence intervals.
https://cran.r-project.org/web/packages/survRM2/vignettes/survRM2-vignette3-2.html
I suggest JMP impelement RMST.
The Compare Groups perspective of the Life Distribution platform may be able to give you the desired result to compare survivability across groups. Try running this script which compares two groups of life distributions and using the Estimate Probability option, compares survival rates at specific intervals (ex. 100, 200, 500, and 1000 time cycles).
Open( "$SAMPLE_DATA/Reliability/Blenders.jmp" );
Life Distribution(
Perspective( Compare Groups ),
Y( :Time Cycles ),
Grouping( :Group ),
Censor( :Censor ),
Censor Code( 1 ),
Confidence Interval Method( Wald ),
Select Distribution( Distribution, Weibull ),
Select Scale( Weibull ),
Tabbed Report( 0 ),
Estimate Probability( 1 ),
Estimate Probability( Compute( [1000, 500, 200, 100] ) ),
SendToReport(
Dispatch(
{"Life Distribution - Compare Groups", "Statistics"},
"Group Homogeneity Tests",
OutlineBox,
{Close( 0 )}
),
Dispatch(
{"Life Distribution - Compare Groups", "Individual Group"},
"",
TabListBox,
{Set Selected( 2 )}
),
Dispatch(
{"Life Distribution - Compare Groups", "Individual Group"},
"",
List Box( 2 ),
{Set Summary Behavior( "Collapse" )}
),
Dispatch(
{"Life Distribution - Compare Groups", "Individual Group"},
"",
List Box( 76 ),
{Set Summary Behavior( "Collapse" )}
)
)
);