spi is greater than 1 however project is behind the schedule

 Is this kind of situation possible?

usually when I see an SPI >1, I perceive this as project is ahead of schedule.

However, while reading PMBOK p. 183, I noticed that "...SPI measures all project work, the performance on critical path must also be analyzed to determined whether project will finish ahead of or behind..."

I can now think of the case when team has very good performance on non-critical path activities which is making SPI > 1, while SPI specifically for critical path is < 1 which is probably going to delay the project.

Am I right in this judgment?

You have correctly interpreted.  Total Earned Value of all the activities might be > Total Planned Value.  But if the performance is bad on critical path activities, the project may be behind the schedule though it is having SPI > 1.

 thank you for your response, Now I am more confident about SPI :)

Definitely it is good point to learn.PMBOK clearly indicates that critical path performances are to be analysed whether project will finish ahead or behind of scheduled date.

But at the same time SPI is a value index and not a time index , and there is only one baseline at a time for a project, SPI is measured against that baseline data.

We should also learn that at any point of time if critical path is ahead or behind of schedule, does not mean cumulatively project will be ahead or behind respectively. because it is also possible that any non critical path will become now critical.