# Software Engineering | Jelinski Moranda software reliability model

The Jelinski-Moranda (J-M) model is one of the earliest software reliability models. Many existing software reliability models are variants or extensions of this basic model.

**Assumptions:**

The assumptions in this model include the following:

- The program contains N initial faults which is an unknown but fixed constant.
- Each fault in the program is independent and equally likely to cause a failure during a test.
- Time intervals between occurrences of failure are independent of each other.
- Whenever a failure occurs, a corresponding fault is removed with certainty.
- The fault that causes a failure is assumed to be instantaneously removed, and no new faults are inserted during the removal of the detected fault.
- The software failure rate during a failure interval is constant and is proportional to the number of faults remaining in the program.

The program failure rate at the ith failure interval is given by,

where

= a proportional constant, the contribution any one fault makes to the overall program

N = the number of initial faults in the program

= the time between the and the failures.

For example, the initial failure intensity is

and after the first failure, the failure intensity decreases to

and so on.

The partial distribution function(pdf) of is

The cumulative distribution function(cdf) of is

The software reliability function is, therefore,