Assume a (replaceable) component or unit has 'k' different ways it can fail. Then these are called failure modes and underlying each failure mode is a failure mechanism. The competing risk model evaluates component reliability by "building up" from the reliability models for each failure mode. Typically the following three assumptions hold for such models:

• Each failure mechanism leading to a particular type of failure (i.e., failure mode) proceeds independently (a very restrictive assumption in the practical sense) of every other mode, at least until a failure occurs. If we assume X₁, X₂,….,X_k as the latent lifetimes due to cause  respectively when the system is exposed to these risks independently, then  is the time to failure of the system. Obviously in a simplistic sense it means we consider a series circuit, such that any one component failing mean the whole system stops functioning and as an illustration one should refer to Figure 12.12.

Figure 12.12: Series system

• The component fails when the first of all the competing failure mechanisms reaches a failure state and the system is said to fail due to cause, . The cause is denoted by , j = 1, 2, …., J. In case if we do not have the information about the cause of failure of the system then the data is said to be masked/censored.
  
  
• Each of the k failure modes has a known life distribution model given by F_k(t).