The following mortality data has been collected for a group of S₀ integrated circuit chips (ICs) over a 4-year period:

Observe that at the end of the 4-year period, none of the S₀ ICs has survived, that is, all have failed. Every IC that fails is replaced with a new one at the end of the year in which it has failed. The life of an IC can be modeled as a four-state recurrent Markov chain. Let the state X_n denote the age of an IC at the end of year n. Construct the transition probability matrix for the Markov chain.  

Transcribed Image Text:

Age i of an IC in years, i Number surviving to age i 0 0 1 2 S, S S 3 3 4 S3 S = 0