Mi	ith stage of multi-stage production systems
Mi′	the merged stage from the first i stages of multi-stage production systems
gi	Mi or Mi′ produces a good product
di	Mi or Mi′ produces a defective product
α 1	probability of M1 transiting from g1 to d1
β 1	probability of M1 transiting from d1 to g1
αi′	probability of Mi′ transiting from gi to di
βi′	probability of Mi′ transiting from di to gi
γi	in case of good coming product, probability of Mi transiting from state gi to di
μi	in case of good coming product, probability of Mi transiting from state di to gi
ηi	in case of defective coming product, probability of Mi transiting from state gi to di
θi	in case of defective coming product, probability of Mi transiting from state di to gi
gigi+ 1	Mi or Mi′ produces good product, Mi+1 produces good product
gidi+ 1	Mi or Mi′ produces good product, Mi+1 produces defective product
digi+ 1	Mi or Mi′ produces defective product, Mi+1 produces good product
didi+ 1	Mi or Mi′ produces defective product, Mi+1 produces defective product
Si(t)	state probability matrix with i stage at time slot t
Ci	state transition probability matrix with i stage
P(git)	probability of producing good product with i stage at time slot t
P(gi)ss	probability of producing good product with i stage in steady-state
ts	settling time for system quality to approach steady-state
LQ	quality loss during transients
QLR(t)	quality loss rate over t time slots
QBN–	quality bottleneck parameters