Modeling Reliability Growth

Reliability growth has been modelled as an exponential decline in the cumulative failure rate that continues indefinitely as long as testing continues. Contrary to this, most reliability growth data show a brief high initial failure rate due to infant mortality followed by a long period of constant low failure rate. A two part failure rate model with an initial exponential decline followed by a constant failure rate usually fits the data and provides a more realistic description of reliability growth. The reliability growth process consists of testing, experiencing failures, finding the failure causes, and redesigning the system to remove them. The cost of reliability growth increases with the number of inherent failure modes and the time needed for them to occur and be removed. The failure modes with the lower failure rates will tend to occur later, as their Mean Time Before Failure (MTBF) is the inverse of the failure rate. Reliability growth testing has diminishing returns, since it takes longer to find and remove the less probable failures.This paper first discusses the reliability bathtub curve and then explains that reliability growth is produced by testing, identifying failure causes, and designing to remove them. A simple model of reliability growth is introduced, with a brief group of early failures followed by a constant failure rate. The cumulative failure rate n(t)/t can decline as rapidly as1/t or t-1butdeclines more slowly if additiona lfailures occur. The 56-failure Crow data seti s used to demonstrate the two-phase model of reliability growth followed by a constant failure rate. 13 additional data sets are modeled, with 9 of the 14 data sets showing reliability growth approximately as n(t)/t =1/t or t-1and substantial final failure rates. The model fits most of the data sets, but 4of the 14 show no reliability growth. The reliability growth period typically includes six failures and extends one-quarter or half the total test time. As reliability growth testing continues, the cumulative failure rate should be tracked to estimate the reliability growth exponent and the final failure rate.