Using Dynamic Reliability in Estimating Mortality at Advanced Ages

Traditionally, the Gompertz’s mortality law has been used in studies that show mortality rates continue to increase exponentially with age. The ultimate mortality rate has no maximum limit. In the field of engineering, the reliability theory has been used to measure the hazard-rate function that is dependent on system reliability. Usually, the hazard rate ( H) and the reliability ( R) have a strong negative coefficient of correlation. If reliability decreases with increasing hazard rate, this type of hazard rate can be expressed as a power function of failure probability, R-1. Many satisfactory results were found in quality control research in industrial engineering. In this research, this concept is applied to human mortality rates. The reliability)(xR is the probability a newborn will attain age x. Assuming the model between)(xH and)(xR is DAxRCBxH))(1() (-+ = , where A represents the survival decaying memory characteristics, B/C is the initial mortality strength, C is the strength of mortality, and D is the survival memory characteristics. Eight Taiwan Complete Life Tables from 1926 to 1991 were used as the data source. Mortality rates level off at a constant B+C for very high ages in the proposed model but do not follow Gompertz’s mortality law to the infinite. In the simulation study, the mean life wil