  Matsushita et al (1992) have done an interesting finding. They observed that
the shape parameter of the Weibull model presented systematic changes over time
and age when applied to mortality data for males and females in Japan. They
have also estimated that this parameter was smaller in the 1891-1898 data in
Japan compared to the 1980 mortality data and they presented an illustrative
figure for females where the values of the shape parameter are illustrated on
the diagram close to the corresponding survival curves. However, they have not
provided an analytical explanation of this behavior of the shape parameter of
the Weibull model. The cumulative hazard of this model can express the additive
process of applying a force in a material for enough time before cracking. To
pass to the human data, the Weibull model and the cumulative hazard can express
the additive process which disabilities and diseases cause the human organism
during the life span leading to healthy life years lost. In this paper we
further analytically derive a more general model of survival-mortality in which
we estimate a parameter related to the Healthy Life Years Lost (HLYL) and
leading to the Weibull model and the corresponding shape parameter as a
specific case. We have also demonstrated that the results found for the general
HLYL parameter we have proposed provides results similar to those provided by
the World Health Organization for the Healthy Life Expectancy (HALE) and the
corresponding HLYL estimates. An analytic derivation of the mathematical
formulas is presented along with an easy to apply Excel program. This program
is an extension of the classical life table including four more columns to
estimate the cumulative mortality, the average mortality, the person life years
lost and finally the HLYL parameter bx. The latest versions of this program
appear in the Demographics2019 website
