بازنگری شاخص کیفیت زندگی

The derivation of the life quality index (LQI) is revisited for a revision. This revision takes into account the unpaid but necessary work time needed to stay alive in clean and healthy conditions to be fit for effective wealth producing work and to enjoyable free time. Dimension analysis consistency problems with the standard power function expression of the LQI are pointed out. It is emphasized that the combination coefficient in the convex differential combination between the relative differential of the gross domestic product per capita and the relative differential of the expected life at birth should not vary between countries. Finally the distributional assumptions are relaxed as compared to the assumptions made in an earlier work by the author. These assumptions concern the calculation of the life expectancy change due to the removal of an accident source. Moreover a simple public acceptance criterion is compared to the LQI criterion.

The life quality index (LQI) is a social indicator suggested by Nathwani et al. [1] to reflect the expected length of “good” life, in particular the enhancement of the quality of life by good health and wealth. The LQI is extensively studied by Rackwitz for its possible role as a mean to obtain the societal affordable level of safety of technical facilities including building structures [2]. The estimation of societal willingness-to-pay for safety is the topic of [3] in which the original derivation of the LQI is given. In the context of a paper by the author on decision modeling and acceptance criteria [4], the life quality index was defined in a slightly more general way than in [1] and [3], in particular focusing on the convex combination coefficient between the contribution to the relative differential of the LQI from the relative differential of the gross domestic product per person and the relative differential of the life expectancy at birth. The author questioned the convenience of the low weight on the money side as compared to the life expectancy side that is advocated both in [1] and [2]. Herein the definition of the LQI is reconsidered to include the unpaid work time in a more rational way than in [4]. Moreover it is pointed out that an unreasonable dimension property of the standard closed form expressions for the LQI makes the expression inconvenient by giving incorrect comparisons of the LQIs for different countries. The conclusion of the analysis is that the combination coefficient in the differential form should not be a function of the work time ratio valid in any given country, but should be fixed at the same value for all countries. An optimality argument points at a reasonable value of the combination coefficient. It is emphasized that the LQI defined in this paper is an extension of the definition used in [1], [2] and [3]. The notation deviates from the notation in these references. Finally the calculation of the effect on the life expectancy of removing an accident source is generalized from the exponential distribution to an arbitrary distribution of the waiting time to the occurrence of the accident.

A revised derivation is given of the convex combination coefficient c in Nathwani, Lind and Pandey's definition of the Life Quality Index on differential form. The derivation includes the time of unpaid work and thereby it leads to a value of c about 0.3, that is, a value about twice the size of the value that predominantly appears in the literature. Dimensional consistency arguments are given for keeping the definition of the LQI on the form Q=Gc[(1−w)E]1−c with fixed c independent of the work time ratio w. This is contrary to what is seen in the literature, where c is usually set to w. The resulting dimensional inconsistency showing up when varying w may unintentional lead to misleading conclusions when comparing the LQI for different societal economies. However, c can be chosen by use of the postulate that there at any time is a societal economy in the world for which the work time ratio is optimal with respect to life quality. Finally it is shown that the Implied Cost of Averting an Accident is insensitive to the choice of the life time distribution type and to the distribution type applied to model the time to the occurrence of the considered type of fatal accident or disease. The acceptance criterion for a risky operation as derived from the criterion of no decrease of the LQI is shown to be satisfied if the public acceptance criterion (27) is satisfied. This criterion is suggested in [4].