Estimation of the reliability function for an object that is improved on the basis of data on the life-lengths and types of failures of an object that is not improved

The author considers a population Π of devices which can fail due to one of the modes of failure Ui, i=1,2,...,k. Assume that each device e in Π has a life which will terminate at time T(e) due to mode Uj. When a device is drawn at random from Π, the pair [T(e),j] is a two-dimensional random variable with probability distribution P(T,j) which determines the marginal survival function R(t)=P{T>t}, called the "reliability function before improvement". The author discusses possible improvement of such a population by procedures of two types. Type I consists of removing from Π all devices with certain unfavorable qualities, for example, those that fail due to Uj within a test period tj for specified j and tj, or those for which one can tell beforehand that they will fail due to a specified Uj. Type II consists of modifying the devices (e.g., by changing the manufacturing process) in a way that will change the probability distribution P(T,j) into some P~(T,j). In view of the multiplicity of modes of failure, this leads to questions dealing with competing risks.