With wide-pulse neutron injection the fission chain fluctuates statistically.A calculation approach is presented, in which numerical solutions of the statistical distribution W_n equations are disassembled and then synthesized.It makes the computation suitable for generalized conditions (with arbitrary time distribution,zero time (t₀) injection probability distribution P(t₀) and number probability distribution S(n) etc.).The equivalent conditions in practical physical models are discussed and expanded from single-medium to multi-medium.In addition, the average computing formulae for required parameters in solving W_n equations are given as well.

The key step for reliability assessment with small sampling is to take advantage of the subjective information and the test data of input parameters. Subjective inference could just offer the reliability some incomplete information which can be generally assumed to exist in the form of either a prior mean or a prior credibility interval. To the trials with the outcomes of either survival-failure or normal distributed parameters, efficient approaches are developed to determine the conjugate prior distributions from the subjective information according to the principle of maximum entropy. The test data of input parameters are also transformed as the prior information of the output parameters according to statistics theory. Bayes theorem is used to synthesize the different informations and numerical examples are presented to illustrate the impact of non-experimental information on the reliability posterior, the needed test number and the reliability assessment.