Several approaches have been proposed object to solve time variant reliability problems in recent decades based on classical probability theory dealing with problems in practice. Indeed the statistical information of complex mechanical systems, such as aircraft or spacecraft, is always hard to be collected. Interval data are encountered frequently in practical engineering problems. An improved non-probabilistic PHI method is proposed in order to guarantee the accuracy of results with time-variant interval-defined. A time variant interval is converted to a stochastic process distributed the truncated normal as well as the up crossing rate is calculated. Considering the variables with the truncated normal distribution, the cumulative failure probability can be estimated using the improved non-probabilistic PHI method. For demonstration and validation purpose, the method is applied in a case representing a mechanical system (a beam) placed in an environment that can have exceptional configuration.