A flexible bathtub hazard model for non-repairable systems with uncensored data

Abstract

This research effort has developed a mathematical model for bathtub shaped hazards (failure rates) for operating systems with uncensored data. The model will be used to predict the reliability of systems with such hazards. Early in the life-time of a system, there may be a relatively large number of failures due to initial weaknesses or defects in materials and manufacturing processes. This period is called the “infant mortality” period. During the middle period of an operating system fewer failures occur and are caused when the environmental stresses exceed the design strength of the system. It is difficult to predict the environmental stress amplitudes or the system strengths as deterministic functions of time, thus the middle-life failures are often called “random failures.” As the system ages, it deterioates and more failures occur. This region of failure is called the “wearout” period. Graphing these failure rates simultaneously will result in a bathtub shaped curve. The model developed for this bathtub pattern of failure takes into account all three failure regions simultaneously. The model has been validated for accuracy by using Halley's mortality table and is used to predict the reliability with both least squares and maximum likelihood estimators.