| Most systems in the real world are subject to deterioration. Modeling and optimal control of deteriorating production processes such as tool wear and tool failure have been important research areas. When (1) the operating conditions of the deteriorating systems vary (deterministically or stochastically), or (2) the deteriorating processes are non-homogeneous (characterized by increasing mean and increasing variance), or (3) if we want to incorporate the information representing the operating conditions of the deteriorating systems from condition monitoring such as vibration signals into the model, the problem becomes more complicated.; This thesis attempts to solve part of the above problems. It focuses on the study and modeling of cutting tool reliability, non-homogeneous tool wear process, cutting tool replacement decision making and operations sequencing when the cutting tools operate in either homogeneous or varying production conditions, and the reliability modeling of the load-sharing 1-out-of-2 systems (with arbitrary failure time distribution for each sub-system). The techniques of proportional hazard modeling and accelerated failure time modeling have been used to incorporate the covariates representing the operating conditions (both internal and external) into the reliability modeling. The random coefficient regression model is used to model the non-homogeneous tool wear process.; For each model, we will attempt to provide complete information in solving the problem including detailed engineering background, model development, maximum likelihood estimation procedures for the unknown parameters, numerical procedures, and numerical examples. |
