This paper presents an integrated platform for multi-sensor equipment diagnosis and prognosis. This integrated framework is based on hidden semi-Markov model (HSMM). Unlike a state in a standard hidden Markov model (HMM), a state in an HSMM generates a segment of observations, as opposed to a single observation in the HMM. Therefore, HSMM structure has a temporal component compared to HMM. In this framework, states of HSMMs are used to represent the health status of a component. The duration of a health state is modeled by an explicit Gaussian probability function. The model parameters (i.e., initial state distribution, state transition probability matrix, observation probability matrix, and health-state duration probability distribution) are estimated through a modified forward–backward training algorithm. The re-estimation formulae for model parameters are derived. The trained HSMMs can be used to diagnose the health status of a component. Through parameter estimation of the health-state duration probability distribution and the proposed backward recursive equations, one can predict the useful remaining life of the component. To determine the “value” of each sensor information, discriminant function analysis is employed to adjust the weight or importance assigned to a sensor. Therefore, sensor fusion becomes possible in this HSMM based framework. The validation of the proposed framework and methodology are carried out in real world applications: monitoring hydraulic pumps from Caterpillar Inc. The results show that the increase of correct diagnostic rate is indeed very promising. Furthermore, the equipment prognosis can be implemented in the same integrated framework.

Diagnostics and prognostics are two important aspects in a condition-based maintenance (CBM) program. However, these two tasks are often separately performed. For example, data might be collected and analysed separately for diagnosis and prognosis. This practice increases the cost and reduces the efficiency of CBM and may affect the accuracy of the diagnostic and prognostic results. In this paper, a statistical modelling methodology for performing both diagnosis and prognosis in a unified framework is presented. The methodology is developed based on segmental hidden semi-Markov models (HSMMs). An HSMM is a hidden Markov model (HMM) with temporal structures. Unlike HMM, an HSMM does not follow the unrealistic Markov chain assumption and therefore provides more powerful modelling and analysis capability for real problems. In addition, an HSMM allows modelling the time duration of the hidden states and therefore is capable of prognosis. To facilitate the computation in the proposed HSMM-based diagnostics and prognostics, new forward–backward variables are defined and a modified forward–backward algorithm is developed. The existing state duration estimation methods are inefficient because they require a huge storage and computational load. Therefore, a new approach is proposed for training HSMMs in which state duration probabilities are estimated on the lattice (or trellis) of observations and states. The model parameters are estimated through the modified forward–backward training algorithm. The estimated state duration probability distributions combined with state-changing point detection can be used to predict the useful remaining life of a system. The evaluation of the proposed methodology was carried out through a real world application: health monitoring of hydraulic pumps. In the tests, the recognition rates for all states are greater than 96%. For each individual pump, the recognition rate is increased by 29.3% in comparison with HMMs. Because of the temporal structures, the same HSMMs can be used to predict the remaining-useful-life (RUL) of the pumps.

This paper is geared toward developing a network of inventory-queue models for the performance modeling and analysis of an integrated logistic network. An inventory-queue is a queueing model that incorporates an inventory replenishment policy for a store, which is a basic modeling element for an integrated logistic network. To achieve this objective, first, this paper presents an analytical modeling framework for integrated logistic chains, in which the interdependencies between model components are captured. Second, a network of inventory-queue models for performance analysis of an integrated logistic network with inventory control at all sites is developed. Then this paper extends the previous work done on the supply network model with base-stock control and service requirements. Instead of onefor- one base stock policy, batch-ordering policy and lot-sizing problems are considered. In practice, the assumption of uncapacitated production is often not true, therefore, GIx/G/1 queueing analysis is used to replace the Mx/G/1 queue based method. To include lot-sizing issue in the analysis of stores, a fixed-batch target-level production authorization mechanism is employed to explicitly obtain performance measures of the logistic chain queueing model. The validity of the proposed model is illustrated by comparing the results from the analytical performance evaluation model and those obtained from the simulation study.

Using a connectivity matrix, we establish a continuum modeling approach with partial differential equations of conservation laws for simulating materials flow in supply chain networks. A number of existing and new constitutive relationships for modeling velocity are summarized or proposed. To effectively treat strong advection components within the modeling system, we apply discontinuous Galerkin (DG) methods for solving production flow in a supply chain network. In addition, a number of DG properties are analyzed for treating network flow. In particular, a nearly optimal error estimate is obtained using a new estimating technique that utilizes two physical meaningful assumptions on the connectivity matrix. Numerical examples are provided to simulate a single node, a serial supply chain and an entire network as well as to investigate the influence of influx variation and node shut-down to the profiles of work in progress (WIP) and outflux. It is shown that the proposed modeling approach is applicable to a large number of scenarios including re-entrant lines and the proposed DG algorithm is robust and accurate for predicting WIP and outflux behaviors.

As a new maintenance method, CBM (condition based maintenance) is becoming more and more important for the health management of complicated and costly equipment. A prerequisite to widespread deployment of CBM technology and practice in industry is effective diagnostics and prognostics. Recently, a pattern recognition technique called HMM (hidden Markov model) was widely used in many fields. However, due to some unrealistic assumptions, diagnositic results from HMM were not so good, and it was difficult to use HMM directly for prognosis. By relaxing the unrealistic assumptions in HMM, this paper presents a novel approach to equipment health management based on auto-regressive hidden semi-Markov model (AR-HSMM). Compared with HMM, AR-HSMM has three advantages: 1) It allows explicitly modeling the time duration of the hidden states and therefore is capable of prognosis. 2) It can relax observations’ independence assumption by accommodating a link between consecutive observations. 3) It does not follow the unrealistic Markov chain's memoryless assumption and therefore provides more powerful modeling and analysis capability for real problems. To facilitate the computation in the proposed AR-HSMM-based diagnostics and prognostics, new forwardbackward variables are defined and a modified forward-backward algorithm is developed. The evaluation of the proposed methodology was carried out through a real world application case study: health diagnosis and prognosis of hydraulic pumps in Caterpillar Inc. The testing results show that the proposed new approach based on AR-HSMM is effective and can provide useful support for the decisionmaking in equipment health management.