Improved Quality Prediction Model for Multistage Machining Process Based on Geometric Constraint Equation

Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.

The GI/M/1 Queue in a Multi-phase Service Environment with Working Vacations and Bernoulli Vacation Interruption

In this paper,we consider a GI/M/1 queue operating in a multi-phase service environment with working vacations and Bernoulli vacation interruption.Whenever the queue becomes empty,the server begins a working vacation of random length,causing the system to move to vacation phase 0.During phase 0,the server takes service for the customers at a lower rate rather than stopping completely.When a vacation ends,if the queue is non-empty,the system switches from the phase 0 to some normal service phase i with probability qi,i=1,2,⋯,N.Moreover,we assume Bernoulli vacation interruption can happen.At a service completion instant,if there are customers in a working vacation period,vacation interruption happens with probability p,then the system switches from the phase 0 to some normal service phase i with probability qi,i=1,2,⋯,N,or the server continues the vacation with probability 1−p.Using the matrix geometric solution method,we obtain the stationary distributions for queue length at both arrival epochs and arbitrary epochs.The waiting time of an arbitrary customer is also derived.Finally,several numerical examples are presented.

Performance analysis of LTE-U coexistence network with WiFi using queueing model

The unforeseen mobile data explosion as well as the scarce of spectrum resource pose a major challenge to the performance of today＇s cellular networks which are in urgent need of novel solutions to handle such voluminous mobile data. Long term evolution-unlicensed （LTE-U）, which extends the LTE standard operating on the unlicensed band, has been proposed to improve system throughput. In LTE-U system, arriving users will contend the unlicensed spectrum resource with wireless fidelity （WiFi） users to transmit data information. Nevertheless, there is no clear consensus as to the benefits of transmission using unlicensed bands for LTE users. To this end, in this paper an analytical model is presented based on a queue system to understand the performance achieved by unlicensed based LTE system taking quality of services （QoS） and LTE-U users＇ behaviors into account. To obtain the stead-state solutions of the queue system, a matrix geometric method is used to solve it. Then, the average delay and utilization of unlicensed band for the LTE-U users is derived by using the queuing model. The performance of LTE-U coexistence is evaluated with WiFi using the proposed model and provide some initial insights as to the advantage of LTE-U in practice.

Ergodicity of Quasi-birth and Death Processes(Ⅰ)

Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.