Research on Management Strategy of Cost-based Intelligent Manufacturing System

[Abstract] The reliability, efficiency and accuracy of CNC machines as work cells of intelligent manufacturing systems (IMS) are criteria to measure the processing level of the latter. In order to improve the reliability of the IMS and reduce the maintenance cost, very sound preventive maintenance and management strategies concerning the CNC machines should be defined. We realized a parameter estimation of our reliability model for CNC machine units in an IMS environment, carried out a linear correlation test and a distribution fitting test for the model and obtained the failure distribution function and failure rate function. We then built a post-failure maintainability model and realized a maintainability evaluation. Following the above analyses, we built a cost-based preventive maintenance cycle model and obtained its optimal value by using the particle swarm optimization (PSO) algorithm. This research and its result can on the one hand guide the setting-up of preventive maintenance planning and management schemes and on the other hand reduce the production cost and enhance enterprise efficiency.


Preface
Over maintenance and lack of maintenance are two common problems that exist in IMS maintenance processes. Excessive preventive maintenance leads to increase of total maintenance cost while lack of preventive maintenance often causes more frequent machine failures and thus increases maintenance cost. The maintenance cost control and the optimal maintenance efficiency demand that the preventive maintenance cycle be soundly defined and the balance be found between the failure time and checking time in order to reduce the maintenance cost per unit time. It is therefore imperative to research on the preventive maintenance and its management strategies [1][2][3][4].
Scholars of the field have carried out a large number of studies. Xiaofeng Wang et al built an equipment reliability model by using the three-parameter Weibull distribution, taking into consideration the preventive maintenance (PM) cost and post maintenance cost caused by accidental failures. They then underwent its parameter optimization by differential evolution algorithm.They also carried out researches on two PM strategies on multi-device series systems [5].
Tantele developed an optimization methodology based on genetic algorithm (GA) principles and Bayesian updating [6]. Abubaker proposed a maintenance cost estimation model within the research and development of this decision support system (DSS). An empirical-based methodology is pursued and validated through case study analysis [7].
Jiang et al, through their analysis of the inertial navigation system and the redundant system of the equipment studied, established the objective/goal function that aimed at the minimalization of the maintenance cost and obtained the equipment's PM cycle. The present research is based on our tracking records of failure time of a machining center over a span of months. The detailed data have permitted us to realize a parameter estimation, a linear correlation test and a distribution fitting test of our reliability model. They have further enabled us to build a model for the post-failure maintainability as well as to carry out its evaluation. In the end, we built a model for the CNC machine's cost-based preventive maintenance cycle, and obtained its optimal value by using the particle swarm optimization (PSO) algorithm.

Parameter Estimation of the Reliability Model
According to previous reliability studies on machining centers, the cumulative failure distribution function abides by the Weibull distribution [15]. The two-parameter Weibull distribution function is : The corresponding reliability function is ： Let the univariate linear regression equation be y A Bx   (3) According to the two-parameter Weibull distribution, formula (1) can be linearly transformed as following: The value F(t) needs to be estimated before calculation. In general, the median rank is used to estimate F(t)，that is : According to the least square method, the parameter estimation is drawn as below: At last we can get that: ˆB

Linear Correlation Test
The linear correlation coefficient is: When  > ( 2, ) n    ， we consider that the linear correlation between X and Y is significant. ( 2, ) n    , the critical value of the correlation coefficient  , can be obtained either by consulting the table or by approximate formula calculation. The latter method is adopted in this paper, the significance level being  = 0.1. Therefore, ( 2, ) n      ， and accordingly, the linear correlation between X and Y is significant. Therefore, the failure distribution of the headstock's subsystem obeys the Weibull distribution theory.

Hypothesis Test of the Fitting of Distribution
Using the "d" test method, we checked the failure time distribution function. If the distribution function obtained from the estimated parameter meet the following conditions, the parameter estimation is well founded. Suppose that: In the formula, F 0 (x) is the original hypothetical distribution function, F n (x) is the empirical distribution function with the sample size being n, and , n D  is the critical value.
For i d ， details are as follows： After carrying out a "d" test on the earlier calculated headstock failure distribution function.

Maintenance Model Establishment
The post-failure maintenance of the machine tools demands research on their maintainability. Therefore, the building-up of maintainability model not only is the key to quantitative research on system maintainability but also lays the foundation for further research on maintenance cost. Table 3 shows the post-failure maintenance time data recorded during field tests at a series machining center. According to experience, the distribution type of the failure repairing time conforms to lognormal distribution, the probability density function of the latter being : In the formula,  is lnt's mean value and  is lnt's variance. The lognormal cumulative distribution function is the following： 2 1 ln 2 We used the maximum likelihood method to estimate its parameters. By assuming that the observed maintenance time at the machining center 1 2 , , n t t t  was a sample of a lognormal distribution population, we obtained the likelihood function as follows： The parameter estimation for lognormal distribution was ：

Maintainability Evaluation
Mean Time To Repair (MTTR) The estimated MTTR value was calculated by the formula: Thus we obtained the mean time taken for repair: MTTR=1.427h.

Preventive Maintenance Cycle Model for Machine Tools
In order to build the preventive maintenance cycle model based on failure rates, we prescribed the following assumptions: We also got the correlation between the total maintenance cost C(T) per unit time and the preventive maintenance cycle, as shown in Figure 2. As the cycle T increases, the C value decreases. When T=2213h, maintenance cost per unit time reaches its minimum value and then gradually increases following the increase of time value.
Therefore, reliable forecast of the preventive maintenance model and optimal maintenance and management of the machining tool can reduce the maintenance cost and enhance the productivity of the enterprise.

Conclusion
In order to improve the reliability and reduce the maintenance cost of the intelligent manufacturing system, it is crucial to formulate sound preventive maintenance and management strategies for the CNC machine tools.
In this research we have realized estimates on the reliability model's parameters of a CNC machine tool in an IMS, and carried out a linear correlation test and a distribution fitting test on the model. We have thus obtained the failure distribution function and the failure rate function. Through this case study.the methodology for model building-up and relevant maintainability evaluation is available and instructive for readers' reference.
In addition to these analyses, we have built a failure rate based preventive maintenance cycle model and optimized it with the particle swarm optimization (PSO) algorithm until it reached its optimal value. The cost-based research methods adopted in this paper and the conclusions it has reached can help IMS machine management teams set up well founded preventive maintenance planning and management schemes in order to reduce the production cost and enhance enterprise efficiency.