Reliability Evaluation for the Running State of the Manufacturing System Based on Poor Information

Abstract

The output performance of the manufacturing system has a direct impact on the mechanical product quality. For guaranteeing product quality and production cost, many firms try to research the crucial issues on reliability of the manufacturing system with small sample data, to evaluate whether the manufacturing system is capable or not. The existing reliability methods depend on a known probability distribution or vast test data. However, the population performances of complex systems become uncertain as processing time; namely, their probability distributions are unknown, if the existing methods are still taken into account; it is ineffective. This paper proposes a novel evaluation method based on poor information to settle the problems of reliability of the running state of a manufacturing system under the condition of small sample sizes with a known or unknown probability distribution. Via grey bootstrap method, maximum entropy principle, and Poisson process, the experimental investigation on reliability evaluation for the running state of the manufacturing system shows that, under the best confidence levelP=0.95, if the reliability degree of achieving running quality isr>0.65, the intersection area between the inspection data and the intrinsic data isA(T)>0.3and the variation probability of the inspection data isPB(T)≤0.7, and the running state of the manufacturing system is reliable; otherwise, it is not reliable. And the sensitivity analysis regarding the size of the samples can show that the size of the samples has no effect on the evaluation results obtained by the evaluation method. The evaluation method proposed provides the scientific decision and suggestion for judging the running state of the manufacturing system reasonably, which is efficient, profitable, and organized.

Dynamic Evaluation of the Degradation Process of Vibration Performance for Machine Tool Spindle Bearings

“…The grey bootstrap maximum entropy method is used to obtain the weighted average values, upper-and lower-bound values for the 8 time series under the condition that the confidence level is 0.05, as shown in Figure 19. Figure 19 shows that the values of variation probability calculated using the method in the Reference [34] (The second method) are larger than those calculated using this method. The variation probability has reached 1 for the 7th time series using the second method, which is less in line with the actual degradation process of OVPS of MTSB.…”

“…The estimated uncertainty is calculated for the variation probability of rolling bearing vibration performance, as shown in Table 7. Figure 19 shows that the values of variation probability calculated using the method in the Reference [34] (The second method) are larger than those calculated using this method. The variation probability has reached 1 for the 7th time series using the second method, which is less in line with the actual degradation process of OVPS of MTSB.…”

“…According to the grey model GM (1,1) [34], suppose the first-order accumulated generating operator (1-AGO) of V β is given by…”

Effect-Cause Analysis and Prediction Convergence of Random Failure Gate in a Probabilistic Competitive Environment with Case Study on Quality Control Process

“…Menzel [3], Hickman [4], and Floyd [5] explained application of advanced probabilistic ideas in the economical oriented topics such as random variable transformations, probabilistic distributions. Xia et al [6] pointed out a new methodology for reliability measurement of a running manufacturing system which may or may not have sample size along with probability distribution. Senol [7] introduced the Poisson process approach to identify the degree for failure mode and effect in reliability analysis.…”