生产过程的动态监测：灰色预测模型的一种应用毕业论文外文翻译(编辑修改稿)

生产过程的动态监测：灰色预测模型的一种应用毕业论文外文翻译(编辑修改稿)内容摘要：

tinues to be monitored. 3 Numerical analysis and conclusions In this section, the simulation results are given. We begin by making the assumption that the process variable has a normal probability distribution. The data points were generated from a normal distribution with mean 3 and variance 1. Sample sizes of 3, 5, and 7 were simulated. When the sample size equals 3, the central line of the Xbar control chart is assumed equal to mean 3, and the standard deviation of the mean is equal to 31.The upper and lower limits of the Xbar control charts are then calculated and equal to )3133,3133( . The same procedures can be applied for sample sizes of 5 and 7, respectively. The process can then be analyzed as per the data obtained and plotted. All programs were written in the MATLAB language and all samples were generated through MATLAB. All results are based on 1000 replications. Once the upper and lower limits of the Xbar control charts are obtained, the performances of the grey predictors and sample means are pared by the calculated ARL. The processes are simulated as incontrol for the first 10 samples and as outofcontrol after the 11th sample. Once a mean shift is detected by points outside the control limits, the ARL will be recorded. We will discuss the following three levels of mean shifts: (i) a mean shift of standard deviations from a target. ., the mean shifts from the target to s+target, where s is a standard deviation of the sample mean described as above (., ns / , where n is the sample size) – in this paper, the target equals 3。 (ii) a mean shift of standard deviations from a target。 (iii) a mean shift of standard deviations from a target. The probability of a Type I error of sample means, and grey predictors under the same control limits are also pared. To understand the sensitivity and influence of the number of subgroups that are used to pute the grey predictors (., the k values are set at 4, 6, 7 and 8) the raw sequence of k samples is defined as  )0()0(3)0(2)0(1)0( , kxxxxx  where k equals 4, 6, 7 or 8, respectively. The results of the observed probability of Type I errors, the ARL for sample means, and the grey predictors for k = 4, are given in Table 1. The other results in the cases of k = 6, 7 and 8 are summarized in Tables 2 to 4. Table 1. Type I error and ARL for x and grey predictors when 4k Sample size Type I error ARL s ＋ target s ＋ target s ＋ target x grey x grey x grey x grey 3 5 7 Table 2. Type I error and ARL for x and grey predictors when 6k Sample size Type I error ARL s ＋ target s ＋ target s ＋ target x grey x grey x grey x grey 3 5 7 Table 3. Type I error and ARL for x and grey predictors when 7k Sample size Type I error ARL s ＋ target s ＋ target s ＋ target x grey x grey x grey x grey 3 5 7 Table 4. Type I error and ARL for x and grey predictors when Sample size Type I error ARL s ＋ target s ＋ target s ＋ target x grey x grey x grey x grey 3 7 2 7 4 3 1 2 5 7 6 9 5 4 7 7 7 2 4 5 6 The Type I error of sample means is virtually fixed on , ., %. This is because the Xbar control charts are based on xx 3 , where x and x are assumed values in Sect. 3. If the process variable has a normal distribution, then the probability of the population mean will fall within 3 standard deviations of the sample mean, and will be about %. From our simulation results, the grey predictor is very sensitive to the number of subgroups, ., the k values. From Tables 1 to 4, the Type I error of grey predictors decreases rapidly when the k value increases. Once the mean shift levels bee larger, the ARLs bee smaller for both methods。 ., it bees easier to detect outofcontrol conditions. When k equals 4 or 6, the performance of the grey predict。