Average run length

Table 4.1. Average run length (ARL)for exceeding an upper or lower control limit 1/p(total), or giving seven results on one side of the center line 1/p(7) of a Shewhart means chart for deviations from the mean indicated...

Table 4.3. Average run length for a CuSum chart with h = 4 and = 0.5 (both in standard deviations of the mean)...

The selection of the threshold H can be based on considerations of average run length (ARL), the average number of samples required to detect a disturbance of specified magnitude. For example, suppose that the objective is to be able to detect if the sample mean x has shifted from the target by a small amount 8. The slack parameter K is usually specified as K = 0.58. For the ideal situation (e.g., normally distributed, uncorrelated disturbances), ARL values have been tabulated for different values of 8, K, and H. Table 8-7 summarizes ARL... 

TABLE 8-7 Average Run Lengths for CUSUM Control Charts... 

Table 3 Average run length to detect a shift of ha vs. subgroup size...

The Asymptotic Mean Square Deviation (AMSD) was used as the performance measure to compare different scenarios, since it incorporates the deviations from the target and the variability (particularly useful when a process is submitted to a disturbance). Besides the use of AMSD, the Average Run Length (ARL) was applied to evaluate the performance of each control chart. 

GC Runger, TR Willemain, and S Prabhu. Average run lengths for CUSUM control charts applied to residuals. Commun. Statist. -Theory Methods, 24(l) 273-282, 1995. 

Fig. 5 Average run length for SPC of uncorrelated data without downsampling.

The performance of multivariate SPC by MSPCA is illustrated based on simulated data from a fluidized catalytic cracker unit. This simulation was provided by Honeywell to the abnormal situation management consortium. The data consist of 110 measured variables and several types of process faults. Only three components are enough to capture most of the variation in the data. The results of multivariate SPC by PCA and MSPCA are compared in Fig. 8 for a slow drift in the slurry pump around. This drift is present in variable numbers 55 and 97, and starts at 5 min and ends at 65 min. Conventional PCA is unable to detect the shift with more than 99% confidence, whereas MSPCA detects the shift consistently with 99 /o confidence after 24 min. The contribution plots for this fault at 20 min shown in Fig. 9 clearly indicate that MSPCA identifies the contributing variables, whereas PCA does not. Further theoretical comparison based on the average run length of steady-state PCA, dynamic PCA and MSPCA are also available [14],... 

Table 1 Average run length rounded up to the next integer for a shift of the mean result by the given amount in numbers of standard deviations of the mean, for CuSum and Shewhart means charts...

An important parameter for evaluating quality control cards and out-of-control situations is the average run length (ARL) which is defined as the average number of registrations in a quality control card for a single out-of-control situation [41]. A high ARL is required should the analytical process run under control. The probability of a false alarm is then very low. On the other hand, a true out-of-control situation should be indicated as quickly as possible, that is, the ARL has to be relatively small. 

With the knowledge of the relative rate constants in eqn [12] and the concentrations of comonomers, the average sequence length of monomer A in a copolymer of A and B can be calculated. This relationship is given by eqn [13] where is the average run length of monomer i in a copolymer of i and j. 

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