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Original Articles

Correction factors for Shewhart and control charts to achieve desired unconditional ARL

, &
Pages 7464-7479 | Received 22 Dec 2015, Accepted 15 May 2016, Published online: 05 Jun 2016

Figures & data

Table 1. Correction factors for various values of , n and m.

Table 2. EARL of corrected (based on ) and, between brackets, uncorrected control charts.

Table 3. Derivatives of the function h, general at point (xy) or specifically at point (KK) for .

Table 4. Correction factors c for various values of , n and m.

Table 5. EARL of corrected and, between brackets, uncorrected control charts.

Table 6. Corrected and, between brackets, uncorrected out-of-control EARL for .

Table 7. Corrected and, between brackets, uncorrected out-of-control EARL for .

Figure 1. 10th, 25th, 50th, 75th and 90th percentiles of the in-control CARLs for and .

Figure 1. 10th, 25th, 50th, 75th and 90th percentiles of the in-control CARLs for and .

Figure 2. 10th, 25th, 50th, 75th and 90th percentiles of the in-control CARLs for and .

Figure 2. 10th, 25th, 50th, 75th and 90th percentiles of the in-control CARLs for and .

Figure 3. 10th, 25th, 50th, 75th and 90th percentiles of the out-of-control () CARLs for and .

Figure 3. 10th, 25th, 50th, 75th and 90th percentiles of the out-of-control () CARLs for and .

Figure 4. 10th, 25th, 50th, 75th and 90th percentiles of the out-of-control () CARLs for and .

Figure 4. 10th, 25th, 50th, 75th and 90th percentiles of the out-of-control () CARLs for and .

Table 8. Phase I (’s) and Phase II (’s) data of torque values.

Figure 5. Control chart of the monitoring of torque values with the proposed control limits. The monitored Phase II sample consists of subgroups of size each.

Figure 5. Control chart of the monitoring of torque values with the proposed control limits. The monitored Phase II sample consists of subgroups of size each.