Research Article

Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart Chart

Table 1

Out-of-control when , , and for , , and .

00.10.20.30.50.71


0.1(339.52, 1013)(342.12, 1021)(344.32, 1028)(346.20, 1033)(349.25, 1042)(351.62, 1050)(354.31, 1058)
0.3(198.43, 591)(207.70, 618)(216.03, 643)(223.55, 666)(236.60, 705)(247.52, 738)(260.93, 778)
0.5(100.86, 299)(109.07, 323)(116.82, 346)(124.15, 368)(137.66, 409)(149.80, 445)(165.86, 493)
0.7(53.16, 156)(58.74, 172)(64.17, 189)(69.47, 205)(79.62, 235)(89.21, 264)(102.57, 304)
1(23.30, 66)(26.19, 75)(29.10, 84)(32.01, 93)(37.82, 110)(43.58, 127)(52.03, 152)
1.5(8.38, 22)(9.44, 25)(10.53, 28)(11.65, 32)(13.98, 39)(16.39, 46)(20.12, 57)
2(4.33, 10)(4.78, 11)(5.26, 13)(5.76, 14)(6.81, 17)(7.93, 21)(9.71, 26)

0.1(290.13, 865)(296.08, 883)(301.21, 899)(305.67, 912)(313.07, 934)(318.95, 952)(325.81, 972)
0.3(94.46, 279)(102.41, 303)(109.95, 326)(117.10, 347)(130.34, 387)(153.17, 455)(158.23, 470)
0.5(32.98, 95)(36.86, 107)(40.71, 119)(44.53, 130)(52.03, 152)(59.32, 174)(69.82, 206)
0.7(14.34, 40)(16.19, 45)(18.08, 51)(19.99, 57)(23.88, 68)(27.83, 80)(33.77, 98)
1(5.93, 15)(6.63, 17)(7.36, 19)(8.12, 21)(9.71, 26)(11.37, 31)(13.98, 39)
1.5(2.76, 5)(2.96, 6)(3.16, 6)(3.38, 7)(3.85, 9)(4.36, 10)(5.19, 13)
2(2.14, 3)(2.19, 3)(2.26, 3)(2.33, 3)(2.50, 4)(2.68, 5)(3.01, 6)

0.1(252.34, 752)(260.12, 775)(266.95, 796)(272.98, 814)(283.15, 844)(291.40, 869)(301.21, 899)
0.3(58.13, 171)(64.06, 188)(69.82, 206)(75.41, 222)(86.08, 254)(96.09, 284)(109.95, 326)
0.5(17.62, 50)(19.87, 56)(22.15, 63)(24.50, 70)(29.10, 84)(33.76, 98)(40.71, 119)
0.7(7.55, 20)(8.49, 22)(9.46, 25)(10.46, 28)(12.54, 34)(14.71, 41)(18.08, 51)
1(3.49, 7)(3.81, 8)(4.15, 9)(4.51, 11)(5.26, 13)(6.07, 15)(7.36, 19)
1.5(2.17, 3)(2.24, 3)(2.31, 3)(2.40, 4)(2.59, 5)(2.80, 5)(3.16, 1)
2(2.01, 2)(2.02, 2)(2.03, 2)(2.05, 2)(2.09, 3)(2.15, 3)(2.26, 3)

0.1(222.52, 663)(231.30, 689)(239.10, 713)(246.07, 733)(258.01, 769)(267.85, 799)(279.77, 834)
0.3(40.35, 117)(44.89, 131)(49.38, 144)(53.79, 158)(62.38, 183)(70.63, 208)(82.34, 243)
0.5(11.49, 31)(12.97, 36)(14.49, 40)(16.04, 45)(19.22, 54)(22.47, 64)(27.43, 79)
0.7(5.10, 12)(5.67, 14)(6.28, 16)(6.90, 18)(8.21, 22)(9.60, 26)(11.79, 32)
1(2.70, 5)(2.88, 6)(3.07, 6)(3.28, 7)(3.72, 8)(4.20, 10)(4.99, 12)
1.5(2.04, 2)(2.07, 3)(2.10, 3)(2.13, 3)(2.22, 3)(2.33, 3)(2.52, 4)
2(2.00, 2)(2.00, 2)(2.00, 2)(2.01, 2)(2.02, 2)(2.03, 2)(2.07, 3)