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. 2023 Nov 8;51(12):2298–2325. doi: 10.1080/02664763.2023.2279015

Table 1.

Values of exact and approximate control limits of Shewhart-type schemes for ratio V, with ARL0=370.

    n = 1 n = 5
    exact appro exact appro
γ ρ LCL UCL LCL UCL LCL UCL LCL UCL
(0.02, 0.02, 0.02) (−0.4, −0.4, −0.4) 0.45774 0.54477 0.45774 0.54477 0.48082 0.51969 0.48082 0.51969
  (0.0, 0.0, 0.0) 0.46412 0.53768 0.46412 0.53768 0.48374 0.51661 0.48374 0.51661
  (0.4, 0.4, 0.4) 0.47205 0.52905 0.47205 0.52905 0.48737 0.51286 0.48737 0.51286
  (0.8, 0.8, 0.8) 0.48372 0.51663 0.48372 0.51663 0.49271 0.50737 0.49271 0.50737
  (0.4, 0.6, 0.8) 0.48354 0.51644 0.48354 0.51644 0.49266 0.50733 0.49266 0.50733
(0.1, 0.1, 0.1) (−0.4, −0.4, −0.4) 0.30966 0.75507 0.30966 0.75507 0.40867 0.60400 0.40867 0.60400
  (0.0, 0.0, 0.0) 0.33413 0.71300 0.33413 0.71300 0.42189 0.58718 0.42189 0.58718
  (0.4, 0.4, 0.4) 0.36672 0.66209 0.36672 0.66209 0.43862 0.56681 0.43862 0.56681
  (0.8, 0.8, 0.8) 0.41909 0.59074 0.41909 0.59074 0.46388 0.53797 0.46388 0.53797
  (0.4, 0.6, 0.8) 0.41514 0.58487 0.41514 0.58487 0.46302 0.53696 0.46302 0.53696
(0.2, 0.2, 0.2) (−0.4, −0.4, −0.4) 0.15979 1.12265 0.15979 1.12265 0.32756 0.72397 0.32756 0.72397
  (0.0, 0.0, 0.0) 0.18946 1.03000 0.18946 1.03000 0.35028 0.68704 0.35028 0.68704
  (0.4, 0.4, 0.4) 0.23532 0.90902 0.23532 0.90902 0.38027 0.64245 0.38027 0.64245
  (0.8, 0.8, 0.8) 0.32504 0.72821 0.32504 0.72821 0.42778 0.57993 0.42778 0.57993
  (0.4, 0.6, 0.8) 0.31004 0.68997 0.31004 0.68997 0.42460 0.57539 0.42460 0.57539
(0.3, 0.3, 0.3) (−0.4, −0.4, −0.4) 0.03668 1.71211 0.03668 1.71211 0.25475 0.86441 0.25475 0.86441
  (0.0, 0.0, 0.0) 0.04893 1.63120 0.04897 1.63145 0.28324 0.80489 0.28324 0.80489
  (0.4, 0.4, 0.4) 0.07248 1.47952 0.07382 1.48710 0.32284 0.73198 0.32284 0.73198
  (0.8, 0.8, 0.8) 0.14804 1.11126 0.15304 1.14560 0.38986 0.62910 0.38986 0.62910
  (0.4, 0.6, 0.8) 0.12596 0.87405 0.12553 0.87447 0.38295 0.61705 0.38295 0.61705
(0.4, 0.4, 0.4) (−0.4, −0.4, −0.4) −0.06817 2.84081 −0.06808 2.84205 0.18882 1.03177 0.18882 1.03177
  (0.0, 0.0, 0.0) −0.11810 3.42365 −0.10673 3.67615 0.21911 0.94908 0.21911 0.94908
  (0.4, 0.4, 0.4) −0.67335 3.91609 −0.26043 -- 0.26415 0.84406 0.26415 0.84406
  (0.8, 0.8, 0.8) −1.58946 3.16179 -- -- 0.34760 0.69127 0.34760 0.69127
  (0.4, 0.6, 0.8) −0.60587 1.60586 -- -- 0.33555 0.66445 0.33555 0.66445
(0.5, 0.5, 0.5) (−0.4, −0.4, −0.4) −0.16448 5.73085 −0.16004 6.00294 0.12868 1.23537 0.12868 1.23537
  (0.0, 0.0, 0.0) −4.84259 9.97458 −0.32562 -- 0.15651 1.13373 0.15651 1.13373
  (0.4, 0.4, 0.4) −8.95535 11.48201 -- -- 0.20169 0.99532 0.20169 0.99532
  (0.8, 0.8, 0.8) −7.16909 8.52497 -- -- 0.29667 0.77885 0.29669 0.77888
  (0.4, 0.6, 0.8) −3.96555 4.96555 -- -- 0.27806 0.72194 0.27806 0.72194
(0.1, 0.2, 0.3) (−0.4, −0.4, −0.4) 0.01917 0.51492 0.01917 0.51492 0.12360 0.33807 0.12360 0.33807
  (0.0, 0.0, 0.0) 0.02213 0.46096 0.02213 0.46096 0.13126 0.32039 0.13126 0.32039
  (0.4, 0.4, 0.4) 0.02629 0.40212 0.02629 0.40212 0.14073 0.30080 0.14073 0.30080
  (0.8, 0.8, 0.8) 0.03254 0.33716 0.03254 0.33716 0.15330 0.27797 0.15330 0.27797
  (0.4, 0.6, 0.8) 0.03078 0.34363 0.03078 0.34363 0.15057 0.28117 0.15057 0.28117
(0.1, 0.3, 0.5) (−0.4, −0.4, −0.4) −0.06376 0.46939 −0.06376 0.46939 0.04566 0.27443 0.04566 0.27443
  (0.0, 0.0, 0.0) −0.07629 0.41007 −0.07629 0.41007 0.04915 0.25706 0.04915 0.25706
  (0.4, 0.4, 0.4) −0.09385 0.34904 −0.09385 0.34904 0.05336 0.23870 0.05336 0.23870
  (0.8, 0.8, 0.8) −0.11932 0.28813 0.11932 0.28813 0.05863 0.21909 0.05863 0.21909
  (0.4, 0.6, 0.8) −0.11090 0.29533 −0.11090 0.29533 0.05729 0.22228 0.05729 0.22228
(0.3, 0.2, 0.1) (−0.4, −0.4, −0.4) 0.63195 2.45540 0.63195 2.45540 0.90225 1.61756 0.90225 1.61756
  (0.0, 0.0, 0.0) 0.69518 2.54426 0.69518 2.54426 0.93341 1.59778 0.93341 1.59778
  (0.4, 0.4, 0.4) 0.76989 2.67117 0.76990 2.67125 0.96809 1.57497 0.96809 1.57497
  (0.8, 0.8, 0.8) 0.85767 2.86115 0.85776 2.86332 1.00749 1.54797 1.00749 1.54797
  (0.4, 0.6, 0.8) 0.89227 2.30478 0.89227 2.30485 1.03180 1.47774 1.03180 1.47774
( 0.5, 0.3, 0.1) (−0.4, −0.4, −0.4) 0.85928 6.00059 0.85931 6.00104 1.30515 2.86248 1.30515 2.86248
  (0.0, 0.0, 0.0) 0.93604 9.06171 0.93962 9.26930 1.33698 2.95625 1.33698 2.95625
  (0.4, 0.4, 0.4) 0.98816 16.19793 1.02313 27.36801 1.36853 3.06579 1.36853 3.06579
  (0.8, 0.8, 0.8) −15.88116 28.50127 1.10654 -- 1.39957 3.19429 1.39957 3.19429
  (0.4, 0.6, 0.8) 1.14422 14.23460 1.17172 23.89700 1.45149 2.89053 1.45149 2.89053

Note: the dash ‘--’ means that the value is not available.