mont4e_sm_ch16_sec09 - Section 16-9 16-37 a) (112-100)/3=4...

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Section 16-9 16-37 a) (112-100)/3=4 b) () 88 96 112 96 (88 112) 2 4 44 ( 4) ( 2) 0.9772 X X PX P P Z PZ μ σ ⎛⎞ −− << = < < =− ⎜⎟ ⎝⎠ =< −< = The probability of detecting is 1-0.9772=0.0228. c) 1/0.0228=43.8596 ARL to detect the shift is about 44. 16-38 a) UCL n = + 3 4 ) 100 106 ( 3 2 106 4 3 100 = = = + b) 96 , 2 2 4 ˆ ˆ = = = = n x 8413 . 0 1587 . 0 1 ) 1 ( ) 5 ( 5 1 2 96 106 2 96 94 ) 106 94 ( = = < < = < < = < < = < < Z P Z P Z P X P X P x The probability that this shift will be detected on the next sample is p = 1 0.8413 = 0.1587. c) 301 . 6 1587 . 0 1 1 = = = p ARL 16-26
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16-39 a) x = 74 01 . σ x = 0.0045 μ = 74.01 7823 . 0 ) 1 1 ( 7823 . 0 )] 22 . 5 ( 1 [ ) 78 . 0 ( ) 22 . 5 ( ) 78 . 0 ( ) 78 . 0 22 . 5 ( 0045 . 0 01 . 74 0135 . 74 ˆ 0045 . 0 01 . 74 9865 . 73 ) 0135 . 74 9865 . 73 ( = = < < = < < = < < = < < = < < Z P Z P Z P Z P Z P X P X P x σ μ The probability that this shift will be detected on the next sample is p = 1 0.7823 = 0.2177. b) 6 . 4 2177 . 0 1 1 = = = p ARL 16-40 a) 148 . 0 326 . 2 344 . 0 ˆ 2 = = = d R ± σ x = 066 . 0 5 148 . 0 ˆ = = n , μ = 14.6 94950 . 0 ) 0 ( 94950 . 0 ) 36 . 4 ( ) 64 . 1 ( ) 64 . 1 36 . 4 ( 066 . 0 6 . 14 708 . 14 066 . 0 6 . 14 312 . 14 ) 708 . 14 312 . 14 ( = = < < = < < = < < = < < Z P Z P Z P X P X P x
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mont4e_sm_ch16_sec09 - Section 16-9 16-37 a) (112-100)/3=4...

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