15_Variable and Other Plans

15_Variable and Other Plans - Spring 2001 Lecture Notes -...

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Spring 2001 Lecture Notes - EMSE 282 - Professor Thomas A. Mazzuchi - 1 VARIABLE AND OTHER SAMPLING PLANS VARIABLE SAMPLING PLANS Merits • Advantages - Same OC Curve can be obtained with smaller sample size. - Variable data provide more information. • Disadvantage - cost/observation greater. - distribution of quality quantity must be known or assumed. - separate plan used for each quality measure. - may lead to a rejection of lots with no defectives. Types • Control of lot or process fraction defective. • Control of lot or process parameter. Assumptions • Quality characteristic is (usually) normally distributed
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Spring 2001 Lecture Notes - EMSE 282 - Professor Thomas A. Mazzuchi - 2 Control of Process Parameters (Usually , ) .5 • Based on hypothesis testing • Design for process mean, one sided, known 5 - Given X N( , ) specify a lower limit X for X (reject if X X ) µÎ 8 # LL - Given we want to accept batches of quality with probability 1 and 1 batches of quality with probability , find n, and X ." 2 L Pr{X X | } Pr{ }  œ œ   L 1 XX /n ..  55 11 L ÈÈ
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Spring 2001 Lecture Notes - EMSE 282 - Professor Thomas A. Mazzuchi - 3 P r { Z } 1 œ  œ X /n L1 . 5 È α z z Êœ œ X " . 5 αα È Pr{X X | } Pr{ }  œ œ   L XX .. #  55 ## ÈÈ L P r { Z } œ X L . 5 # È " z X L . 5 " # È Solving the equations z and z œ L α" # yields n , and X œœ ”• ÐÑ  # zz z z L "" " α 5. . 1 12 # Since n is rounded up to an integer value, the solution for X does not L g u a r a n t e e X thus use any of the three expressions or z/n L 1 2 œ H È È .5 α " an average, based on your concern for and Same can be done for upper limit X U - OC Curve Pr{X X | } 1 ( ) Vs L X .F . L . 5 È
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Spring 2001 Lecture Notes - EMSE 282 - Professor Thomas A. Mazzuchi - 4 - E x a m p l e .015, .1675, .1525, .05, .10 5 ..α " œœ œ œ œ 12 z 1.2816, z 1.6449 Êœ œ n = 8.57 9 ”• (1.2816 1.6449)*.015 .1675 .1525 # ¸¸ X .1591 L 1.2816*.1675 1.6449*.1525 1.2816+1.6449 œ¸ • Design for process mean, two sided, known 5 - Given X N( , ) specify a upper X and lower X limit for X µÎ 8 .5 # UL
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Spring 2001 Lecture Notes - EMSE 282 - Professor Thomas A. Mazzuchi - 5 - Given we want to accept batches of quality with probability 1 and 1 batches of quality and with probability , find n, X , and X .. " 2L 2U LU P r { X X X | } 1 1 ŸŸ œ œ α z and z Êœ œ XX /n /2 /2 L1 U1  55 αα ÈÈ
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Spring 2001 Lecture Notes - EMSE 282 - Professor Thomas A. Mazzuchi - 6 Pr{X X X | } Pr{X X| } LU L 2L 2L ŸŸ œ ¸ Ÿ œ œ .. " z Êœ X /n L2 L . 5 " È Pr{X X X | } Pr{X X | } U 2U 2L œ ¸ Ÿ œ œ " z X U2 U . 5 " È one equation redundant, solve for n, X , and X . Using 1, 2, and 3 yields n œ ”• (z z 2 " α Ñ /2 2L 5 " X and X z / n z / n z/n 1/ 2 2 2L 2U œœ   HH ÈÈ .5 αα "" again both forms will not hold as n is rounded to integer. As before use top or bottom expressions or an average depending on concern for and α" - OC Curve Pr{X X X | } ( ) ( ) Vs XX œ .F F .
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15_Variable and Other Plans - Spring 2001 Lecture Notes -...

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