HW4-Solutions

HW4-Solutions - Homework #4 (Solutions) Problem 6.1 (a) for...

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Homework #4 (Solutions) Problem 6.1 (a) for n = 5, A 2 = 0.577, D 4 = 2.114, D 3 = 0 1 2 1 2 x 2 x x 2 R 4 R R 3 34.5 34.2 34.2 34.00 24 3 4 2 4.71 24 UCL 34.00 0.577(4.71) 36.72 CL 34.00 LCL 34.00 0.577(4.71) 31.29 UCL 2.115(4.71) 9.96 CL 4.71 LCL 0(4.71) 0.0 m m x x x x m R R R R m x A R x x A R D R R D R 0

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The process is not in statistical control; x is beyond the upper control limit for both Sample No. 12 and Sample No. 15. Assuming an assignable cause is found for these two out-of-control points, the two samples can be excluded from the control limit calculations. The new process parameter estimates are: 2 x x x R R R ö 33.65; 4.5; / 4.5/ 2.326 1.93 UCL 36.25;CL 33.65;LCL 31.06 UCL 9.52;CL 4.5;LCL 0.00 x x R R d
(b) ö Pr{ LSL} Pr{ USL} Pr{ 20} Pr{ 40} Pr{ 20} 1 Pr{ 40} 20 33.65 40 33.65 1 1.93 1.93 ( 7.07) 1 (3.29) 0 1 0.99950 0.00050 p x x x x x x           Problem 6.2* (a) MTB > Stat > Control Charts > Variables Charts for Subgroups > Xbar-R The process is in statistical control with no out-of-control signals, runs, trends, or cycles. (b) 2 ö 4, 10.33, 6.25, / 6.25/ 2.059 3.035 X n x R R d . Actual specs are 350 5 V. With x i = (observed voltage on unit i 350) 10: USL T = +50, LSL T = 50 USL LSL 50 ( 50) ö 5.49 ö 6 6(3.035) P C   , so the process is capable.

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MTB > Stat > Quality Tools > Capability Analysis > Normal (c) MTB > Stat > Basic Statistics > Normality Test A normal probability plot of the transformed output voltage shows the distribution is close to normal.
Problem 6.5* (a) MTB > Stat > Control Charts > Variables Charts for Subgroups > Xbar-S (Volume) Under “Options, Estimate” select Sbar as method to estimate standard deviation. The process is in statistical control, with no out-of-control signals, runs, trends, or cycles.

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This note was uploaded on 02/14/2012 for the course IE 530 taught by Professor Ravindran during the Spring '97 term at Purdue University.

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HW4-Solutions - Homework #4 (Solutions) Problem 6.1 (a) for...

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