48663 Assignment - SPC and Taguchi loss Function 1) What is meant by "robust design"? 2) Records of...

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48663 Assignment - SPC and Taguchi loss Function 1) What is meant by "robust design"? 2) Records of a critical parameter in a production process produce a normal curve. If samples of siz e N are taken then the sample averages also produce a normal curve which may be used to cons truct a control chart. Why are the two normal curves different and by what factor? 3) An automated tube bending operation produces parts with an included angle =95.5°. The process is a statistical control and the values of the included angle are normally distributed with a standard deviation = 0.34°. The design specification on the angle = 94.0°± 1.0°. (a) Determine the process capability. (b) If the process could be adjusted so that its mean =94.0°, what would be the value of the process capability index be? 4) Ten samples of size n=7 have been collected from a process in statistical control, and the dimension of interest has been measured for each part. (a) Determine the values of the centre, LCL and UCL for the ¯and R charts. The calculated values of ¯and R for each sample are given below (measured values are in mm). (b) Construct the control charts and plot the sample data on the charts. s XXXXXXXXXX10 ¯ XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXR XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXIn a statistical control extrusion process the diameter of the extrudate has been measured for each part .The calculated values of ¯and R for 7 sample for 6 parts are given below (measured values are in mm). (a) Determine the values of the centre, LCL and UCL for ¯and R charts.. (b) Construct the control charts and plot the sample data on the charts. s XXXXXXXXXX ¯ XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXR XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXThe Taguchi loss function for a certain component is given by L(x) = 9400(x-N) 2 , where x = the actual value of the dimension of critical importance and N is its nominal value. Company management has decided that the maximum loss that can be accepted is $15. (a) If the nominal dimension is 42.00 mm, at what value should be tolerance on this dimension be set? (b) Does the value of the nominal dimension have any effect on the tolerance that should be specified? 7) Two alternative manufacturing processes, A and B, can be used to produce a certain dimension on one of the parts in an assembled product. Both processes can be produce parts with an average dimension at the desired nominal value. The tolerance on the dimension is ±0.10 mm. the output of each process follows a normal distribution. However, the standard deviations are different. For process A, s = 0.08 mm; and for process B, s = 0.11. Production costs per piece for A and B are $15.00 and $6.00, respectively. If inspection and sortation is required, the cost of is $0.85 per piece. If a part is found to be defective, it must be scrapped at a cost equal to its production cost. The Taguchi loss function for this component is given by L(x) =3000(x-N) 2 , where x = value of the dimension and N is its nominal value. Determine the average cost per piece for the two processes. Z XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX0.499

David · Accepted Answer

1) The concept behind robust design is to ensure that small deviations during production and 
assembly operations do not unfavorably affect the product quality in terms of specifications and 
performance. 
It recognizes the fact it is too expensive to eliminate totally the variations and deviations which 
occur during the production and assembly operations. Instead it is cost effective to incorporate 
the concept of “robust design” during the product development stage itself. 
 
2) Two curves are different because normal distribution depends upon the sample size (N) of the 
sample selected for observation. Greater the value of N, closer will be the two curves. 
Both curves differ in shape due to the difference in the mean and standard deviation of the 
process and sample. 
 
3)  
a. Calculate the process capability.
Here, µ is an included angle, σ and is a standard deviation. 
Therefore, PC = 95.5o   3(0.34o) 
                         = 95.5o   1.02o 
Hence, the upper and lower limits of the process capability range are 94.48o to 96.52o. 
b. Write the design specification on the angle. 
PC = 94.0˚± 1.0o 
The upper and lower limits of the process capability range are to 93o to 95o. 
Calculate the process capability index.
Therefore, PCI= (95o – 93o) / (6*0.34o) 
                          = 0.9803 
Hence, the process capability index is 0.9803
4)  
a.  Find the mean of the sample averages.
     = (8.22+8.15+8.20+8.28+8.19+8.12+8.20+8.24+8.17+8.23)/10 
     =82/10=8.

48663 Assignment - SPC and Taguchi loss Function 1) What is meant by "robust design"? 2) Records of a critical parameter in a production process produce a normal curve. If samples of siz e N are taken...

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