# The Money Pit Mortgage Company of Problem 6 made some changes to the process

The Money Pit Mortgage Company of Problem 6 made some changes to the process and undertook a process capability study. The following data were obtained for 15 samples of size 5. Based on the individual observations, management estimated the process standard deviation to be 4.21 (days) for use in the process capability analysis. The lower and upper specification limits (in days) for the mortgage process times were 5 and 25. a. Calculate the process capability index and the process capability ratio values. b. Suppose management would be happy with three-sigma performance. What conclusions is management likely to draw from the capability analysis? Can valid conclusions about the process be drawn from the analysis? c. What remedial actions, if any, do you suggest that management take?

 First we will calculate the Process Capability Ratio (Cp) Cp is defined as the ratio of the range of design specifications to the range of the process variation which for most companies is 6*SD where SD is standard deviation. So Cp= (USL-LSL)/(6*SD) Here USL = 25 & LSL = 5 So Cp=(25-5)/(6*4.21)=0.7918 Here since Cp < 1 then it means that the process range is greater than the tolerence range and process is not capable of producing within design specifications all the time. Now let us calculate Process Capability Index. Sum of Mean Sample Size X double Bar Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 M n M/n Mean 11 12 8 6 13 12 17 16 13 14 17 9 15 14 9 186 15 12.4 Now process capability index is given by Cpk = ((X double bar – LSL)/(3*SD) , (USL-X double bar)/(3*SD))=((12.4-5)/(3*4.21),(25-12.4)/(3*4.21)) Cpk=(0.5859,0.9976)=0.5859 Process capability ratio has already indicated that process is not capable of producing within design specifications . Now Cpk is less than 1 it further indicates that process mean has moved closer to the one of the lower or upper design specifications and it will generate defects. So what inference management can draw is that process is not capable and defects will be generated which will inflate the costs. The advice to the management is to improve the process and redesign the product & adjust the process so that process center coincides with the design center.
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