The Money Pit Mortgage Company is interested in monitoring the performance of th
ID: 421152 • Letter: T
Question
The Money Pit Mortgage Company is interested in monitoring the performance of the mortgage process. Fifteen samples of five completed mortgage transactions each were taken during a period when the process was believed to be in control. The times to complete the transactions were measured.
The Money Pit Mortgage Company 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 4.24?(days) for use in the process capability analysis. The lower and upper specification limits? (in days) for the mortgage process times were 3 and 19
Calculate the process capability index and the process capability ratio values.
The process capability index
Upper Cpk = _____.
(Enter your response rounded to three decimal places.?)
Part B.
The process capability index must be compared to a critical value to judge whether a process is capable. If Upper Cpk
is greater than or equal to the target process capability? ratio, we can say the process is capable. If it is less than the target process capability? ratio, either the process average is too close to one of the tolerance limits and is generating defective output or the process variability is too large. A critical value for the ratio of 1.0 is used to achieve? three-sigma quality.
Part C.
What remedial? actions, if? any, do you suggest that management? take?
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(a)
Estimate of process mean = mean of the sampling distribution = 10.1333
Process STDEV = 4.24
USL = 19; LSL = 3; Required process mean = (19+3)/2 = 11; so, the process mean of 10.1333 is shifted.
Cpk = Min{(USL - Process mean) / (3*STDEV), (Process mean - LSL) / (3*STDEV)}
= Min((13 - 10.1333)/(3*4.24), (10.1333 - 3)/(3*4.24)) = 0.225
Upper Cpk = (13 - 10.1333)/(3*4.24) = 0.225
(b)
The upper Cpk being less than 1.0, the process is incapable.
(c)
The process standard deviation should be reduced to improve the Cpk value. This can be done by developing standard operating procedures and providing people with training of how to operate using these SOPs.
Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Average Mean 9 9 5 13 10 8 14 13 10 11 15 6 12 11 6 10.13333 Range 9 14 5 12 11 11 9 16 15 12 6 7 13 11 12 10.86667