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 4.93 ​(days) for use in the process capability analysis. The lower and upper specification limits​ (in days) for the mortgage process times were 4 and 22 .                                                                                                                                                Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Mean 8 9 5 13 10 10 14 13 10 11 13 6 12 11 6 Range 11 14 5 12 11 9 9 16 15 12 8 7 13 11 12

a. Calculate the process capability index and the process capability ratio values. The process capability index Upper C Subscript pk =

Answer 1

Process capability index (Cpk) compares the output of an in-control process to the specification limits.

process capability index formula is given below:

for mean, we use the estimated value, = (8+9+5+.....+11+6)/15 = 10.07

C_pk = min [ (22-10.07)/3*4.93 , (10.07-4)/3*4.93 ]

= min [ 0.81 , 0.41 ]

= 0.41

We would like to have Cpk at least 1.0 which correspond to 0.27% rejects based on the specifications. Hence, this is not a good process. If possible, reduce the variability or/and center the process.

Process capability ratio (C_p) does not take into account the offset in the mean, formula is given below:

  C_{p = (USL-LSL)/ 6}

_{= (22-4)/6*4.93 = 0.61}