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 4.85 ​(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 7 9 5 13 10 8 14 13 10 11 15 6 12 11 6
Range 8 12 3 10 9 7 7 14 13 10 5 5 11 9 10
Calculate the process capability index and the process capability ratio values?

Answer 1

Answer:

Process Capability Index = 0.412

Process Capability Ratio = 0.62

Explanation:

The Process Capability Index $C_{pk}$ is given by the formula:

$C_{pk} = min[\frac{\bar{\bar{X}} - LSL}{3 \sigma} , \frac{USL - \bar{\bar{X}} }{3 \sigma}]$

$\bar{\bar{X}} = \frac{7+9+5+13+10+8+14+13+10+11+15+6+12+11+6}{15} \\\bar{\bar{X}} = 10$

Lower Limit, LSL = 4

Upper Limit, USL = 22

Standard Deviation, $\sigma = 4.85$

$C_{pk} = min[\frac{\bar{\bar{X}} - LSL}{3 \sigma} , \frac{USL - \bar{\bar{X}} }{3 \sigma}]\\C_{pk} = min[\frac{10 - 4}{3 * 4.85} , \frac{22 - 4 }{3 *4.85}]\\C_{pk} = min[0.412, 0.825]\\C_{pk} = 0.412$

Process capability ratio:

$C_p = \frac{USL - LSL}{3 \sigma}$

$C_{p} = \frac{22-4}{6*4.85} \\C_{p} = 0.62$