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 4.98 ​(days) for use in the process capability analysis. The lower and upper specification limits​ (in days) for the mortgage process times were 9 and 23.                                                                                                                                                Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Mean 13 15 11 19 16 14 20 19 16 17 20 12 18 17 12 Range 6 11 2 9 8 6 6 13 12 9 5 4 10 8 9 a. Calculate the process capability index and the process capability ratio values. The process capability index Upper C Subscript pkequals nothing. ​(Enter your response rounded to three decimal places.​) The process capability ratio Upper C Subscript pequals nothing. ​(Enter your response rounded to three decimal places.​) b. Suppose management would be happy with​ three-sigma performance. What conclusions is management likely to draw from the capability​ analysis? Since Upper C Subscript pk is ▼ greater than equal to less than the critical​ value, the process ▼ is is not capable at the​ three-sigma level. Since Upper C Subscript p is ▼ less than greater than equal to the critical​ value, this indicates that ▼ the process variability is too large the process is not centered adequately . c. What remedial​ actions, if​ any, do you suggest that management​ take? A. Management should use a lower target process capability ratio. B. The specification limits must be revised. C. The variability of the process must be greatly reduced. D. Nothing. The process is capable.

Answer 1

	Average of data	µ	15.93
	Standard deviation of Data	σ	4.98
	Upper Specification Limit (USL)	USL	23
	Lower Specification Limit (LSL)	LSL	9
	Process Capability	Cp = (USL – LSL)/6σ Cp = (23 – 9)/(6*4.98)	Cp = 0.4685
	Upper Cpk	Upper Cpk = [(USL - µ) / (3σ)] Upper Cpk = (23 – 15.93)/(3*4.98)	0.4732
	Lower Cpk	Lower Cpk = [(µ - LSL) / (3σ)] Lower Cpk = (15.93 – 9)/(3*4.98)	0.4638
	Process Cpk	Cpk = Min (Upper Cpk, Lower Cpk) = Min ([(USL - µ) / (3σ)],[(µ - LSL) / (3σ)])	=min(0.4732, 0.4638) = 0.6836

a. Calculate the process capability index and the process capability ratio values.

The process capability index, C_pk = 0.4732

Process capability ratio, C_p = 0.4685

b. According to 3-sigma performance the critical value is 1, if capability is less than 1 not capable and more than 1 the process is capable.

Since Cpk less than critical value, the process is not capable at the three sigma level.

Since Cp is less than critical value, this indicates that process variability is too large.

c.

Remedial actions,

Correct Option: The variability must be greatly reduced.

(Since the Cp < 1 and also Cpk <1, the process control limits way beyond specification limits.