Question

1.)Ready Care is currently using SPC as a means for investigating its process. However, they want to determine if they are currently aligned with customer expectations. The marketing team has determined that customers expect some sort of a wait and are not likely to complain if the wait does not exceed 35 minutes. Operations has determined that the process mean is 25.25 and the standard deviation of the process is 2.5.

Knowing this, what is the capability ratio (Cp) for this process?

2.)What is the Capability Index (Cpk) for the situation in Question 1?

3.)What can be concluded about the process?

a. It is capable of meeting customer expectations

b. It is not capable of meeting customer expectations

c. It is in control

d. It is out of control

4.)If Ready Care wanted to expand the current offering (i.e., add more diagnostic services), what would happen?

a. Processing times would go down

b. More variance would be induced into the process

c. Customers would be happy with an increased wait time

d. There would be no change in the process

5.) If an offering change led to more process variance, what would happen to the capability measures?

a. They would both remain the same

b. Cp would go up while Cpk would go down

c. Cp would go down while Cpk would go up

d. They would both go down

Answer 1

Important formula:

Cp = (USL-LSL)/6*Standard Deviation

Cpk = lower value of Cpu and Cpl

Cpu = (USL - Mean)/3*Standard Deviation

Cpl =(Meann - LSL)/3*Standard Deviation

1	B	C	D
2		Value	Remarks
3	Mean Data	25.25	Given Data
4	Standard Deviation	2.5	Given Data
5	Upper Specification Limit - USL	35	Given Data
6	Lower Specification Limit - LSL	0
7	Lower Bound for the Process Capability Index - a or Cpl	3.367
8	Upper Bound for the Process Capability Index - b or Cpu	1.300
9	Process Capability Index Cpk = Min of [ a,b ]	1.300	Here, Cpk is 1.300, or Cpk is not equal to Cp, hence, we can conclude that Process is not centered and process has produced the desired result of Four Sigma Quality standard
10	Process Capability Cp	2.333	Here, Cp is 2.33 which is more than 2 value or Cp value for Six sigma level, Thus, process is capable to produce the desired result within the alloted tolerance zone,

Formula:

1	B	C	D
2		Value	Remarks
3	Mean Data	25.25	Given Data
4	Standard Deviation	2.5	Given Data
5	Upper Specification Limit - USL	35	Given Data
6	Lower Specification Limit - LSL	0
7	Lower Bound for the Process Capability Index - a or Cpl	=(C3-C6)/(3*C4)
8	Upper Bound for the Process Capability Index - b or Cpu	=(C5-C3)/(3*C4)
9	Process Capability Index Cpk = Min of [ a,b ]	=MIN(C7:C8)	Here, Cpk is 1.300, or Cpk is not equal to Cp, hence, we can conclude that Process is not centered and process has produced the desired result of Four Sigma Quality standard
10	Process Capability Cp	=(C5-C6)/(6*C4)	Here, Cp is 2.33 which is more than 2 value or Cp value for Six sigma level, Thus, process is capable to produce the desired result within the allotted tolerance zone,

here, process is meeting the four sigma quality level and process is capable of meeting six sigma quality, hence, answer for 3)

a) It is capable of meeting customer expectations

4) Expanding the current offering will lead to increase variation in the service level, as process data will be more dispersed, hence, correct answer is b. More variance would be induced into the process

5) More process variance will lead to increase of standard deviation, looking at the above mentioned formula, we can see that Cp and Cpk value always inversely proportional to Standard deviation value, so, more standard deviation means less Cp or Cpk value, Hence, correct answer is d. They would both go down, other options are not matched, hence, other options are eliminated,