Question

As part of an insurance company’s training program, participants learn how to conduct an analysis of clients’ insurability. The goal is to have participants achieve a time in the range of 32 to 47 minutes. Test results for three participants were: Armand, a mean of 36.0 minutes and a standard deviation of 3.0 minutes; Jerry, a mean of 34.0 minutes and a standard deviation of 3.0 minutes; and Melissa, a mean of 39.5 minutes and a standard deviation of 3.0 minutes.

a.Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
  

Participants	Cpk	Cp	Capable ?
Armand			(Click to select)   Yes   No
Jerry			(Click to select)   No   Yes
Melissa			(Click to select)   Yes   No

b.Can the value of the C_pk exceed the value of C_p for a given participant?

• Yes

• No

Answer 1

Answer a) Here, we will apply the following formula, to calculate the capability index for all the three participants:

Cpk =

Cp =

Where,

i) For Armand,

By replacing the appropriate values, we get:

, and

Hence,

ii) For Jerry,

By replacing the appropriate values, we get:

Hene,

iii) For Melissa,

By replacing the appropriate values, we get:

Hence,

Cp for all 3 participants =

Conclusion:

As we know that the participant whose Cpk ≥ 1, he/she is judged as capable. Here, as we note, all the 3 participants have Cpk < 1. Hence, we conclude that neither of the participants should be judged as capable.

Answer b) Here, we can easily observe that the value of Cpk can not exceed the value of Cp for any of the given participants.

Reason: Cp measures the only variation in the process considering the difference between upper specification limit and lower specification limit divided by 6 times the standard deviation. However, Cpk considers the minimum value of the difference between the upper / control limits from the mean and dividing the value by 3 times standard deviation value. Which leads to the value of Cpk being less than or equal to Cp and not more than that