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 38.0 minutes and a standard deviation of 2.0 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 2.4 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)  Yes  No
Melissa			(Click to select)  No  Yes

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

• Yes

• No

Answer 1

The Cpk formula is

Cpk = min (CpU, CpL)

CpU = (USL – mean)/3SD

CpL = (mean – LSL)/3SD

The Cp formula is

Cp = (USL – LSL)/6SD

Here,

USL = 47

LSL = 32

Mean and SD varies depending on the candidates.

a.

Armand

Cpk = min of (47-38)/(3*2) and (38-32)/(3*2) = 1

Cp = (47-32)/(6*2) = 1.25

Capable = Yes

Jerry

Cpk = min of (47-34)/(3*3) and (34-32)/(3*3) = 0.22

Cp = (47-32)/(6*3) = 0.83

Capable = No

Melissa

Cpk = min of (47-39.5)/(3*2.4) and (39.5-32)/(3*2.4) = 1.02

Cp = (47-32)/(6*2.4) = 1.04

Capable = Yes

b.

Cpk value cannot exceed the Cp value