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 45 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 37.0 minutes and a standard deviation of 2.0 minutes; and Melissa, a mean of 38.5 minutes and a standard deviation of 1.9 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	0.67 0.67 Incorrect		Yes Incorrect
Jerry	Not attempted
Melissa		Not attempted

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

• Yes

• No

Answer 1

ARMAND

UPPER SPECIFICATION = 45
LOWER SPECIFICATION = 32
PROCESS MEAN = 36
STANDARD DEVIATION = 3

Cpk = MINIMUM((UPPER SPECIFICATION - MEAN) / 3 * STANDARD DEVIATION), (MEAN - LOWER SPECIFICATION) / 3 * STANDARD DEVIATION)

Cpk = MINIMUM((45 - 36) / 3 * 3), (36 - 32) / 3 * 3)
Cpk = MINIMUM(1, 0.4444)
Cpk = 0.44

SINCE Cpk = 0.44 < 1, THE PROCESS IS NOT CAPABLE.

JERRY

UPPER SPECIFICATION = 45
LOWER SPECIFICATION = 32
PROCESS MEAN = 37
STANDARD DEVIATION = 2

Cpk = MINIMUM((UPPER SPECIFICATION - MEAN) / 3 * STANDARD DEVIATION), (MEAN - LOWER SPECIFICATION) / 3 * STANDARD DEVIATION)

Cpk = MINIMUM((45 - 37) / 3 * 2), (37 - 32) / 3 * 2)
Cpk = MINIMUM(1.3333, 0.8333)
Cpk = 0.83

SINCE Cpk = 0.83 < 1, THE PROCESS IS NOT CAPABLE.

MELLISA

UPPER SPECIFICATION = 45
LOWER SPECIFICATION = 32
STANDARD DEVIATION = 1.9

Cp = (UPPER SPECIFICATION - LOWER SPECIFICATION) / (6 * STANDARD DEVIATION)

Cp = (45 - 32) / (6 * 1.9)
Cp = 1.14

THE PROCESS IS LESS THAN 1.33 AND THEREFORE, IS CAPABLE WITH TIGHT CONTROL.

2. NO, Cpk IS NOT CENTERED AND THEREFORE CANNOT BE MORE THAN Cp