As part of an insurance company’s training program, participants learn how to co
ID: 419484 • Letter: A
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 3.0 minutes; Jerry, a mean of 37.0 minutes and a standard deviation of 2.0 minutes; and Melissa, a mean of 39.5 minutes and a standard deviation of 2.2 minutes.
Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
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 3.0 minutes; Jerry, a mean of 37.0 minutes and a standard deviation of 2.0 minutes; and Melissa, a mean of 39.5 minutes and a standard deviation of 2.2 minutes.
a.Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Explanation / Answer
Following may be noted:
Cp = (Upper specification limit, USL – Lower specification Limit, LSL ) / 6 x Standard deviation
Cpk = Minimum ( ( USL – m ) /3 x Sd , ( m – LSL) / 3 x Sd )
Where,
USL = 47 minutes , LSL = 32 minutes
M -= mean
Sd = Standard deviation
Therefore , Cp for Armand = ( 47 – 32 ) / 6 x 3 = 15/18 = 0.833
Cpk for Armand = Minimum ( ( 47 – 38) / 3 x 3 , ( 38 – 32 ) / 3 x 3 )
= Minimum ( 9/9 , 6/9)
= Minimum ( 1 , 0.666)
= 0.666
Therefore , Cp for Jerry = ( 47 – 32 ) / 6 x 2 = 15/12 = 1.25
Cpk for Jerry = Minimum ( ( 47 – 37) / 3 x 2 , ( 37 – 32 ) / 3 x 2 )
= Minimum ( 10/6, 5/6)
= Minimum ( 1.666, 0.833)
= 0.833
Cp for Melissa = ( 47 – 32 ) / 6 x 2.2 = 15/ 13.2 = 1.136
Cpk for Melissa = Minimum ( ( 47 – 39.5) / 3 x 2.2 , ( 39.5 – 32 ) / 3 x 2.2 )
= Minimum ( 1.136 , 1.136 )
= 1.136
For a process to be conforming to 6 sigma limits, it is essential that Cp as well as Cpk both have values > 1 .
As evident from above data . it is only Melissa which conforms to above criteria . Therefore , we would consider participant Melissa to be most capable.
Participant
Cp
Cpk
Capable
Armand
0.833
0.666
No
Jerry
1.25
0.833
No
Melissa
1.136
1.136
Yes
Participant
Cp
Cpk
Capable
Armand
0.833
0.666
No
Jerry
1.25
0.833
No
Melissa
1.136
1.136
Yes
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