As part of an insurance company’s training program, participants learn how to co
ID: 460905 • 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 37.0 minutes and a standard deviation of 3.0 minutes; Jerry, a mean of 37.0 minutes and a standard deviation of 3.0 minutes; and Melissa, a mean of 39.5 minutes and a standard deviation of 3.1 minutes.
a. Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Yes or No
Participants Cpk Cp Capable? Armand n/a Jerry n/a Melissa n/aExplanation / Answer
a) Cpk=min((Mean-lower limit)/3*Stddev),(upper Limit-lower mean)/3*Stddev)
Armand=Min(37-32)/3*3),(47-37)/(3*3))=Min(5/9,10/9)=5/9=0.55
Jerry=Min(37-32)/3*3),(47-37)/(3*3))=Min(5/9,10/9)=5/9=0.55
Melissa=Min((39.5-32)/(3*3.1)),((47--39.5)/(3*3.1))=min(0.8065 ,0.8065)=0.8065
Cp=(Upper Spec-Lower Spec)/6*stddev
Armand=(47-32)/6*3=15/18=0.833
Jerry=(47-32)/6*3=0.833
Melissa=(47-32)./6*3.1=15/18.6=0.806
The Cp is less than1 which means process range is greater than tolerance range and the process is not capable of producing with in design specifications.
Cpk index is also less than 1 for all the three participants which means process has moved close to one of the upper or lower design specifications and it will generate defect. so none is capable.
b)Cpk can not exceed Cp
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