A well-known trainer of a soccer team is thinking about making the soccer ball roll faster on the turf in games at the local arena. He noticed a new method of adding artificial grass, which promises a higher ball velocity. However, FIFA requires at least 80% natural grass on the soccer turf (that is, between 80% & 100% natural grass) with a process capability ratio Cp of at least 0.6. There are three companies that provide the service but work with a different accuracy: sigma(company a)=6%, sigma(company B)=5% and sigma (company c)=4%. The more accurate (lower standard deviation sigma) companies charge more, but the trainer wants to spend as little as possible. Which company should the trainer choose? Explain why.
The Process Capacity Index is a tool where both the process variability and the process specifications are used to determine whether the process is "capable" to deliver the required results.
In this question we have our upper limit (USL) as 100 and lower limit (LSL) as 80 and the variable figures are at 6%; 5% and 4%.
Cp = USL - LSL 1) = 100 - 80 / (0.6*6) = 5.56
6σ
2) = 100 - 80 / (0.6*5) = 6.67
3) = 100 - 80 / (0.6*4) = 8.33
The most economical and good quality layout of the new turf for the football ground would be option "B".
The reason would be it would cover about 87% area with natural grass and rest with good quality permitted grass. Secondly, this would cost most economical as well.
A well-known trainer of a soccer team is thinking about making the soccer ball roll faster...
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