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Colaco has a target of 16.00 ounces of liquid for each of their cans of soda. The current process is producing cans of soda with a mean of 15.97 ounces and a standard deviation of .04 ounces. What is the process capability if the upper tolerance limit is 16.1 and the lower tolerance limit is 15.9 ounces assuming a 99.7% quality level is required (+/- 3 standard deviations)? Is the process capable?

Respuesta :

Solution: We are given:

[tex]\mu=15.97,\sigma=0.04[/tex]

The process capability is

Upper tolerance limit is 16.1

Lower tolerance limit is 15.9

Now let's find the upper and lower limit of the given process assuming a 99.7% quality level is required (+/- 3 standard deviations):

[tex]Lower-limit=\mu-3 \sigma[/tex]

                         [tex]=15.97-3 \times 0.4[/tex]

                         [tex]=15.85[/tex]

[tex]Upper-limit=\mu+3 \sigma[/tex]

                         [tex]=15.97+3 \times 0.4[/tex]

                         [tex]=16.09 [/tex]

Since the lower and upper limits are beyond the given tolerance limits, therefore the is not capable.