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Studies on a bottle-filling machine indicate that it fills bottles to a mean of 16 ounces with a standard deviation of 0.10 ounces. What is the process specification, assuming the Cpk index of 1?

Respuesta :

Answer:

LSL = 15.7

USL = 16.3

Step-by-step explanation:

[tex]\bar x[/tex] = Mean = 16 ounces

σ = Standard deviation = 0.1 ounces

[tex]C_p=1[/tex]

[tex]C_p=\frac{USL-LSL}{6\sigma}\\\Rightarrow USL-LSL=6\sigma \times C_p\\\Rightarrow USL-LSL=6\times 0.1\times 1\\\Rightarrow USL-LSL=0.6[/tex]

Now to find USL and LSL

As range is 6σ for finding USL and LSL we have to take value of 3σ

[tex]LSL=16-0.3\\\Rightarrow LSL=15.7[/tex]

[tex]USL=16+0.3\\\Rightarrow LSL=16.3[/tex]

∴ LSL = 15.7

USL = 16.3

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