Question

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?

Answer 1

Answer:

LSL = 15.7

USL = 16.3

Step-by-step explanation:

$\bar x$ = Mean = 16 ounces

σ = Standard deviation = 0.1 ounces

$C_p=1$

$C_p=\frac{USL-LSL}{6\sigma}\\\Rightarrow USL-LSL=6\sigma \times C_p\\\Rightarrow USL-LSL=6\times 0.1\times 1\\\Rightarrow USL-LSL=0.6$

Now to find USL and LSL

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

$LSL=16-0.3\\\Rightarrow LSL=15.7$

$USL=16+0.3\\\Rightarrow LSL=16.3$

∴ LSL = 15.7

USL = 16.3