Question

(Vetro Inc) Vetro Inc. is a glass manufacturer that produces glasses of every shape and type. Recently it signed a contract to supply round glasses to Switch, a Swiss watch manufacturer. The specifications require the diameter to be between 4.96 cm and 5.04 cm. With the current production process, Vetro Inc. manages to produce glasses whose diameter is, on average, equal to 5 cm; however, a closer inspection reveals some variability in the process, with the diameter of the glass being normally distributed with standard deviation equal to 0.01cm. 1. What is the capability index (score) of Vetro Inc.? [7.2] 2. What is the maximum standard deviation allowed for the process to meet the rigorous six-sigma standards? [7.2]

Answer 1

Answer:

Answer is explained in the explanation section below.

Explanation:

Data Given:

LSL = 4.96 cm

USL = 5.04 cm

Mean = 5 cm

SD = 0.01 cm

1. Capability Index:

Cpk = min ( $\frac{USL - Mean }{3SD}$ , $\frac{Mean - LSL}{3SD}$ )

So, now, we need to find the following:

$\frac{USL - Mean }{3SD}$ = $\frac{5.04 - 5 }{3 * 0.01}$

$\frac{USL - Mean }{3SD}$ = $\frac{0.04}{0.03}$

$\frac{USL - Mean }{3SD}$ = 1.33

Similarly,

$\frac{Mean - LSL }{3SD}$ = $\frac{5 - 4.96 }{3 * 0.01}$

$\frac{Mean - LSL }{3SD}$ = $\frac{0.04}{0.03}$

$\frac{Mean - LSL }{3SD}$ = 1.33

So,

Cpk = min ( $\frac{USL - Mean }{3SD}$ , $\frac{Mean - LSL}{3SD}$ ) = 1.33

2. Maximum Standard deviation allowed.

Let SD be maximum standard deviation allowed.

So,

Mean - 3SD = 4.96     Equation 1

Mean + 3SD = 5.04    Equation 2

Subtracting Equation 2 from 1, we have

6SD = 5.04 - 4.96

6SD = 0.08

SD = 0.0133