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A supplier makes packaging cartons for a customer, with a length normally distributed around a mean of 150mm. Due to the cavity in the filling machine, the carton must be no longer than 157 mm and no shorter than 143mm. The process standard deviation is 2.5mm.
a. What is the process capability Cp?
b. Calculate the percentage of non-conforming cartons of the process. Please type your answer in numerical numbers with 4 decimal places (not percentages).

Respuesta :

Answer:

a) Cp=0.93

b) The probability of having non-conforming items is P=0.0051.

As percentage is 0.51%.

Step-by-step explanation:

a) The Cp is a measure of the capability of the process to produce items within the specifications.

It can be expressed as:

[tex]C_p=\frac{USL-LSL}{6\sigma} =\frac{157-143}{6*2.5}=\frac{14}{15}= 0.93[/tex]

Where USL: upper specification limits

LCL: lower specification limits

b) The upper and lower specifications are equally distant from the mean (±7mm), so we can calculate z as:

[tex]z=\pm(x-\mu)/\sigma=\pm7/2.5=\pm2.8\\\\P(143<X<157)=P(-2.8<z<2.8)=0.99488\\\\1-P(143<X<157)=1-0.99488=0.00512[/tex]

The probability of having non-conforming items is P=0.0051.

As percentage is 0.51%.

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