# Statistic problems help

• Jun 9th 2006, 07:46 AM
Samyeo
Statistic problems help
The specifications for one dimension of part of a ski binding are 1.50 plus or minus 0.002 centimeter. When the manufacturing facility, makes parts of this general size, the process has a standard deviation of measurement of 0.0015 centimeter. Suppose that the company wishes to produce 10,000 parts that are within the specifications and that it operates the process centered at 1.500 centimeters. All parts that are outside the specifications are scrapped, and the company will receive only $1.00 for each of them. It costs the company$36 to produce each part.
a. How many parts should the company start so that it can expect
10,000 good parts to be completed?
b. What would be the cost of internal failure in this situation?

:o
• Jun 9th 2006, 08:30 AM
CaptainBlack
Quote:

Originally Posted by Samyeo
The specifications for one dimension of part of a ski binding are 1.50 plus or minus 0.002 centimeter. When the manufacturing facility, makes parts of this general size, the process has a standard deviation of measurement of 0.0015 centimeter. Suppose that the company wishes to produce 10,000 parts that are within the specifications and that it operates the process centered at 1.500 centimeters. All parts that are outside the specifications are scrapped, and the company will receive only $1.00 for each of them. It costs the company$36 to produce each part.
a. How many parts should the company start so that it can expect
10,000 good parts to be completed?
b. What would be the cost of internal failure in this situation?

:o

What proportion of bindings are out of spec?

In spec bindings are within $\displaystyle 2/1.5$ standard deviations of the mean this
includes (looking this up in a table of the standard normal distribution)
$\displaystyle 81.7578 \%$ of bindings made, so $\displaystyle 18.2422 \%$ are out of spec.

a) If $\displaystyle N$ parts are started the expected number in spec is:

$\displaystyle N 0.817578=10000$,

so:

$\displaystyle N=10000/0.817578 =12231.2..$

So the company will have to start $\displaystyle 12232$ (rounding up).

b) Cost to start $\displaystyle 12232$ is $\displaystyle 12232\times 36$
so the cost to start the rejects is $\displaystyle 2232\times 36$, and the
return on them is: $\displaystyle 2232\times 1$ so the cost of these failures
is:

$\displaystyle 2232\times 35= \$ 78120\$

RonL