Business, 10.03.2020 04:52, avablender

You are part of the Operations Team at Gamma motors, investigating the painting process. The painting machine naturally requires an average of 10 hours to complete with a standard deviation of 2 hours. After some observation, you determine that the process seems to have a lot of breakdowns. Based on the data you collected, the average time between failures of the painting machine appears to be a mere 200 hours with a standard deviation of 50 hours. Repair times after a failure average 10 hours with a standard deviation of 10 hours. The factory only has one painting machine, which is the only machine at the workstation.

a. Identify the Effective Process Time (te):
b. SCV of Effective Process times (Ce2):
c. Standard Deviation of Effective Process times (Sigmae):

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answered: savage5447

Part a: The effective time is 10.5 hours.

Part b: The SCV of Effective Process times is 0.130.

Part c: The value of the Standard Deviation of the Effective process times is 3.80

Explanation:

Part a:

The effective time t_e is given as

$t_e=\dfrac{t_p}{A}$

Here t_p is the time taken to complete the paint job which is given as 10

A is the availability which is given as

$A=\dfrac{M_{TBF}}{M_{TBF}+M_R}$

here M_TBF is the mean time between failures which is given as 200 hours

M_R is the mean repair time which is given as 10 hours so

$A=\dfrac{M_{TBF}}{M_{TBF}+M_R}\\A=\dfrac{200}{200+10}\\A=\dfrac{200}{210}=0.9524$

So the effective time is calculated as

$t_e=\dfrac{t_p}{A}\\t_e=\dfrac{10}{0.9524}\\t_e=10.499\approx 10.5\\$

So the effective time is 10.5 hours.

Part c:

The Standard Deviation of the Effective process times is given as

$\sigma_e^2=\left(\dfrac{\sigma_p}{A}\right)^2+\dfrac{(M_R^2+\sigma_R^2)(1-A)t_p}{AM_R}$

Here

σ_e is the standard deviation of the effective process time which is to be calculated

σ_p is the standard deviation of time taken to complete the paint job given as 2

A is the availability calculated above as 0.9524

M_R is the mean time of repair given as 10

σ_R is the standard deviation of time taken to repair given as 10

t_p is the time taken to complete a paint job which is given as 10

so the equation becomes

$\sigma_e^2=\left(\dfrac{\sigma_p}{A}\right)^2+\dfrac{(M_R^2+\sigma_R^2)(1-A)t_p}{AM_R}\\\sigma_e^2=\left(\dfrac{2}{0.9524}\right)^2+\dfrac{(10^2+10^2)(1-0.9524)*10}{0.9524*10}\\\sigma_e^2=4.4098+9.9958\\\sigma_e^2=14.4056\\\sigma_e=\sqrt{14.4056}\\\sigma_e=3.7954$

So the value of the Standard Deviation of the Effective process times is 3.80

Part b

The SCV of Effective Process times is given as

$C_e^2=\dfrac{\sigma_e^2}{t_e^2}$

here both values of σ_e and t_e are calculated in above parts as 3.89 and 10.5 respectively so the equation becomes.

$C_e^2=\dfrac{\sigma_e^2}{t_e^2}\\C_e^2=\dfrac{3.80^2}{10.5^2}\\C_e^2=0.130$

So the SCV of Effective Process times is 0.130

answered: Guest

1 all nations face the problem of scarcity because there are limited resources and unlimited wants. nations do not have enough factors of production to produce everything that their population wants. entrepreneurial resources initiate businesses to make new goods and services; labor resources produce goods and services.

2 there are four factors of production: natural resources, labor resources, capital resources, and entrepreneurial resources. natural resources are raw materials from nature that are used to produce goods. trees, water, and grains are natural resources. some natural resources, such as wheat and cattle, are renewable

3 wants

things that you do not need to have in order to survive, but would like to have

needs

things that you must have in order to survive

goods

physical products

services

tasks that a business perform for customers

resources

items that people can use to make or obtain what they need or want

determine

to settle or decide by choice of alternatives or possiblities

4 i really dont know

answered: Guest

Ibelieve it would be choice a ($24,630)

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You are part of the Operations Team at Gamma motors, investigating the painting process. The paintin...