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):

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

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

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

So the effective time is calculated as

So the effective time is 10.5 hours.

Part c:

The Standard Deviation of the Effective process times is given as

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

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

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.

So the SCV of Effective Process times is 0.130

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