Question

Maintenance of Production Facility

A production facility has several 3-D printing machines which need maintenance for two reasons. Maintenance type A: a sensor may have detected a fault, e.g. an oil leak. Maintenance type B: the quality of the printed product is unacceptable. Each maintenance requirement occurs at random and independently of other requirements for maintenance, with characteristics summarized in the following table:

Maintenance Type	Average rate of occurrence per week totalled over all 3-D printing machines in the production facility	Cost of maintenance
A	6.7 (maintenance events per week)	$430 (per maintenance event)
B	2.1 (maintenance events per week)	$2600 (per maintenance event)

What is the probability of exactly 6 maintenance events of type A in half a week?

Question 45 options:

	<0.02
	Between 0.02 and 0.04
	Between 0.04 and 0.06
	Between 0.06 and 0.08
	>0.08

Question 46 (1 point)

Maintenance of Production Facility

A production facility has several 3-D printing machines which need maintenance for two reasons. Maintenance type A: a sensor may have detected a fault, e.g. an oil leak. Maintenance type B: the quality of the printed product is unacceptable. Each maintenance requirement occurs at random and independently of other requirements for maintenance, with characteristics summarized in the following table:

Maintenance Type	Average rate of occurrence per week totalled over all 3-D printing machines in the production facility	Cost of maintenance
A	6.7 (maintenance events per week)	$430 (per maintenance event)
B	2.1 (maintenance events per week)	$2600 (per maintenance event)

What is the standard deviation of the total cost of maintenance of both type A and type B events for one week?

Question 46 options:

	<$2000
	Between $2000 and $4000
	Between $4000 and $6000
	Between $6000 and $8000
	>$8000

Question 47 (1 point)

Maintenance of Production Facility

A production facility has several 3-D printing machines which need maintenance for two reasons. Maintenance type A: a sensor may have detected a fault, e.g. an oil leak. Maintenance type B: the quality of the printed product is unacceptable. Each maintenance requirement occurs at random and independently of other requirements for maintenance, with characteristics summarised in the following table:

Maintenance Type	Average rate of occurrence per week totalled over all 3-D printing machines in the production facility	Cost of maintenance
A	6.7 (maintenance events per week)	$430 (per maintenance event)
B	2.1 (maintenance events per week)	$2600 (per maintenance event)

What is the probability of more than 2 maintenance events of type B in one week?

Question 47 options:

	<0.2
	Between 0.2 and 0.4
	Between 0.4 and 0.6
	Between 0.6 and 0.8
	>0.8

Question 48 (1 point)

Maintenance of Production Facility

A production facility has several 3-D printing machines which need maintenance for two reasons. Maintenance type A: a sensor may have detected a fault, e.g. an oil leak. Maintenance type B: the quality of the printed product is unacceptable. Each maintenance requirement occurs at random and independently of other requirements for maintenance, with characteristics summarized in the following table:

Maintenance Type	Average rate of occurrence per week totalled over all 3-D printing machines in the production facility	Cost of maintenance
A	6.7 (maintenance events per week)	$430 (per maintenance event)
B	2.1 (maintenance events per week)	$2600 (per maintenance event)

What is the standard deviation of the number of maintenance events of type A in one week?

Question 48 options:

	<2
	Between 2 and 4
	Between 4 and 6
	Between 6 an 8
	>8

Answer 1

45.

For half a week, Average rate of occurrence maintenance events of type A = 6.7/2 = 3.35

Assuming Poisson distribution, X ~ Poisson(3.35)

probability of exactly 6 maintenance events of type A in half a week

= P(X = 6) = exp(-3.35) * 3.35^6 / 6! = 0.0689

Between 0.06 and 0.08

46.

Total Cost = 430A + 2600B

Variance of Total Cost = Var(430A + 2600B)  

For Poisson distribution, Var(X) = Average rate

Standard deviation of Total Cost = = 3928.719

Between $2000 and $4000

47.

Probability of more than 2 maintenance events of type B in one week

= P(Y > 2) where Y ~ Poisson(2.1)

= 1 - (P(Y = 0) + P(Y = 1) + P(Y = 2))

= 1 - [exp(-2.1) * 2.1^0 / 0! +  exp(-2.1) * 2.1^1 / 1! + exp(-2.1) * 2.1^2/ 2! ]

= 1 - (0.1224564 + 0.2571585 + 0.2700164)

= 0.3504

Between 0.2 and 0.4

48.

Standard deviation of the number of maintenance events of type A in one week

= = 2.59

Between 2 and 4