Question

A company currently using an inspection process in its material receiving department is trying to install an overall cost reduction program. One possible reduction is the elimination of one inspection position. This position tests items for which the probability of a material defect averages 0.01. By inspecting all items, the inspector is able to remove all defects. The inspector can inspect 50 units per hour. The hourly rate including fringe benefits for this position is $10. If the inspection position is eliminated, defects will go into product assembly and will have to be replaced later at a cost of $11 each when they are detected in final product testing.

Assume that the line will operate at the same rate (i.e., the inspection rate) if the inspection operation was eliminated.

a-1. If the inspector position is eliminated, what will the hourly cost of defects be? (Round your answer to 2 decimal places.)

Cost per hour            $

a-2. Should this inspection position be eliminated based on costs alone?

	Yes
	No

b. What is the cost to inspect each unit? (Round your answer to 2 decimal places.)

Cost per unit            $

c. Is there benefit (or loss) from the current inspection process? How much? (Input all amounts as positive values. Round your answers to 2 decimal places.)

	Hourly	Per unit
(Click to select)LossBenefit	$	$

Answer 1

Probability of a material defect = 0.01

Rate of inspection = 50 units / hour

Hourly cost of inspection = $10

Penalty cost for defect at final product testing = $11

Ans a1)

Number of units tested per hour = 50

Average number of defective material used for production per hour = Probability of defect *  Number of units tested per hour

= 0.01 * 50

= 0.50

Average hourly cost of defects = Average number of defective material used for production per hour * Penalty cost for defect at final product testing

= 0.5 * 11

= $5.50

Ans a2)

Average hourly cost of defects without inspection = $5.50

Hourly costs of inspection = $10

Yes, it would thus be advisable to remove the inspection position as it reduces the overall cost of the production line from $10 to $5.50

Ans b)

Cost to inspect each unit = Hourly cost of inspection / Number of units inspected per hour

= 10 / 50

= $0.20

Ans c)

Hourly cost of current inspection = $10

Hourly cost without inspection = $ 5.5

Hourly loss from the current inspection process = $10 - $5.5 = $4.5

Cost per unit without inspection = Average hourly cost of defects / Number of units inspected per hour

= 5.5 / 50

= $0.11

Loss per unit from the current inspection process = Cost to inspect each unit - Cost per unit without inspection

= $0.20 - $0.11

= $0.09