Output from a process contains 0.05 proportion of defective units. Defective uni

Question

Output from a process contains 0.05 proportion of defective units. Defective units that go undetected into final assemblies cost $20 each to replace. An inspection process, which would detect and remove all defectives, can be established to test these units. The inspector, who can test 18 units per hour (which matches the current production rate), would be paid $8 per hour, including fringe benefits. Assume that the line will operate at the same rate (i.e., the current production rate) regardless of whether or not the inspection operation is added a-1. Without the inspector, what is the current hourly cost of defects? (Round your answer to 2 decimal places.) Cost per hour a-2. Should an inspection station be established to test all units based on costs alone? OYes O No a-3. If the inspection operation is added, what would be the cost to inspect each unit? (Round your answer to 2 decimal places.) per unit b. What would be the benefit (or loss) from establishing the inspection process? (Input the amount as a positive value. Round your answer to 2 decimal places.) (Click to select) per unit Benefit Loss

Explanation / Answer

Defect Proportion = 0.05

Cost to replace a defective piece = 20

Production Rate = Inspection Rate = 18 units/hour

Cost of Inspection Personnel = 8/hour

No. of defects per hour = 18 * 0.05 = 0.9

A1) Hourly Cost of defect without inspector = No. of defects per hour * Cost of Replacement = 0.9* 20 = 18

A2) Yes, in this case, we should take the decision of establishing inspection station on the basis of costs.But, in general, we usually don't find uniform defect rate in a production, so just considering the costs would not be enough.

A3) 0.9 defect is expected to occur in one hour and inpector needs to be paid 8 per hour

Thus 1 defect would cost through inspector =(8/0.9)= 8.88

B) As the cost per unit through inspector is less than the cost of replacement per unit, we shall achieve a benefit of = 20 - 8.88 = 11.12

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USL = 5.005

LSL = 4.995

Mean = 5.001

Std Dev = 0.04

Cpu = (USL-Mean)/ 3*Std Dev = 0.033

Cpl = (Mean-LSL)/ 3*Std Dev = 0.05

Cpk = Min(Cpu, Cpl) = 0.033

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