C. A company is reviewing its policy of putting each sub-assembly bought in from outside through a detailed inspection process on delivery. The firm can either inspect or not inspect. The sub-assembly may either come up to the required quality standard (90 % of the time), or fail to do so (10 % of the time).
It costs K10 to inspect a sub-assembly and another K10 to put right any defect found at that stage. If the sub-assembly is not inspected and is then found to be faulty at the finished goods stage the cost of rework is K40.
Advise the firm what to do
To advise the firm on what to do, we need to consider the costs and probabilities associated with different options. Let's break down the options and calculate the expected costs.
Option 1: Inspect every sub-assembly
- Cost of inspection: K10 per sub-assembly
- Probability of finding a defect: 10% (0.10)
- Cost of defect found during inspection: K10
Expected cost per sub-assembly = Cost of inspection + (Probability of finding a defect * Cost of defect found during inspection)
Expected cost per sub-assembly = K10 + (0.10 * K10)
Expected cost per sub-assembly = K10 + K1
Expected cost per sub-assembly = K11
Option 2: Do not inspect sub-assemblies
- Probability of a sub-assembly being faulty: 10% (0.10)
- Cost of rework if a faulty sub-assembly is found: K40
Expected cost per sub-assembly = Probability of a sub-assembly being faulty * Cost of rework if faulty
Expected cost per sub-assembly = 0.10 * K40
Expected cost per sub-assembly = K4
Comparing the expected costs:
- Option 1 (Inspect every sub-assembly): K11 per sub-assembly
- Option 2 (Do not inspect sub-assemblies): K4 per sub-assembly
Based on the calculations, it is more cost-effective for the company to not inspect the sub-assemblies and bear the cost of rework if a faulty sub-assembly is found at the finished goods stage. Therefore, the company should choose Option 2 and not inspect the sub-assemblies.