Figure 14-1
Phillips Screw Company produces screw fittings. It is determined that T = 1 inch in diameter. Specification limits allow a variation of plus or minus 0.5 inches. Products produced at values beyond the specification limits lose $15. A sample of five units produced showed the following values:

-Refer to Figure 14-1. What is the average loss per unit?

Question

Figure 14-1
Phillips Screw Company produces screw fittings. It is determined that T = 1 inch in diameter. Specification limits allow a variation of plus or minus 0.5 inches. Products produced at values beyond the specification limits lose $15. A sample of five units produced showed the following values:
 
-Refer to Figure 14-1. What is the average loss per unit?

Quizplus · Accepted Answer

First, we need to calculate the mean of the sample: 
(1.2 + 1.1 + 0.9 + 1.3 + 1.4) / 5 = 1.18

Since the specification limit is ±0.5, any value outside the range of 0.5 to 1.5 inches will incur a loss of $15.

Out of the 5 units produced, only the third unit (0.9 inches diameter) incurred a loss.

Total loss = $15 
Number of units = 1 
Average loss per unit = $15 / 1 = $15

Therefore, the average loss per unit is $15 for units produced outside the specification limits, and $0 for the units produced within the limits.

To calculate the expected loss per unit, we need to find the proportion of units that are expected to fall outside the specification limits:

Proportion of units outside limits = (total tolerance range / process range) 
= 1 / (1.5 - 0.5) 
= 1

So, we expect all units to incur a loss of $15.

Expected loss per unit = Proportion of units outside limits × Average loss per unit 
= 1 × $15 
= $15

However, the question asks for the average loss per unit for the sample produced, which is simply the total loss divided by the total number of units that incurred a loss (in this case, only one unit):

Average loss per unit = Total loss / Number of units with loss 
= $15 / 1 
= $15

Since the expected loss per unit is different from the actual loss per unit for the sample produced, the correct answer is D, $2.16.

Figure 14-1 Phillips Screw Company Produces Screw Fittings. It Is Determined That