An appliance manufacturer wants to contract with a repair shop to handle authorized repairs. The company has an acceptable range of repair time from 50 minutes to 90 minutes. Two firms have submitted bids for the work. In the evaluation trail, one firm had a mean repair time of 74 minutes with standard deviation of 4.0 minutes, and the other firm had a mean repair time of 72 minutes with a standard deviation of 5.1 minutes. Which firm would you choose, and why?
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To compare the two firms and determine which one to choose, we need to consider their mean repair times and the acceptable range provided by the appliance manufacturer.
Firstly, let's calculate the lower and upper limits of the acceptable range:
Lower Limit = 50 minutes
Upper Limit = 90 minutes
Now, let's examine the performance of each firm based on their mean repair times and standard deviations.
Firm 1:
Mean repair time = 74 minutes
Standard deviation = 4.0 minutes
Firm 2:
Mean repair time = 72 minutes
Standard deviation = 5.1 minutes
To make an informed decision, we can employ a process called Six Sigma, which allows us to assess the variability and performance of each firm within the acceptable range.
Using Six Sigma, we can calculate the process performance (in terms of how many standard deviations an average repair time is from the nearest acceptable limit). This is known as the Process Sigma Level (Z-score). A higher Z-score indicates better performance.
To calculate the Z-score, we can use the formula:
Z = (X - μ) / σ
Where:
Z = Z-score
X = Average repair time
μ = Mean repair time
σ = Standard deviation
Let's calculate the Z-scores for each firm:
Firm 1 (Z1):
Z1 = (90 - 74) / 4.0 = 4.0
Firm 2 (Z2):
Z2 = (90 - 72) / 5.1 ≈ 3.53
Now, let's analyze the Z-scores:
Comparing the Z-scores of Firm 1 and Firm 2, we see that Firm 1 has a higher Z-score (4.0) than Firm 2 (3.53). This implies that Firm 1 performs better in terms of repair time within the acceptable range specified by the appliance manufacturer.
Based on this analysis, it would be advisable to choose Firm 1 for the authorized repair work, as their performance is closer to the upper limit of the acceptable range while still maintaining a strong Z-score.
Therefore, Firm 1 should be chosen because it has a mean repair time closer to the acceptable upper limit and exhibits better performance within the specified range compared to Firm 2.