Determining the Optimal Warranty Period for Electric Scooters Based on Lifespan Expectancy

When it comes to providing excellent customer service and guarantee, manufacturers must carefully consider the warranty period they offer on their products. For electric scooters, which have an average lifespan of 12 years with a standard deviation of 1.5 years, determining the appropriate length of a guarantee can be crucial for maintaining customer satisfaction while also managing costs. Here we will explore how to calculate the optimal duration of this warranty if a manufacturer is prepared to replace 3% of the scooters under guarantee that fail. ### Understanding the Distribution of Lifespan
Electric scooters' lifespans follow a normal distribution, allowing us to use statistical methods to determine the guarantee length. The normal distribution is symmetrical, and the standard deviation tells us how spread out the distribution is around the mean. #### Calculating the Guarantee Period Using Z-Scores
To calculate the duration of a guarantee in a way that only 3% of scooters are expected to fail, we need to determine the 'z-score' that corresponds to the 97th percentile of a normal distribution (since 3% fail, we are covering up to 100% - 3% = 97%). In standard normal distribution terms, this roughly equates to a z-score of 1.88.
With the following formula, we can calculate the guarantee cutoff point:

guarantee cutoff point = mean lifespan + (z-score × standard deviation)
Using our values:

guarantee cutoff point = 12 + (1.88 × 1.5)
This gives us a guarantee cutoff point of approximately 14.82 years. Therefore, a manufacturer should offer a guarantee of up to nearly 15 years to ensure that no more than 3% of the electric scooters fail within the warranty period. ### Implications for Manufacturers
Offering a guarantee that spans nearly 15 years places an emphasis on quality and customer loyalty. It signals that the manufacturer is confident in their product's longevity, and it ensures that customers feel secure in their purchase. However, manufacturers must also weigh the costs of such guarantees, as well as the advancements in technology that may make electric scooters obsolete well before the end of the warranty period. In conclusion, while a nearly 15-year guarantee can be a powerful marketing tool and a testament to product quality, manufacturers need to consider their whole product lifecycle and market trends when determining the warranty length for electric scooters.