How Long Should an Electric Scooter Guarantee Last to Cover 5% Failures?

If you're a manufacturer of electric scooters, determining the optimal length of a guarantee to cover a specific percentage of product failures is crucial for customer satisfaction and cost management. In this article, we explore how long of a guarantee you should offer if you aim to replace 5% of the scooters that fail, given that the average life of an electric scooter is 15 years with a standard deviation of 1.75 years. We’ll walk through the necessary calculations assuming a normal distribution for the scooter lifespans. Let's delve into the statistical approach to find the ideal guarantee period.

Understanding the Normal Distribution

First, it's essential to understand that the lifespans of electric scooters are normally distributed. This means the data follows a bell-curve shape, where most values cluster around the mean, and fewer values lie at the extremes. The mean life of the scooters is 15 years, and the standard deviation, which measures the spread of the data, is 1.75 years.

Using Z-Score to Determine Guarantee Period

A Z-score can help identify the point at which 5% of the scooters will have failed. The Z-score represents the number of standard deviations a data point is from the mean. You can find the Z-score corresponding to the 5th percentile in a standard normal distribution table or using a statistical calculator.

For a one-tailed Z-score reflecting the bottom 5%, the Z-value is approximately -1.645.

Applying Z-Score Calculation

Using the formula to convert Z-score to a lifespan value:

$$
X = μ + Zσ
$$

Where:

• X is the lifespan value,


• μ (mu) is the mean lifespan (15 years),


• Z is the Z-score (-1.645), and


• σ (sigma) is the standard deviation (1.75 years).

Plugging in the values:

$$
X = 15 + (-1.645 * 1.75) = 15 - 2.87875 ≈ 12.12
$$

Conclusion

Based on the calculation, the manufacturer should offer a guarantee of approximately 12.12 years if they are willing to replace 5% of the scooters that fail. This ensures that only about 5% of the scooters, which are expected to fail earlier than the guarantee length, will be eligible for free replacement.

Do remember to also consider factors like potential changes in technology, model upgrades, and customer expectations when setting the guarantee period.