Reliability prediction using Weibull analysis

Reliability Estimation Using Weibull Analysis for Automotive Power Window Regulators

In one of my previous experiences as a Test Engineer for automotive power window regulators, I encountered a unique requirement from a customer that challenged our usual testing approach. The customer specified that our product must meet a reliability of 90% with a confidence level of 50%.

This was surprising, as we had never faced such a requirement before. Typically, customers would only specify the number of cycles the product needed to endure, and we would perform tests up to those cycles, reporting pass or fail based on the results. This new approach introduced a fresh perspective on how reliability is evaluated, requiring us to dive deeper into statistical analysis.

After discussing this with our team, one of our colleagues, who had previous experience with such reliability specifications, guided us through the process. He helped us understand how to evaluate reliability at a specified confidence level and how to design tests accordingly. This experience not only met the customer's needs but also introduced us to a structured way of integrating Weibull analysis into our testing methodology.

Methodology for 90% Reliability with 50% Confidence Level

Let’s walk through the steps of the methodology we used to calculate the reliability of our product:

Step 1: Choose the Number of Samples

We decided to select 6 samples based on the testing capabilities available.

Step 2: Run the Test Until All Samples Fail

We performed the test until all 6 samples had failed, noting the failure cycles for each sample.

Step 3: Rank the Failure Cycles

We ranked the failure cycles in ascending order. For example, the failure cycles could be: 40,000, 35,000, 50,000, 65,000, 55,000, and 45,000.

Step 4: Calculate the Median Rank

We calculated the median rank for each sample using the median rank formula.

Step 5: Calculate ln(ln(1/(1−MedianRank))

This step involves calculating the natural log of the natural log of the inverse of (1 − median rank).

Step 6: Calculate ln(Cycles)

We also calculated the natural logarithm of the failure cycles for each sample.

Step 7: Plot the Graph in Excel

In Excel, plot the graph with the following axes:

• X-axis: ln(Cycles)
• Y-axis: ln(ln(1/(1−MedianRank)))

This graph will show the relationship between failure cycles and the median rank, which is essential for analyzing the product's reliability.

Step 8: Calculate the Slope (B)

By fitting a linear trendline to the graph in Excel, we obtained the slope, which represents the beta shape factor (B). The slope indicates how the failure rate changes over time (whether it’s constant, increasing, or decreasing).

Step 9: Calculate Reliability

Finally, we used the following formula to calculate the reliability at the desired confidence level:

R=(1−C)1nLB R = (1 - C)^{{1}/{nLB}}

Where:

• C = Confidence (50%)
• n = Number of samples (6)
• L = Customer Usage (Number of cycles the product wishes to meet, e.g., 50,000)
• B = Beta shape factor (calculated from the graph)

By applying this formula, we determined whether the product could meet the 90% reliability requirement at the specified confidence level.

Conclusion

Incorporating Weibull analysis into our testing methodology helped us meet the customer’s reliability requirement and provided a structured approach to evaluating product reliability in a statistical context. This process enables manufacturers to set realistic expectations for product lifespan and ensure their products meet or exceed customer expectations.