Predicting the Quality Defect Rate: A Stochastic Approach from Automotive Field Data

SUMMARY & CONCLUSIONSThe risk assessment based on the analysis of field failures is a crucial aspect of the warranty cost calculations. In the automotive industry, the statistical approach relies mainly on the Weibull analysis, utilizing both failed and in-service parts (suspensions) to estimate failure rates. The extrapolation of the Weibull shape parameter (the beta value) is a robust indicator of the failure rate and the associated failure mechanism. When beta is inferior to 1.5, the parts usually fail due to early failure supposedly due to quality issues; the failure rate is decreasing, since all non-quality parts are due to be recalled within a relatively short period of time. Beta superior to 1.5 indicates a fast degradation, which is often associated with design flaws; the failure rate is increasing, and because it is a design issue, virtually all the parts in the field are at risk of failure. In the case that beta = 1 the failure rate is constant, symptomatic of multiple failures occurring during the warranty period.This paper addresses the situation when non-quality issues provoke a fast degradation of the components, therefore showing an increasing failure rate (beta > 1,5 and small Weibull scale parameter eta within the WR period). The Weibull analysis with the probability of part failure is more complex, because the risk assessment must take into consideration that not all the parts are subject to the quality issues. On the other hand, an appropriate probability of failure (absolute number of parts affected) needs to consider the amount of non-quality parts that have been delivered. This percentage is often difficult to quantify, and it can vary by production period. Some tools can distinguish between the two populations to provide estimation and the distribution of each population (ie. mixed Weibull estimation) when data are mature enough.In this study, a new methodology permits to estimate with good accuracy the percentage of non-quality parts within the total population of product in service in the early stage when most of the signal is representing one population, thus allowing a better extraction of the number of failed parts within the warranty period, and a more accurate estimation of the warranty costs. A statistical model based on the Wiener process (diffusion model) is used to determine whether the data exhibits a trend and quantify if there is a threshold of the diffusionprocess. This threshold represents the percentage of non-quality parts, framed within confidence intervals to reflect the inherent uncertainties associated with limited data and the stochastic nature of the process.A numerical example illustrates how the methodology is practically applied on a set of automotive warranty data. This approach enables a more informed and timely assessment of quality issues, facilitating proactive interventions and mitigating potential risks.In conclusion, the new method developed promises a more precise estimation of warranty costs, enabling proactive interventions and effective mitigation of potential risks associated with quality issues.