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Increasing Failure Rate Detector For Systematic Early Detection Of Warranty Claims

IP.com Disclosure Number: IPCOM000249089D
Publication Date: 2017-Feb-03
Document File: 2 page(s) / 445K

Publishing Venue

The IP.com Prior Art Database

Abstract

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Increasing Failure Rate Detector For Systematic Early Detection Of Warranty Claims

Warranty spend of technical products is typically driven by product inherent reliability. Reliability has several aspects, among them product failures resulting from manufacturing issues – typically showing up at low time in service – as well as durability issues (due to lack of design robustness), which, by definition, only show up at high time in service and are hardly visible at low time in service (see Figure 1).

Figure 1: Durability issues result in Increasing Failure Rates (IFRs) and can be interpreted as “time bombs” w.r.t. warranty claims and spend.

Issues due to “Increasing Failure Rates” (IFRs) can only be addressed after detection – the earlier the better. Assume a 5% failure probability at the end of a warranty period of 2 years, 1000 products potentially affected built per day and 20 days of production per month: In this (simplified) scenario, the ability to identify this problem one month earlier than today would result in 1000 prevented warranty claims with both their financial bottom line impact and the accompanying loss of customer satisfaction due to lack of basic quality.

Once detected, statistical theory of “Survival Analysis” allows adequate mathematical modelling of inherent failure rates and thus estimation of resulting claims over time – but a practical, easy-to-apply way allowing systematic scanning of a warranty database (even in a “rough” manner) was missing. How to detect issues deserving systematic modelling?

From statistical theory, the Weibull distribution is known to describe most reliability phenomena reasonably well. While there might be better fits for some situations, the Weibull model has the ability to capture decreasing, constant and increasing failure rate trends due to its mathematical flexibility. It is furthermore known that for Weibull distribution with parameters α and β and Rb,a(t)referring to the reliability at a point of time t, a plot of ln(t) versus ln(-ln(Rb,a(t))) reveals a straight line, as

ln[-ln(Rb,a(t))] = b*[ln(t)] – b*ln(a)

is both the description of a straight line with slope β and intercept –β*ln(α) and equivalent to the reliability description of the Weibull distribution, Rb,a(t) = exp[-(t/a)b].

It should be noted that the quality of the “straight line fit” as described by the value of the coefficient of determination, R2, can be interpreted as a measure of quality of the Weibull fit to the underlying (warranty) data (values of R2 range from 0 to 1, in case of a perfect fit, R2=1).

 

Figure 2: The appropriate plot reveals a straight line (left) with a slope greater than one indicating an IFR; utilization of the Weibull parameters allows prediction of reliability at 24 months in service. As the data is described very well by the straight line (R2=0.9975!), the model describes the reliability function trend extremely well.

If the Weibull distribution fits the data...