Growth Curve Analysis of Cumulative Automobile Defects

Abstract

We study properties of cumulative defects for an industrial production through growth curve model in presence of nondecaying correlation structure within the number of successive defects accumulated over time. In automobile industry incidence per thousand vehicles (IPTV) is computed as number of failures observed in a month divided by sale quantity of a specified production batch for a specific lag period (from production to sale); the ratio is then multiplied by 1,000 to be called IPTV. For a batch of sold items it is seen that IPTV and the cumulative IPTV up to a time point may be approximated by Weibull distributions to a first degree. Such intriguing phenomena rules out independence of variables, as Weibull distribution is not closed under convolution. Postulating a simple model we show that such phenomena may be attributed to the presence of long range correlation in reported defects over consecutive time segments of sold objects from a production batch due to a common cause that regulates the growth pattern of cumulative IPTV. The observed correlation structure may be explained by the model.