Estimating the number of product failures: a theoretical approach
Amniattalab, Ayda (2018) Estimating the number of product failures: a theoretical approach. [Thesis]
In this thesis, we propose a stochastic process describing the total number of failed items under warranty over time. This stochastic process consists of a sales process represented by a stochastic point process and a process counting the total random number of repairs applied to an arbitrary item of this product. Combining these two stochastic processes yields a representation of the counting process of the total random number of failed items returned to the manufacturer within their warranty period. To fit the proposed parametric model to a large data set we need to estimate separately the intensity measure of both the failure and sales process. To estimate the intensity measure of the cumulative sales process we use some well known parametric functions and apply linear regression techniques. Also, under the assumption that a repair does not change the age of the particular item of the product it can be shown that the counting process of failures is a non-homogenous Poisson process and so we need to estimate the cdf of the time to the first failure. Since our data set is censored we apply the Maximum Likelihood principle for censored data and use as a parametric class the class of Weibull distributions. Our approach serves as an alternative to the time series based approaches for cases where item tracking information is available.
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