## 7 Concluding Remarks and Discussion  
The reliability assessment of products is a critical activity for different processes and systems, thus it is important to consider that the analyzed data are free of any contamination that can cause inaccurate conclusions. Furthermore, as the measuring process is an integral part of reliability testing, it is also important to establish some control schemes over the measuring system's performance. Such that, a certain performance of the system leads to a predetermined performance of the product's reliability assessment. In the case of degradation modeling, the measuring error causes variation in the first-passage time distribution. Based on this, it may be expected that the reliability assessment under contaminated data may be underestimated. In this article, it is considered that a gamma process governs the observed degradation with measurement error, and it is assumed that the error can be described by a Gaussian distribution with mean zero and standard deviation \(\sigma\). Thus, the true degradation is obtained by deconvoluting the observed degradation and the measurement error. In order to control the measurement error in terms of the reliability assessment, the first-passage time distributions of the observed and the true degradation are compared in terms of some proposed indices. A general scheme was proposed to establish the differences between distributions in order to obtain the desired accuracy of the assessment. From the case study, it was observed that depending on the reliability estimation of interest; it is possible to establish a maximum level of the standard deviation of the measurement error. This enables to control the measuring system. It is essential to define critical levels of the indices for the first-passage time distributions, such that a maximum level of error can be established. These critical values can be defined by considering the maximum difference between the reliability estimation of interest between the true and contaminated first-passage distributions. Following the proposed scheme, the permissible error can be determined as described in the case study. Furthermore, a scenario  
Figure 9: Comparison of reliability functions for the observed degradation and the true degradation under Gaussian and logistic measurement errors. to deal with non-Gaussian measurement errors is presented to extend the deconvolution approach applicability. There are several opportunities for further research in the proposed scheme of this article. Although the gamma process has been widely used in degradation modeling, other stochastic processes can be used to describe the observed degradation, such as the inverse-Gaussian process, geometric Brownian motion and the Wiener process. The deconvolution modeling proposed in this paper can be extended by considering any of these processes. Although, the implementation for some process may result more complex, as the CFs of the inverse Gaussian and geometric Brownian motion do not have closed expressions, which impose interesting challenges for the implementation of the deconvolution approach. Furthermore, other sources of uncertainty can be included in the degradation modeling. It has been found that the consideration of random effects accounts for the accuracy of the reliability estimations. Indeed, these sources imply certain mathematical complexity which should be added to the computational complexity of the deconvolution approach. For this, different deconvolution algorithms proposed in the literature may be considered to obtain approximations of true variables obtained from measurement error contaminated processes. The CV, variation, mean and percentiles are considered as indices to measure the differences between first-passage time distributions. Nevertheless, some other metrics can be studied with the same purpose.