## 1 Introduction
It has only be considered to model the measurement error in degradation processes based on the inverse Gaussian and Wiener processes [30]. Furthermore, [PERSON] et al. [30] demonstrated the applicability of deconvolution to obtain reliability assessments without measurement error, but a control scheme over the performance of the measurement system is not considered. Important information about the deconvolution process can be found in [PERSON] [31], [PERSON] and [PERSON] [32] and [PERSON] [33]. The importance of considering the measurement error in the modeling of degradation processes relies on obtaining accurate reliability assessments. However, it is also important to establish a control scheme over the measurement error, such that a desired estimation can be obtained under a controlled level of error. This means that a certain range of the observed measurement error caused by measuring devices, methods and environmental conditions can be established and maintained in order to achieve a desirable reliability assessment [4]. Usually, the reliability assessment based on degradation modeling is carried out by considering the first-passage time distribution of the degradation paths [34]. Thus, some variation of the first-passage times is expected from the observed degradation and the true degradation. This means that a certain level of permissible measurement error leads to a certain range of variation of the parameters of the first-passage time distribution. By controlling such variations, it is possible to obtain accurate life estimations, which are quite important in the definition of maintenance programs [35] or in the establishment of product warranties. Other approaches for reliability monitoring are based on control charts [36], these procedures are important to study the deterioration of systems which leads to determine maintenance policies and process availability improvement [37, 38, 39], as discussed in the degradation modeling with measurement error. The main focus of this article is to establish a scheme to control the measurement error to obtain certain reliability assessments under a defined performance of the measurement system, where the performance is defined by the measurement error. The proposed scheme consists of first estimating the observed degradation parameters with measurement error under the gamma process. Then, the measurement system is assessed via a repeatability and reproducibility (R&R) study in the aims of obtaining information about the total variance contribution of the measuring process. It is considered that the measurement error is normally distributed with mean zero and that an estimation of the standard deviation \(\sigma\) can be obtained from the total variation of the measurement system captured by the R&R study. The deconvolution approach is then performed to obtain the true degradation. As the function of the true degradation does not have a close analytical expression, we fitted the deconvoluted true degradation to different stochastic processes. Once the best fitting stochastic process is selected, the true first-passage distribution is characterized and compared to the observed first-passage time distribution by using different indices. Such indices are based on the coefficient of variation, the variance, the mean and the percentiles of the two distributions. By considering a critical value for any of the four indices, a certain level of performance of the coefficient of variation, variance, mean and percentile can be achieved under a certain value of \(\sigma\). The defined value of \(\sigma\) can be used to control the measurement system in order to obtain a desired accuracy of the reliability assessment. The proposed scheme is implemented in a case study which consists of crack propagation data of an electronic device. The rest of the article is organized as follows. In Section 2, the modeling of the observed degradation based on a gamma process is presented. In Section 3, the method to obtain the true degradation based on deconvolution is introduced.