In this work, we show the influence of sensor system measurement uncertainties to sensor system reliability and ways to meet reliability targets. A general model to handle measurement uncertainties is defined and the according influence to reliability is presented, which is defined as probability of meeting specification requirements. Initial step is to optimize sensor systems concerning lowest influences of sensor system parameter fluctuations to the measurement uncertainty using statistical optimization methodologies. In case the influence of unknown nuisance parameters cannot be sufficiently suppressed, such parameters may be additionally measured in order to further reduce measurement uncertainties. The remaining uncertainties are again addressed using statistical optimization methodologies. Finally, measurement uncertainty also affects the reliability of such a system. For sensor systems in safety critical applications it may thus be required to include measures such as redundancy. This is also included in the investigations. Further examples for explained optimization methodologies of measurement uncertainty reduction are presented.

Introduction

Our modern world is fully digitized: starting from consumer goods such as mobile phones, TVs and body scales, going to vehicles such as cars, airplanes and trains to automated production lines based on human-robot-interaction. All of these electronic devices need a way to interface to the real, physical world: commonly, sensor systems present a way to realize this interfacing. These sensor systems present the means for electronic systems to comprehend their environment. Depending on the application, it is more or less important that this comprehension is truthful and dependable. As soon as a physical quantity of interest and its representation (analog or digital) from sensor systems differ too much in value, this is either useless – in case of the smart watch which does not reliably sense our heart frequency – or dangerous in case of the accelerometer which is in charge of the airbag control. Sensor system reliability is thus a major concern, not only in terms of customer satisfaction, but also for safety reasons. In this work, we consequently present means to define and quantize reliability by introducing a general mathematical model. Ways to improve the sensor systems’ reliability are presented: one way is to use optimization methods of the existing systems using statistic optimization techniques [1], another way is to additionally measure known, correlated disturbing influences and compensate those [2, 3], and also a combination of both approaches is possible. Where the effort is justified by the application, redundancy can be a way to improve the sensor system reliability, especially for safety requirements. The latter is often the case in standardized safety related automotive applications [4]. 1.1. Sensor system definition A general abstraction of a sensor system is illustrated in Fig. 1. Here θ is the physical quantity of interest. Depending on the employed sensor effect, this is further converted into the electrical domain by the sensor front-end or subsequent circuitry. It is now an (analog or digital) electrical quantity and represented by the Random Variable (RV) Y. A RV basically is a function which, besides possible deterministic variables, also depends on random, i.e. unknown, inputs. In system theory, such functions, which describe the way of how a system acts on a quantity of interest, are often also called transfer-functions. Here, it is assumed that Y depends on systematic influences (bias-voltage, calibration-parameters, stress etc.) [2, 3] as well as random influences (noise, Electro Magnetic Interference (EMI) etc.) introduced by the sensor front-end and/or respective circuitry. To reconstruct the physical quantity from the electrical representation Y, a mapping function as part of the digital signal processing is necessary. This mapping function is termed an estimator for the physical quantity of interest and its sensor system output value is often denoted as θ ̂to indicate the relation to the true physical quantity of interest (θ). This estimation even can be performed inside the sensor system with electrical output values interpreted in the same physical quantity as θ [۱].