One-sided tolerance interval in a two-way balanced nested model with mixed effects

In many research areas (such as public health, environmental contamination, and others) one deals with the necessity of using data to infer whether some proportion (%) of a population of interest is (or one wants it to be) below and/or over some threshold, through the computation of tolerance interval. The idea is, once a threshold is given, one computes the tolerance interval or limit (which might be one or two - sided bounded) and then to check if it satisfies the given threshold. Since in this work we deal with the computation of one - sided tolerance interval, for the two-sided case we recomend, for instance, Krishnamoorthy and Mathew [5]. Krishnamoorthy and Mathew [4] performed the computation of upper tolerance limit in balanced and unbalanced one-way random effects models, whereas Fonseca et al [3] performed it based in a similar ideas but in a tow-way nested mixed or random effects model. In case of random effects model, Fonseca et al [3] performed the computation of such interval only for the balanced data, whereas in the mixed effects case they dit it only for the unbalanced data. For the computation of twosided tolerance interval in models with mixed and/or random effects we recomend, for instance, Sharma and Mathew [7]. The purpose of this paper is the computation of upper and lower tolerance interval in a two-way nested mixed effects models in balanced data. For the case of unbalanced data, as mentioned above, Fonseca et al [3] have already computed upper tolerance interval. Hence, using the notions persented in Fonseca et al [3] and Krishnamoorthy and Mathew [4], we present some results on the construction of one-sided tolerance interval for the balanced case. Thus, in order to do so at first instance we perform the construction for the upper case, and then the construction for the lower case

Online weight estimation in a robotic gripper arm

This paper presents a novel methodology for online, fast and accurate weight estimation technique in a robotic gripper arm. The laboratory setup is inspired from several real life applications of weight estimation in moving cranes, e.g. loading containers in a shipyard, iron scrapping in steel industry, etc. The weight needs to be estimated within a specified time interval and within a tolerance interval for accuracy. The results indicate that the proposed method is suitable for this kind of application and an improvement of 30% has been achieved compared to the current state of work

Model based control strategies for a class of nonlinear mechanical sub-systems

This paper presents a comparison between various control strategies for a class of mechanical actuators common in heavy-duty industry. Typical actuator components are hydraulic or pneumatic elements with static non-linearities, which are commonly referred to as Hammerstein systems. Such static non-linearities may vary in time as a function of the load and hence classical inverse-model based control strategies may deliver sub-optimal performance. This paper investigates the ability of advanced model based control strategies to satisfy a tolerance interval for position error values, overshoot and settling time specifications. Due to the presence of static non-linearity requiring changing direction of movement, control effort is also evaluated in terms of zero crossing frequency (up-down or left-right movement). Simulation and experimental data from a lab setup suggest that sliding mode control is able to improve global performance parameters

Inertial tolerancing and capability indices in an assembly production

International audienceTraditional tolerancing considers the conformity of a batch when the batch satisfies the specifications. The characteristic is considered for itself and not according to its incidence in the assembly. Inertial tolerancing proposes another alternative of tolerancing in order to guarantee the final assembly characteristic. The inertia I2 = σ2 + δ2 is not toleranced by a tolerance interval but by a scalar representing the maximum inertia that the characteristic should not exceed. We detail how to calculate the inertial tolerances according to two cases, one aims to guarantee an inertia of the assembly characteristic the other a tolerance interval on the assembly characteristic by a Cpk capability index, in the particular but common case of uniform tolerances or more general with non uniform tolerances. An example will be detailed to show the results of the different tolerancing methods

Tolerance Limit-based Estimation of the Proportion of Non-conforming Parts in a Multiple Stream Process

The conventional way to characterize the proportion of non-conforming parts in a process is to calculate process capability indices and transform them into a ratio. These widely used indices are able to give digestible information about the ratio of non-conforming parts if some assumptions are fulfilled. A correct estimation method should be based on the output distribution of the process, and the uncertainty of the parameter estimates should be considered, as well. In this article, a special case of the output distribution is examined: a mixture of normal distributions is considered. In practice, this output distribution appears if a multiple stream process is investigated. The novelty of this study is to apply the tolerance interval-based estimation method for the proportion of non-conforming parts in a case study of a multiple stream process and to qualify the limitations of the proposed estimation method. A simulation study is performed to investigate the bias, mean square error, and root mean square error of the estimates from the two estimation methods (process performance index-based and tolerance interval-based) for different sample sizes for each stream (N ). It was found that, if it may be assumed that the speed of the streams is equal in the case of the sample sizes investigated (N = 25, 50, 100 per head), the proposed (tolerance interval-based) method overestimates the proportion of non-conforming parts while the conventional (process performance index-based) method underestimates it. The tolerance-limit based estimation method has asymptotically better properties than the process performance index-based estimation method

A proposition of 3D inertial tolerancing to consider the statistical combination of the location and orientation deviations

Tolerancing of assembly mechanisms is a major interest in the product life cycle. One can distinguish several models with growing complexity, from 1-dimensional (1D) to 3-dimensional (3D) (including form deviations), and two main tolerancing assumptions, the worst case and the statistical hypothesis. This paper presents an approach to 3D statistical tolerancing using a new acceptance criterion. Our approach is based on the 1D inertial acceptance criterion that is extended to 3D and form acceptance. The modal characterisation is used to describe the form deviation of a geometry as the combination of elementary deviations (location, orientation and form). The proposed 3D statistical tolerancing is applied on a simple mechanism with lever arm. It is also compared to the traditional worst-case tolerancing using a tolerance zone