Model tolerance

Figure 2.12 Modelling tolerance risk using a sguared relationship...

These assumptions are fairly restrictive and difficult to fidfil in practice. However, the CMB model tolerates some deviations, which increase the final uncertainties of the source eontribution estimation (Watson et al., 1998). 

Kinematic tolerancing is one of many techniques proposed to model tolerances (Hong and Chang 2002). In kinematic tolerancing the tolerance chain is treated as a kinematic loop with virtual links, with the understanding that the movements of these links are actually small displacements of the part s geometric features (here called functional element, or FE) within their prescribed tolerance zones. 

Placing proposed tolerances at locations demanded by functions of the product by use of an assembly model. Tolerance type is identified according to the selected geometric elements and features. 

The above-proposed approaches allow the accuracy of external calibration to be approached without access to the sample position. The exact method of calibration selected will depend on the applications requirements and modeling tolerances (e.g. PLS for isomer-splitter or band-area integration for DLC measurements). 

Dynorphin may also influence nociception at the spinal level. The levels of prodynorphin mRNA and immunoreactive dynorphin increase in the chronic inflammatory arthritic model (158). Dynorphin also inhibits morphine or P-endorphin-induced analgesia in naive animals and enhances analgesia in tolerant animals, indicating that this peptide may have a regulatory role in opioid analgesia (159). This effect does not appear to be mediated by a classical opioid receptor, since des-tyrosine dynorphin, which does not bind to opioid receptors, also antagonizes morphine analgesia (160). 

The novel agent sulofenur (69) has entered clinical trials based on its broad spectmm antitumor activity in tumor models, its unusual mechanism of action, and its lack of cross-resistance to other agents (33). In Phase I clinical trials, the dmg was well tolerated and some clinical responses were noted. 

Neural networks have the following advantages (/) once trained, their response to input data is extremely fast (2) they are tolerant of noisy and incomplete input data (J) they do not require knowledge engineering and can be built direcdy from example data (4) they do not require either domain models or models of problem solving and (5) they can store large amounts of information implicitly. 

To determine if a process unit is at steady state, a program monitors key plant measurements (e.g., compositions, product rates, feed rates, and so on) and determines if the plant is steady enough to start the sequence. Only when all of the key measurements are within the allowable tolerances is the plant considered steady and the optimization sequence started. Tolerances for each measurement can be tuned separately. Measured data are then collec ted by the optimization computer. The optimization system runs a program to screen the measurements for unreasonable data (gross error detection). This validity checkiug automatically modifies tne model updating calculation to reflec t any bad data or when equipment is taken out of service. Data vahdation and reconciliation (on-line or off-line) is an extremely critical part of any optimization system. 

Figure 2.2 (a) Tolerance versus production costs of various processes (b) comparison of cost-tolerance models (Dong, 1993)... 

Note that the squared relationship which was initially used to model the degree of difficulty in obtaining more capable tolerances for a given manufacturing route and product design is being returned by the power law. Similarly, a relationship between the process capability index Cp and q for the components analysed is shown in... 

The initial design is analysed using CA at a component level for their combined ability to achieve the important customer requirement, this being the tolerance of 0.2 mm for the plunger displacement. Only those characteristics involved in the tolerance stack are analysed. The worst case tolerance stack model is used as directed by the customer. This model assumes that each component tolerance is at its maximum or minimum limit and that the sum of these equals the assembly tolerance, given by equation 2.16 (see Chapter 3 for a detailed discussion on tolerance stack models) ... 

Today s high technology products and growing international competition require knowledgeable design decisions based on realistic models that include manufacturability requirements. A suitable and coherent tolerance allocation methodology... 

The choice of tolerance model must be both realistic and applicable as a design tool... 

The role of advanced statistical and optimization methods in the tolerance model... 

Sufficient data on process distributions and costs must be collated to characterize manufacturing processes for advanced tolerance models. 

Proper assignment of tolerances is one of the least well-understood engineering tasks (Gerth, 1997). Assignment decisions are often based on insufficient data or incomplete models (Wu et al., 1988). The precise assignment of the component tolerances for this combined effect is multifarious and is dictated by a number of factors, including ... 

The combination of the cost model and the optimization method will then give an augmented model from which the allocation of the component tolerances are optimized for competitive results. Optimization methods have also been extended to include procedures that select the most cost-effective manufacturing process for each component tolerance in the assembly stack (Chase and Parkinson, 1991). 

Research looking into tolerance allocation in assembly stacks is by no means new. A current theme is towards an optimization approach using complex routines and/ or cost models (Lin et al., 1997 Jeang, 1995). Advanced methods are also available, such as Monte Carlo Simulation and Method of Moment. ) (Chase and Parkinson, 1991 Wu et al., 1988). The approach presented here is based on empirical process capability measures using simple tolerance models, cost analogies and optimization... 

Many references can be found reporting on the mathematical/empirical models used to relate individual tolerances in an assembly stack to the functional assembly tolerance. See the following references for a discussion of some of the various models developed (Chase and Parkinson, 1991 Gilson, 1951 Harry and Stewart, 1988 Henzold, 1995 Vasseur et al., 1992 Wu et al., 1988 Zhang, 1997). The two most well-known models are highlighted below. In all cases, the linear one-dimensional situation is examined for simplicity. 

In general, tolerance stack models are based on either the wor.st case or statistical approaches, including those given in the references above. The worst case model (see equation 3.1) assumes that each component dimension is at its maximum or minimum limit and that the sum of these equals the assembly tolerance (initially this model was presented in Chapter 2). The tolerance stack equations are given in terms of bilateral tolerances on each component dimension, which is a common format when analysing tolerances in practice. The worst case model is ... 

The statistical model makes use of the fact that the probability of all the components being at the extremes of their tolerance range is very low (see equation 3.2). The statistical model is given by ... 

The bilateral tolerance stack model including a factor for shifted component distributions is given below. It is derived by substituting equations 3.11 and 3.18 into equation 3.2. This equation is similar to that derived in Harry and Stewart (1988), but using the estimates for Cp and a target Cp for the assembly tolerance... 

In addition to understanding the statistical tolerance stack models and the FMEA process in developing a process capable solution, the designer should also address the physical assembly aspects of the tolerance stack problem. Any additional failure costs determined using CA are independent of whether the tolerances assigned to the assembly stack are capable or not. As presented in Chapter 2, the Component... 

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