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Save Money By Understanding Variance and Tolerancing

By Stuart Kay Team Consulting Ltd, Ickleton, Cambridge, UK

Article first appeared in Medical Device Link, June 2007

Manufacturing processes are inherently variable, which results in component and assembly variance. Unless process capability, variance and tolerancing are fully understood, incorrect design tolerances may be applied, which will lead to more expensive tooling, inflated production costs, high reject rates, product recalls and excessive warranty costs. A methodology is described for correctly allocating tolerances and performing appropriate analyses.

Effects of incorrect tolerances

Tolerances on component and assembly dimensions are crucial to the success of a medical device.

Incorrectly specified tolerances can lead to more expensive tooling, high reject rates, product recalls and substantial warranty costs. However, specifying tolerances correctly requires an understanding of process variance and process capability and this is not always available to the engineer or draftsman working on the product or process.

Process variation, typically the result of small changes in the tooling, process parameters and materials, means there will always be variation in the measured dimensions of components. Similarly, assemblies exhibit variance, partly because of the variance they inherit from the constituent components and partly because of variance in assembly processes.

A medical device's performance can be strongly influenced by component and assembly variance, thus every functionally critical component and assembly dimension is toleranced. The intention is that every device will assemble and function as intended, providing the tolerances are not exceeded because of the process variance.

However, an incomplete understanding of tolerancing and the related subject of process variance can lead to inappropriate tolerances being applied. Even if undertaken with the best of intentions, a subsequent tolerance analysis will give misleading results and wastes resources (remember the adage: garbage in, garbage out). Furthermore, tolerance analyses can be poorly executed on sound tolerances. One of the most common errors is to calculate the worst case tolerance stacks and then revise the component tolerances so that the assembly will "always fit together." This can result in extremely tight tolerances on the component dimensions, which increases tooling and production costs. Indeed, the processes may be inherently incapable of consistently producing parts or assemblies within the stated tolerances. Although 100% inspection can identify failed assemblies, this is costly, time-consuming, and the lost production can be hugely expensive. In some cases, the problem may not be apparent immediately, which will lead to failures in the field and, ultimately, product recalls and substantial warranty costs.

Performing a worst case tolerance analysis can therefore be a costly mistake. The underlying reasoning is that manufacturing processes produce parts with part-to-part and batch-to-batch variance, and it is extremely unlikely that assemblies will be produced that consist entirely of components in their worst-case condition. This may sound like common sense, but worst-case tolerance stack analyses are still undertaken on numerous occasions and these commonly result in poorly allocated tolerances that cause significant quality-related production problems.

Optimum timing

Variance- and tolerance-related problems often result in high reject rates that erode profit margins. In some cases this occurs during scale-up, but it can also emerge after a device has been in full production for a period of several years. It is, therefore, prudent for companies undertaking due diligence or risk management exercises to include an assessment of the capability of a medical device's design to ensure there are no potential variance- or tolerance-related problems.

These exercises are highly worthwhile, yet the best time to pay attention to variances and tolerances is when developing new designs or processes. In fact, they can be considered as early as the conceptual design phase, when risks can be evaluated prior to further investment being made. Applying a rigorous method to allow an informed decision to be made is much more likely to yield long-term benefits than taking decisions based on experience or "guesstimates." It should not be forgotten that most of a product's ongoing quality-related costs are fixed during the earliest stages of a device's development.

Variance and tolerancing clearly have to be considered together, yet variance also goes hand-in-hand with process capability. A detailed discussion of process capability is outside the scope of this article, but it must be appreciated that component and assembly dimensions cannot be properly toleranced without taking into account process capability.

How to optimise tolerances

A methodology has been developed for allocating and optimising tolerances and performing appropriate analyses (Figure 1). The methodology, which makes use of mathematical modelling and commercially available software, builds on a thorough knowledge of toolmaking, manufacturing processes and the principles of process capability. Clearly, the methodology is not applied to noncritical dimensions and assemblies. When it has been used, no toolmaker or moulder has raised any objections or been unable to achieve the given tolerances.

The methodology takes a statistical approach, based on predicted process capability, in which the component and assembly tolerances are allocated in accordance with a realistic representation of the manufacturing processes involved. Commercial software packages are used: one "as is" to allocate process-capable tolerances and others as tool kits for building mathematical models that enable statistical analyses and optimisations to be performed.

Starting with the identification of the performance objectives of the critical assemblies, and therefore the critical dimensions, rational mathematical models are developed, based on the nominal dimensions and tolerances.

Next, using Tolerance Capability Expert1 (TCE), an expert system software package (Capra Technology, Walkington, UK), the user selects the proposed production process, material and design characteristic to predict the likely process capability for a given dimension and tolerance. Importantly, the software manufacturer says analysis shows a 98% correlation between the predicted results and data from statistical process control records.

After using TCE to confirm the original or revised tolerances, mathematical modelling and analysis are performed in Excel2 or Mathcad.3 If the overall predicted process capability is inadequate with respect to the stated objectives, one or more aspects of the design or process will need to be reconsidered before revised data can be analysed.

Excel spreadsheets are used for relatively simple models and have the advantage that the models can be easily shared among the project team. Mathcad is used for more complex models or scenarios; again, the files can be shared, but this software is not as widely used as Excel. Depending on the analysis required, it may be that one or more models, simulations and analyses are necessary. Both Excel and Mathcad can be used for performing statistically based tolerance analyses such as Root Sum Squared4 based on process capability data, as well as assessments such as variance sensitivity, process capability and tolerance bands.

Mathcad's greater capability also supports the programming of high-level equations such as for three-dimensional, time-based, spring-loaded or power-dependent systems, and it enables Monte Carlo simulations5 to be performed for multi-dimensional tolerance analyses. Complex assemblies, systems and processes can therefore be investigated, and multi-dimensional assessments performed such as process capability for normal and nonnormal distributions.

Once a mathematical model has been created, it provides opportunities for optimisation without reverting to unrealistically tight tolerances. This enables selected parameters to be varied with the aim of achieving the specified goal. Each iteration is calculated automatically by the PC-based software and enables a "better" product to be designed, whether the goal relates to an aspect of performance, weight, cost or any other parameter that is built into the model.

Extending uses

The methodology described above has been used, where appropriate, in the design and development of medical devices. It is also applicable throughout the lifecycle of a medical device. It can be applied during the conceptual design and proof of principle phases (typically to establish a design's manufacturability) and the detailed design phase, through scale-up and during full production, often as part of a due diligence exercise or to investigate quality-related problems. Quality-orientated programmes such as Six Sigma, Lean Manufacturing and the Process Analytical Technologies initiative from the United States Food and Drug Administration are currently important topics for manufacturers of medical devices. Regardless of which of these are adopted, an understanding of variance and tolerancing will be highly beneficial.

Furthermore, the approach is not restricted to the dimensions of components and assemblies; it can be applied to almost anything that can be modelled mathematically. For example, Mathcad has been used to analyse variance in the inhalation airflow resistance of a medical device, and to investigate the ranges of thermal comfort experienced in a clean room. The methodology could also be applied to processes such as drug production, for example, as part of a risk analysis or troubleshooting exercise.

The author's company has invested resources in developing the Excel and Mathcad tools; other organisations could replicate the work using these or similar software packages. TCE is readily available, but currently it is not widely used in medical device development. It should also be noted that commercial packages exist for tolerance analysis, either as standalone tools or as add-on modules within suites of computer-aided design software, although experience has shown these to be restrictive compared with bespoke mathematical modelling. Moreover, they do not all assist with the allocation of process capable tolerances. Without this starting point, there is a significant risk that considerable effort will be wasted in the pursuit of results that turn out to be meaningless or misleading. All of which underlines the importance of having a sound understanding of process capability, variance and tolerancing to improve quality and reduce cost.

Stuart Kay is Senior Engineering Consultant at Team Consulting Ltd, Abbey Barns, Duxford Road, Ickleton, Cambridge CB10 1SX, UK, tel. +44 1799 532 700, e-mail: stuart.kay@team-consulting.com; www.team-consulting.com

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