# Six Sigma and Simulation: Part 2

By Jeff Joines (Associate Professor In Textile Engineering at NCSU)

This is the second of the three part series on Six Sigma, Lean Sigma, and Simulation. The first part explained the Six Sigma methodologies. Recall the goal of the DMAIC continuous improvement methodology is to control/reduce process variability of a current process or product while the Design for Six Sigma process DMADV is used to design a new process or product with minimal variability before creation. Simulation modeling can be employed in almost every phase of either methodology.

Define

Six Sigma practitioners have to estimate the cost savings for each project to be certified or justify the project typically. However, most of these cost forecasts are made on point estimates of key parameters (i.e., raw material cost, customer/product demand, cost of capital, currency rates, etc.). By employing Monte Carlo simulation, variability and/or ranges on these point estimates can be employed to provide a more reliable estimate. Along these lines, several projects have been proposed and simulations can be utilized to help management perform project selection based on resource constraints and objectives.

Analyze and Improve

During the Analysis and Improve phases, Design of Experiments (Full, Fractional, Mixed, etc.) is the most common tool utilized which provides a base line to illustrate improvement when changes are made as well identifying factors of interest to control or change. The normal baseline measure is defined as the process capability (Cpk) which is an indication of the ability of a process to produce consistent results – the ratio between the permissible spread and the actual spread of a process. The Cpk index takes into account off centeredness and defined as the minimum of (USL-Mean)/ 3? or (Mean-LSL)/ 3? where USL and LSL are the upper and lower specification limit. A six sigma process is normally distributed with a Cpk value greater than 1.5.

Using the real system is better in terms of capturing all complexities, interactions, etc. However as simulation practitioners, we recognize when that might be possible or viable. The following lists examples where simulation modeling in terms of Monte Carlo or process simulation can be used.

• If the product or process does not exist as is the case in a Design for Six Sigma, simulation models can be used to ascertain capability of a new process and product before implementation. For example, tolerance stack up of individual parts or processes can be determined. Take parts or processes which are within tolerance individually (e.g., bearing and a shaft) but the assembly process might not be capability owing to the tolerance stack up problem which occurs in manufacturing, service, and transactional processes.
• The cost of performing a DOE with replications is too high (e.g., raw material cost, cost of shutting down current process). We have worked with companies in developing process and Monte Carlo simulation models that could be used to determine their capabilities and ascertain the potential improvement in their changes.
• The time of running the set of experimentation makes it impractical to determine the baseline or ascertain the improvements of a process. While working with a large company and their six sigma process improvement team with a complex global supply chain, one of their projects was to reduce inventories of a series of products with a ten to twelve week lead time. The team had to evaluate six inventory policies, indentify which one of three suppliers was best, etc. The DOE with sufficient replications would have taken years to complete and made the project useless without the simulation model. Also, most of the data driving the model was based on lead-times which are not normally distributed.
• Think of systems where there are multiple processes that feed one another (e.g., departments, plants, etc.) which contain only five or six factors each. Transfer functions can be generated from a traditional DOE on each individual process but not the entire system. A simulation model can be used to combine each individual transfer function into determining the capability of the whole system as well as testing a wider range of values.
• There are several environments, where performing a DOE is impractical or impossible. For example, we have trained dozens of people associated with hospital systems from around the country in Six Sigma. Simulation modeling and analysis allows these practitioners to be able ascertain process capability with a model because the real system cannot be used since patient care is at stake. Other environments where we have used simulation modeling instead of the real system is in processes which are transactional like the banking or insurance industries.

Control

Simulation can also be used as a process control aid as the process is being implemented to determine potential problems.

Hopefully it is apparent that simulation experts already posses the skills that can greatly help Six Sigma projects. These types of projects are not unique but just general simulation models we are know how to build. They only require us to learn the Six Sigma language as well as the need to calculate Cpk statistics. I find it easier to work with Six Sigma people because of their statistical training for understanding input and output analysis even though they typically have only used the Normal distribution. In Six Sigma and Simulation: Part 3, the use of simulation in the Lean Sigma world will be addressed.