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Multi-Vari Studies, How to Quickly Find 85% of the Variation in a Product or Service

The name “Multi-Vari” was given to this form of analysis by L.A. Seder in his classic paper “Diagnosis with Diagrams,” which appeared in Industrial Quality Control in January and March 1950.  The premise is to utilize graphics to understand where the variation in a process exists.  Is it excessive variation within a single piece, excessive variation from piece to piece, or is the variation excessive from time to time.  If we are relating this to service delivery substitute “service delivery to customers”, “service delivery from customer to customer”, and “service delivery from time to time” in the previous sentence.

Multi-Vari Studies are often classified as either a “Nested Design” or a “Crossed Design.”  In the Nested Design the data is collected without making changes to the process to investigate where the variation is coming from.  It could be positional which is within piece variation, it could be cyclical which is consecutive piece-to-piece variation, or it could be temporal which is time-to-time variation such as day-to-day, or week-to-week.  The following graphic is an example where we are trying to find the source of process variation with regard to warp in a glass container.

From this Nested Design Multi-Vari Chart we can clearly see that Machine Section 7 is very different than any other section on the machine.  Section 7 becomes the target for variation reduction.  The question becomes, “Why is it so different than the rest of the machine?”

In the Crossed Design the plan is to test changes to the process in a balanced manner following an on or off strategy.  In the Crossed Design either 2 or 3 potential variation contributor process variables are studied at 2 different settings.  Analysis of Variance is often added as part of the study to provide detailed statistics that support what the graphic analysis portrays.  The ANOVA provides the verdict of “guilty beyond a shadow of a doubt” to support what we see graphically.  The following graphic is an example where we are trying to minimize the time it takes to boil a cup of water in a microwave oven.

From this Crossed Design Multi-Vari Chart it is clear that to minimize the time to boil a cup of water in a microwave oven the container should be rotated, located 4 inches off center, and covered.  To add further proof to this graphic finding an ANOVA (analysis of variance) was conducted with the following results.

The sources of variation are Cover, Rotate, and Location.  Each are significant with p values that are less than .0009 (assume worst case for unknown digit of 9) which equates to a confidence level of at least of 99.91%.

Multi-Vari Studies provide a graphic means to quickly find 85% of the variation in a product or service.  I think you will find this technique to be useful.

What is the difference between Process Sigma and Process Capability?

In both cases of Process Sigma and Process Capability we are talking about performance relative to the Customer’s requirements.  Is there a difference?  Is one measure better than the other?  These are good questions which you will be able to answer by reading on.

The difference between the Six Sigma metric of Process Sigma and Process Capability relates to the definitions of these performance metrics.  In both cases the Customer Specifications are compared to process performance.  For metrics that can be measured on a continuous scale the process mean and standard deviation must be calculated.  If the metrics from the process are discrete, or attributes, then the percent defective is calculated.  In either case the process performance as measured on a control chart should exhibit only natural random patterns of variation, or what is often called common cause variation over time.

Process Sigma
Process Sigma is defined by numeric levels that are related to a process’s output of defects per million opportunities.  Defects are defined as any failure to meet the customer’s specifications.  Process yield is used to look up the Process Sigma level from a table.  Yield is based on Defects (D), Units Processed (N), and the number of Opportunities (O) for a defect to occur.  Once the yield is calculated the Process Sigma can be found in the table below.


Find the Process Sigma level in the table above.

If the process output can be measured on a continuous scale the process average and standard deviation are used in a formula that compares the average to the closest specification, whether it is the Upper Specification or the Lower Specification we choose the one closest to the process average.  Basically we are making this a one sided specification.  The standard normal distribution is used to estimate the defect rate which can then be converted to yield and use the above table to look up the Process Sigma level.
The other method is to calculate the Z statistic which estimates the number of standard deviation units the average is away from the closest specification which is based on the standard normal distribution.  We then add a 1.5 sigma shift to the calculated Z statistic which gives us the Process Sigma level directly.  The 1.5 sigma shift has been a matter of contention, but it is part of the definition of Process Sigma.  The following is the formula.

The definition of Process Sigma is that at a level of 6 on the scale there will be only 3.4 defects per million opportunities.  The process is assumed to remain stable over time and if it drifts in one direction at a time of 1.5 sigma there will be no more than 3.4 defects per million under the tail of the distribution outside of the Customer’s Specification.  When we calculate the Z statistic we add the 1.5 sigma shift to give us the Process Sigma level directly.

Process Capability
Process Capability assessment begins with control charts to evaluate the stability over time for the process.  For the Process Capability study to be meaningful the process must exhibit only common cause variation, which are natural patterns of random variation.

In the case of Attribute, or discrete variables, data the Process Capability becomes the centerline of the Control Chart, or the average p, c, or u depending upon the chart being used.  In the example below the average p, or fraction non-conforming, is 0.076, or 7.6% defective.  The chart is in statistical control so the capability is the overall process average of percent defective.

In the case of continuous variables data the mean and standard deviation from the stable, or in statistical control, process comes into play.  We will describe 2 of the many Process Capability Indices.  The first is the Cp which compares total process variation to the total width of the specification.  The second is Cpk which takes into consideration centering of the process within the specification so we look at ½ of the process variation compared to the closest specification limit.

The Cp formula below divides the specification width by the measured process spread of 6 standard deviations.  A fully capable process has a Cp = 1.33 or greater.

The Cpk formula below divides the absolute value of the difference between the process average and the closest specification by ½ of the measured process spread of 3 standard deviations.  A fully capable process has a Cpk = 1.33 or greater.

The Cp value indicates how capable a process can become if it is perfectly centered.  The Cpk value indicates how much work is needed to get centered.  In the following table notice that for a Cpk = 1.33 the Process Sigma = 5.5.  A process that operates at a Process Sigma = 6 has a Cpk = 1.50.  The Z Value is the number of standard deviation units away from the specification when the data is converted to a standard normal distribution.

Table of conversions from Z to Cpk and Process Sigma.

Both measures of performance use that same statistics to be computed.  Whether you prefer Process Capability or Process Sigma the key is to apply the metrics consistently.  To be valid your process must be in a state of statistical control and exhibit only common cause variation.

SIPOC Approach to As Is Analysis

SIPOC is an acronym that stands for Suppliers, Inputs, Process Steps, Outputs, and Customers.  This high level process mapping method is ideal for diagnosing and analyzing the current state, or As Is condition of any business process.  The following outlines the SIPOC approach to As Is analysis and improvement solution identification.

The first task is to assemble a small team, 3-5 people, who play roles within the process under analysis that are familiar with the activities that take place within the process.  You may find that this team collectively knows the process from end to end even if some of the team members individually do not.  The team identifies the one key performance metric that defines success or failure for the process.

SUPPLIERS are the functional groups that provide the essential ingredients for the process to perform.  Create this list may include actual supplier companies that are contracted for goods and services as well as the internal groups and individuals that provide the things that make the process tick.  You may miss a few initially, but you can always add suppliers during the process mapping activity when they are identified.  If the process needs something, which Supplier provides it?

INPUTS are the essential ingredients provided by the Suppliers.  Those ingredients could be materials, goods, services, data, instructions, decisions, documents, analyses, or whatever the process requires.  For each Supplier make a list of all the inputs they provide.

PROCESS STEPS are the 5 high level steps from the beginning to the final outcome for the process.  Start with Step 1 and Step 5.  That defines the end to end scope of the As Is process analysis.  You can think of the process steps as the 5 key value stream steps.  Fill in Steps 2 through 4 after Step 1 and 5 are defined.  The performance metric should be measureable at Step 5 to determine process success or failure.

OUTPUTS are the result of each individual step in the process.  After completing Step 1 what is the thing that is generated by this process step.  In some cases a process step may have multiple outputs.  When you list the outputs they are in groups associated with their respective process step and should flow in order from 1 through 5.

CUSTOMERS are the recipients of the process outputs.  The process step generates something and it goes to a functional group which is either internal to the process or external to the process.

With the SIPOC Process Map completed the team collectively has a better overall understanding of the process from end to end.  Now is the time to challenge the process to identify where the issues are.  What are the causes of either success or failure based on the key performance metric?  Brainstorm using the Cause and Effect, or Fishbone Diagram.  This technique identifies the potential causes of the process issues.

To develop solutions the SCAMPER brainstorming technique is very useful.  In this structured method the SCAMPER acronym is used to challenge the process for improvements by asking what could be Substituted, Changed, Adapted or Amplified, Modified, Put to other uses, Eliminated, or Replaced / Removed / Rearranged.  Now you know the SIPOC approach to As Is analysis and improvement solution identification.

Designing Environmental Sustainability Programs using Process Design for Six Sigma

Environmental Sustainability is in the best interest of the Global Economy and Global Corporate Citizenship.  More and more companies are global in nature especially when you consider their supply chains and the total life cycle of their goods and services.  Environmental consciousness is increasing in importance and a key for competing in the global economy.

Customizing your company’s approach to defining and applying environmental best practices requires a systematic approach for process design.  Process Design for Six Sigma (DFSS) follows a five phased approach, namely Define, Measure, Analyze, Design, and Validate (DMADV).

The Define Phase is the Development Project Definition.  In this phase the scope, or depth and breadth, of the Environmental Sustainability Program is defined.  Here is where the resources are committed to the project, the project is planned, and the review points with specific deliverables are defined.

The Measure Phase is Requirements Definition.  In this phase the Voice of the Customer (VOC) is captured which in turn is translated in the requirements for the Environmental Sustainability Program.  The VOC comprises your suppliers, your company, your customers, and the countries where you conduct business.  This comprehensive view of the VOC requirements drives the right sizing of the program.  A Functional Model of what Environmental Sustainability has to accomplish and provide is aligned and prioritized using the VOC.  At this stage requirements are fully defined
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The Analyze Phase is better described as the Conceptual Design.  What must be accomplished to meet the VOC has been documented with the prioritized functional model.  To meet the functional requirements processes are designed at the conceptual level using the SIPOC (Suppliers, Inputs, Process Steps, Outputs, and Customers) Process Mapping method.  In this method only five process steps are addressed which keeps the maps at a high level.  Information System requirements are defined to support each SIPOC Process that has been designed.  Performance Metrics are also defined.  Estimates of cycle frequency, cycle time, and staffing for each SIPOC all also determined.  Organizational requirements are conceptualized as well.

The Design Phase is Detailed Design.  The conceptual designs are now converted into detailed process maps.  This is the future state design of the Environmental Sustainability Program’s processes for execution.  Pilot testing takes place at this stage along with finalizing organizational requirements.  Work instructions, procedures, and policies are documented for efficient execution of the processes that will drive the Environmental Sustainability Program.

The Validate Phase is the final phase of DMADV.  In this phase the new processes go through final testing and debugging of support systems, validation of performance metrics, and implementation on a full scale.

Process Design for Six Sigma is the structured approach for any organization to determine just what Environmental Sustainability means for them.  Process DFSS guides the development of the processes that will meet your Environmental Sustainability goals and objectives.

Going Green with Six Sigma

The efficient approach to Going Green for any company is to follow the five phased DMAIC improvement process of Six Sigma.  Going Green can mean different things to different organizations.  You will have to define what Going Green means for your organization.
Defining your problems with waste management and setting your goals for waste reduction and savings is the first step.  The structured approach of the Define Phase in a Six Sigma project is the best approach to accomplish this.  The deliverables are your Problem Statement, Goal Statement, Constraints, Assumptions, Guideline’s for the Team, Green Requirements, and a Project Plan.  Types of waste that are often tackled are:

• Cardboard,
• Wood Pallets and Crates,
• Banding,
• Plastic,
• Rags,
• Cans and Bottles,
• Paper,
• Metal,
• and Hardware. 

For these types of waste establish the baseline of Total Pounds of Waste, the Good is Recycled Pounds, the Bad or Defect is Land Fill Pounds.  Use this to set your process yield and process sigma level in the Measure Phase.

The Measure Phase for Going Green is all about establishing how you will measure your waste as previously defined and establishing your organization’s baseline performance.  Without the baseline performance you won’t be able to measure the green impact and savings from your Going Green Six Sigma Project.  One approach is analogous to the Mass Balance equation where Mass is conserved between inputs and outputs which must remain equal.

The Mass Balance Equation
Total of Material and Consumables Input = Output of Saleable Goods and Services + Waste to Atmosphere + Waste to Water Supply + Waste to Landfill + Hazardous Waste + Recyclables 
Your organization will have to determine the extent to apply this equation.

In the Analyze Phase the Team evaluates the waste categories and how and where they are created.  Is it a process issue, a policy issue, or just that we have always treated waste that way?  Once you understand where it is coming from then you can develop the creative solutions that will transform landfill waste into recyclable waste.  Depending upon the scope of the project the team may also be addressing other waste components of the mass balance equation.

In the Improve Phase the Team investigates alternatives for how to handle the multiple waste categories and how to minimize their creation.  Many items that were always sent to the landfill if separated can become recyclable.  In many cases recyclables can generate revenue.  The costs of storage and hauling can then be reduced.  This in turn changes the ratios of Total Waste to Recyclable Waste and to Landfill Waste.  Going Green has cost reduction and revenue enhancement benefits.

In the Control Phase the Team implements the policies, procedures, and work instructions to handle the waste categories.  Arrangements are made with waste and recycling organizations to handle the waste categories per the improvements identified.  Ongoing measurements are put in place to continue to drive landfill waste reduction and increase recyclables.  Similarly if the project scope was larger the other categories of waste would be included as well.  This is how Going Green is accomplished with the Six Sigma DMAIC approach to solving problems.

Tracking Performance over Time

Tracking performance over time can be accomplished using either one of two methods which are Run Charts or Control Charts.  Both methods use time as the baseline and the performance measure as the measurement that is tracked over time.  The major differences in the methods relate to the measures of demarcation on the charts.  Run Charts have a center line that represents the mid point of the measurement that is being tracked.  Control Charts have a center line that represents the average of the measurement that is being tracked and lines above and below the centerline that are estimates of 3 standard deviations about the average of the measurements.

In both of the charts time is the X axis.  The data is plotted in succession over time.  The charts can be segmented by specific time periods such as setting the baseline and after improvements have been implemented.  You will easily see the before and after results.  We can measure the difference between the before average and the after average to calculate the magnitude of the improvement.

Tracking of performance is also a control for maintaining the gains from the improvements.    The Run Chart or the Control Chart provides a method to continuously evaluate performance and point out when corrective actions should be taken or when the process should be left alone.

Whenever we contemplate improving a process the baseline for the critical performance metric(s) must be established before any corrective actions are taken.  By doing this you will always be able to evaluate the impact of the improvements by measuring from the baseline to the future state of process performance.  In the rare case where the corrective action doesn’t work the tracking charts will point that out quickly so an alternative action can be taken.  I am sure that you can remember when a great idea just did not work so it is always best to track performance to validate the actual impact of our improvement efforts.