Size matters

Q: What are some key measurables that determine what size project is necessary to remedy issues related to cost of poor quality (COPQ)? It is very easy to create a large project to solve a small problem.

Andrew Levine
Greenville, SC

A: It is actually the magnitude of certain measurables themselves—the benefits—that helps justify the desired size or cost of a project. When considering these project-structure issues, a good place to start is with general types of problems, solutions and methods. Project size is tied to what types of problems and potential solutions are within the project’s scope.

There are two types of problems: special cause and common cause. You are either eliminating an unusual situation or trying to improve on the usual situation itself. Special-cause problems require bringing a process into control using Six Sigma tools, such as root cause analysis and classic problem-solving techniques. Common-cause problems can be more diverse and challenging, and can be placed into three categories:

  1. Improving the current process, or optimizing, may require statistical tools (such as design of experiments), lean tools (such as elimination of waste) or both.
  2. Reengineering adds another level of complexity because subject matter knowledge of the process or technology combined with design for Six Sigma may be needed to improve one or more elements of the process.
  3. Innovating or creating involves coming up with an entirely new process, possibly using an even higher level of subject matter expertise, as well as systematic creativity and idea-generation tools.

The project charter is a good place to identify which type of problem you’re dealing with, define the specific scope and identify resource needs.

COPQ, which consists primarily of appraisal, internal failure and external failure costs, is actually a potential measurable. The further downstream that failures or losses are caught, the more they affect the COPQ and justify a larger project.

For example, a project to reduce internal failures, such as scrap and rework, detected during inspection would theoretically provide a smaller benefit than one to reduce external failures, such as customer complaints, which may affect full replacement costs, lost business and legal or regulatory issues. The higher the potential COPQ savings, the more likely a larger project can be justified.

It’s also worth discussing what exactly is meant by a "big" project. In management’s eyes, project size is related to investment. How much is the organization willing to invest in the people, cost of capital investments and raw materials, and time (charged project hours, as well as calendar time)?

The answer, of course, is that it depends on the potential benefits. Other than decreasing various aspects of COPQ, benefits could include the generation of new business or the preservation of existing business via the elimination of risks.

Measurables commonly include forecasted return on investment, which is the ratio of the project’s benefits versus the cost. Six Sigma practitioners often use the Pareto Priority Index (PPI):

 savings x probability of success 
   cost x time to completion

Including probability of success is not trivial. In addition to distinguishing among projects, you can strategically increase applied resources as a project’s success becomes more certain.

I have used PPI to prioritize many projects mathematically, while management added another low, medium or high multiplicative factor to the equation for intangibles, such as strategic alignment and the potential translatability of the solution to other processes or businesses.

To characterize a project more accurately, you can use historical information—if it’s available—to estimate standard times and resources for different types of projects, tasks and tools. Average or median estimates can then be calculated and applied to predict future project requirements.

Scott A. Laman
Senior manager and Six Sigma Black Belt
Teleflex Inc.
Reading, PA

High and low

Q: Normally, Cp is higher than Cpk. But, in some cases, it is possible for Cpk to be higher than Cp. In which situation is it possible that the Cpk value is higher than the Cp value? Could you provide a real-world example?

Sjaak Reijnders
Eindhoven, The Netherlands

A: Assuming a normal distribution of process variation (if necessary, a proper transform is applied to the process variable) in the case of a two-sided specification, the process capability indexes are defined as

in which µ is the mean and s is the standard deviation of the process or product characteristic, USL is the upper specification limit and LSL is the lower specification limit.

When the process mean is at the midpoint of the specification range,

Cpk and Cp are identical, and when the process mean is at a distance from the midpoint of specification range, Cpk is less than Cp. The relationship between the two indexes is for the same process or two different processes having the same specification ranges and standard deviations.

The process capability is characterized by the Cp index when the process mean is at the midpoint of the specification range, and it is characterized by the Cpk index when the process mean is at a certain distance from the midpoint.

Wider specification range, smaller process variation standard deviation and smaller deviation of the process mean from the midpoint of the specification range increase the respective process capability indexes and proportion of the process output within the specification limits.

Because Cpk is less than or equal to Cp for processes with the same specification ranges and standard deviations, Cpk gets larger than the original Cp only when the specification range is sufficiently increased or the process standard deviation is sufficiently reduced to overcome the reduction of the process capability caused by the deviation of the process mean from the midpoint of the specification range.

For example, with a USL of 100, LSL of 90, and s of 1, the midpoint of the specification range is

With no deviation of the process mean from the midpoint of the specification range, the mean is 95 and

Under the normal distribution, 573 parts per billion are out of the specification limits. With a 2.5-unit deviation of the process mean from the midpoint of the specification range, the mean is 97.5 and

With such a process mean shift from the midpoint of the specification range, approximately six parts per thousand—a million times more than the centered process—are outside the specification limits.

The Cpk in this example is two times smaller than the Cp is. Using the calculation of Cpk centered around a mean of 95 gives you a Cpk and Cp of 1.67.

Now, consider another process that has the same midpoint of 95, the same standard deviation of 1 and the same mean of 97.5 but a wider specification range, with a USL of 103.5 and an LSL of 86.5. For these specification limits,

This makes Cpk larger than Cp, which was 1.67 in the previous example for the centered process with a tighter specification range, and the separation increases as the specification range gets wider. A similar effect is achieved with the original specification limits and the process standard deviation reduced to less than 0.5.

The practical conclusion from this discussion is that to achieve the required high process capability with a given specification range, the process shift from the midpoint of the specification range and its random variation need to be minimized through improvements of the process and of its operation.

The proportion of the process output within specification limits can be calculated for the normal distribution case in Microsoft Excel with the following entry:

normdist(USL, µ, σ, true) – normdist(LSL, µ, σ, true).

Estimates of the process mean and standard deviation can be used in the calculation, along with the t-distribution for estimation of the proportion of the process output within the specification range. These results can also be generalized to one-sided specifications.

Jeffrey E. Vaks
Roche Molecular Diagnostics
Pleasanton, CA

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