September 20, 2004
Six Sigma and CMM
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Jack Horgan - Contributing Editor

by Jack Horgan - Contributing Editor
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Six Sigma began in 1986, when Bill Smith, a senior engineer and scientist at Motorola, introduced the concept to standardize the way defects are counted in response to increasing complaints from the field sales force about warranty claims. CEO Bob Galvin embraced the approach as the key to addressing quality concerns. The Six Sigma Quality Program was formally launched in 1987 with goals to “Improve product and service quality ten times by 1989, and at least one hundred fold by 1991. Achieve Six Sigma capability by 1992”. Six Sigma became central to Motorola's strategy of delivering products that were fit for use by customers. The application of Six Sigma was a major factor in
winning the Malcolm Baldrige National Quality Award in 1988, the first year the award was given.

In 1996 Jack Welsh, the legendary CEO at General Electric, established a goal of becoming a six sigma quality company by the year 2000. Welsh credits the Six Sigma quality initiative with "changing the DNA of the company, it is now the way we work - in everything we do and in every product we design.” In 1999, Six Sigma contributed $2 billion to operating income for GE.

According to GE, “Six Sigma is a highly disciplined process that helps us focus on developing and delivering near-perfect products and services”. For GE the key concepts of SixSigma are:

Critical to Quality: Attributes most important to customers
Defect: Failure to deliver what the customer wants
Process Capability: What your process can deliver
Variation: What the customer sees and feels
Stable Operations: Ensuring consistent, predictable processes
Design for Six Sigma: Designing to meet customer requirements

Some Mathematical Background

Before delving into Six Sigma, we should first review some mathematical and statistical concepts. If one makes repeated and sufficiently precise measurements of a characteristic feature (area, volume, capacitance, resistance, frequency, ..) of a manufactured part or the duration of an activity, one does not get an endless series of identical values but rather a distribution of values. If there is no systematic skew, the frequency distribution is called a Gaussian or Normal distribution which is symmetric about a mean value (µ). This distribution is the familiar bell-shaped curve described by the equation:

where µ (mu) is the mean value and σ (sigma) is the standard deviation given by the equation:

The distribution is narrow if σ is narrow and broad if it is large. The square of the standard deviation (σ2) is called the variance. One can calculate the percentage of measurements that fall inside and outside the ranges of σ± nσ as shown in the diagram.

Figure 1 Gaussian/Normal Distribution

Showing percent within ±ns of the mean.

A defect is a measurable characteristic outside the range of customer acceptance define by upper and lower specification limits. A defect is a source of irritation for the customer. Yield is defined the percentage within acceptable limits. If the measurements conform to the normal distribution, it should be straightforward to determine the yield and the number of defects. There is however a subtlety. Long experience has shown that most manufacturing processes experience a shift (due to drift over time) of 1.5 standard deviations so that the mean no longer equals target. If this sigma shift is taken into account, one can generate the table below showing defects per million
opportunities (DPMO), i.e. number lying outside ± nσ of the mean.

Table 1 Defects per million opportunities

Function of nσ

Note: there may be numerous opportunities for defects in any given product or service.

Six Sigma is a business-driven, multi-faceted approach to process improvement, reduced costs, and increased profits. With a fundamental principle to improve customer satisfaction by reducing defects, its ultimate performance target is virtually defect-free processes and products (3.4 or fewer defective parts per million). In some industries or occupations (air traffic controller, surgeon, pharmacist) even a single defect can be catastrophic. In some industries (US Postal Service) the sheer volume of products or services delivered is such that even 3.4 dpmo can have significant consequences.

The Six Sigma process for existing products and processes is defined by the acronym DMAIC, pronounced “de-may-ick”, referring to five interconnected phases.
Define the project goals and customer (internal and external) deliverables

Measure the process to determine current performance

Analyze and determine the root cause(s) of the defects

Improve the results by redesigning the process and by eliminating defects

Control future process performance to ensure improvements are permanent
A second Six Sigma process is defined by the acronym DMADV, pronounced “duh-mad-vee”, for define, measure, analyze, design, and verify new processes or products that are trying to achieve Six Sigma. DMADV is sometimes referred to as Design for Six Sigma (DFSS).

An easily understood example of a Six Sigma project might be the drive thru at the local fast food restaurant. The customer requirements are a) food is still hot when customers gets to their destination b) the content of order is correct c) the change is correct and d) the time spent waiting is reasonable. One assumes that the same menu and prices are offered to drive thru customers as those who order inside.

The Six Sigma team would take measurements of wait times (time in line before ordering, time from order to delivery) at different times during the day and week, measurements of the temperature of different foods as a function of time from receipt of order and from time of delivery and so forth. They would also look at the local competition and possibly get data from other areas. Targets would be established for maximum wait time, for acceptable temperature and for the time that food remains above that temperature, and so forth.

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-- Jack Horgan, Contributing Editor.


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