By Mark Friedman and Howard Gitlow

Six Sigma has been called the latest incarnation of Total Quality Management (TQM). The name simply means that customer-specified tolerances for acceptable output are six standard deviations (sigma) from the mean. Major corporations that practice its application include Motorola, General Electric, and Allied Signal. Companies whose products or services are produced under a Six Sigma philosophy are, essentially, perfect.

Six Sigma management has high training costs, ranging anywhere from $1,300 to upwards of $20,000 per employee. Outside organizations and consulting firms also offer Six Sigma training, with costs running as high as $30,000 per person. Six Sigma management is implemented through teams whose goal is to improve or innovate processes such that they produce approximately 3.4 defects per million opportunities.

Many observable phenomena can be graphically represented as a bell-shaped curve that looks something like Exhibit 1. The interval created by the mean plus or minus two standard deviations contains 95.44% of the data in a normal distribution, and the interval created by the mean plus or minus three standard deviations contains 99.73% of the data in a normal distribution. The interval created by the mean plus or minus six standard deviations contains 99.9999998% of the data in a normal distribution.

Normal distribution. When measuring any process, it can be shown that its outputs vary in size, shape, look, feel, or any other measurable characteristic. This variability is measured by a statistic called the “standard deviation.” If stated specification limits of unacceptable output is equal to three standard deviations from the mean, statisticians expect 2,700 defects per million. When stated specification limits are six standard deviations from the mean, statisticians expect two defects per billion opportunities.

Voice of the Customer

Specifications state a boundary that applies to individual units of a product or service. In Six Sigma these specification limits are called the “voice of the customer.”

An individual unit of product or service is considered to conform to a specification if it is on or inside the boundary. Individual unit specifications are made up of a nominal value and an acceptable tolerance from that. The nominal value is the desired value for process performance mandated by the customer’s needs or wants. The tolerance is an allowable departure from a nominal value established by designers that is deemed nonharmful to the functioning of the product or service. Specification limits are the boundaries created by adding and/or subtracting tolerances from a nominal value, for example:

An example of a specification can be seen in a monthly accounting report that must be completed in seven days but no earlier than four days (lower specification limit) and no later than ten days (upper specification limit).

Voice of the Process

Six Sigma management promotes the idea that the voice of the process should take up no more than half of the tolerance allowed by the voice of the customer, a process that transforms inputs into outputs through the addition or creation of value. Exhibit 2 shows the “voice of the process” for the accounting function with an average of seven days, a standard deviation of one day, and a predictable normal distribution. It also shows a nominal value of seven days, a lower specification limit of four days, and an upper specification limit of 10 days. The accounting function is referred to as a Three Sigma process because the process mean plus or minus three standard deviations is equal to the specification limits in other terms, USL = M + 3 sigma and LSL = M – 3 sigma. This scenario will yield 2,700 defects per million opportunities from a normal distribution table, or one early or late monthly report in 30.86 years [(1/.0027)/12].

Exhibit 3 shows the same scenario as above, but the process average shifts by 1.5 standard deviations over time. This is not an uncommon phenomenon. The 1.5 standard deviation shift in the mean results in 66,807 defects per million opportunities, or one early or late monthly report in 1.25 years [(1/.066807)/12].

Exhibit 4 shows the same scenario as Exhibit 2 except that the “voice of the process” only takes up half the distance between the specification limits. The process mean remains the same as in Exhibit 2, but the process standard deviation has been reduced to one-half day through application of process improvement. In this case, the resulting output will exhibit two defects per billion opportunities, or one early or late monthly report in 41,666,667 years [(1/.000000002)/12].

Exhibit 5 shows the same scenario as Exhibit 4, but the process average shifts up or down by 1.5 standard deviations over time. The 1.5 standard deviation shift in the mean results in 3.4 defects per million opportunities, or one early or late monthly report in 24,510 years [(1/.0000034/12]. This is the definition of Six Sigma quality.

DMAIC Model

The relationship between the voice of the customer, the voice of the process, and the DMAIC (define-measure-analyze-improve-control) model is explained in Exhibit 6. The left side of the exhibit shows an old flowchart with its three-sigma output distribution. The right side shows a new flowchart with its six-sigma output distribution. The method used in Six Sigma management to move from the old flowchart to the new flowchart through improvement of a process is the DMAIC model.

Example. The define phase involves preparing a business charter, understanding the relationships between suppliers-inputs-process-outputs-customers (SIPOC), and gathering and analyzing “voice of the customer” data to identify the critical to quality (CTQ) characteristics important to customers.

Top management assigned a Six Sigma team to review the production of a monthly report by the accounting department. This involved identifying the need for the project, the costs and benefits, the resources required, and the time frame. The team determined that management wants a monthly accounting report to be completed in seven days. They also determined that the report should never be completed in less than four days and never later than 10 days. Team members identified the project charter as follows:

The measure phase involves developing operational definitions for each CTQ variable, performing studies to determine the veracity of the measurement procedure, and establishing baseline capabilities.

First, the members of the Six Sigma team defined “variability in cycle time” such that all relevant personnel agreed upon the definition. Second, they performed a study to determine the veracity of the measurement process. Finally, the team members collected baseline data about variability in cycle time, and statistically analyzed it.

The analysis phase involves identifying upstream variables (X) for each CTQ; operationally defining, collecting baseline data, performing studies to determine the veracity of the measurement process, and establishing baseline capabilities for each X; and understanding the effect of each X on the CTQ.

Team members identify all input and process variables that affect variability in cycle time, known as X. This activity, referred to as process mapping, includes flowcharting. In this project, team members identified the relevant Xs as:

Next, team members operationally define the above Xs and perform studies to determine the veracity of their measurement systems. Team members then collect baseline data to determine the current status of each X. For example, the number of signatures required before releasing the report may affect the average time to process the report, or the accounting clerk preparing the report may dramatically affect the variability in cycle time to produce the report. Finally, team members study the data and develop hypotheses about the relationships between the Xs and the CTQ. In this case, X1, X3, X7, and X10 were found to be critical to the reduction in the variability of the cycle time to produce the accounting report. The other Xs did not substantially affect the CTQ.

The improvement phase involves designing experiments to understand the relationship between the CTQs and the Xs, determining the optimal levels of critical Xs that minimize variability in the CTQs, developing action plans to implement the optimal level of the Xs, and conducting a pilot test of the revised process.

Team members conducted an experiment to identify the optimal levels of the critical Xs identified in the analysis phase in order to minimize variation in the time to produce the accounting report. The experiment revealed that team members had to work with the personnel responsible for line items A and C to decrease the average and standard deviation of days to forward the line items to the department. The experiment showed an interaction between the clerk preparing the report and the supervisor correcting the report. A pilot run of the revised process showed it to generate a predictable normal distribution of days to produce the report, with a mean of seven days and a standard deviation of one-half day.

The control phase involves avoiding potential problems with the Xs in risk management and mistake-proofing, standardizing successful process revisions, controlling the critical Xs, documenting each control plan, and turning the revised process over to the process owner.

Team members determine and avoid potential problems with X1, X3, X7, and X10 using risk management and mistake-proofing techniques. They establish procedures to ensure the coupling of clerks and supervisors and data collection methods to identify and resolve future problems in the reporting process. The new process is standardized and fully documented. At this point, team members turn the revised process over to the process owner. The process owner continues to work toward improvement, that being the distribution of days to produce the report. This translates to a report being early or late about once every 24,500 years.

Opportunities and Challenges

Six Sigma offers both opportunities and challenges. Companies wishing to implement Six Sigma need to make sure that proposed processes are designed within the parameters of good business practice. Because the data gathering and analysis phases are of critical importance, the CPA will be called upon to verify the veracity and timeliness of the data. Also, companies that hire outside consultants to produce new or revised processes would be well advised to have a CPA review the documentation prior to acceptance of the Six Sigma team’s reports by the process owner.