SIX SIGMA BASICS

SIX SIGMA BASICSJoe KurianDefinition of a Process

A process is a collection of interacting components that transform inputs into outputs toward a common aim, called a mission statement.

TransformationThe transformation, involves the addition or creation of value in one of three aspects: time, place, or form. An output has "time value" if it is available when needed by a user. For example, you have food when you are hungry, or material inputs are ready on schedule. An output has "place value" if it is available where needed by a user.

Variation in a Process

The outputs from all processes and their component parts may be measured; the measurements invariably vary over time and create a distribution of measurements. The distribution of measurements of the outputs from a process over time is called the Voice of the Process (VoP). Variation is well understood by Process Capability.

Feedback Loops

No feedback loop:Special cause only feedback loop:Special and common cause feedback loop: DEFINITION OF QUALITY (VOICE OF THE CUSTOMER)Goalpost View of QualityQuality meant "conformance to valid customer requirements." That is, as long as an output fell within acceptable limits, called specification limits, around a desired value, called the nominal value (denoted by m), or target value, it was deemed conforming, good, or acceptable. We refer to this as the "goalpost" definition of quality. The nominal value and specification limits are set based on the perceived needs and wants of customers. Specification limits are called the Voice of the Customer (VoC).

USL = upper specification limit = nominal + tolerance andLSL = lower specification limit = nominal tolerance.

A service example A monthly accounting report that must be completed in 7 days (nominal) but no earlier than 4 days (LSLnot all the necessary data will be available) and no later than 10 days (USLthe due date for the report in the board meeting). Continuous Improvement View of Quality

Quality is a predictable degree of uniformity and dependability, at low cost and suited to the market.The Taguchi Loss Function, called the Loss curve in figure, expresses the loss of deviating from nominal within specifications: the left hand vertical axis is "loss," and the horizontal axis is the measure, y, of a quality characteristic.Taguchi Loss Function

L(y) = k(y m) = Taguchi Loss Functiony = the value of the quality characteristic for a particular item of product or service,m = the nominal value for the quality characteristic, andk = a constant, A/dA = the loss (cost) of exceeding specification limits (e.g., the cost to scrap a unit of output), andd = the allowable tolerance from the nominal value that is used to determine specification limits

Diameter of ball bearing (y)Value of Taguchi Loss Function (L[y])181.00191.00201.00210.64220.36230.16240.04250.00260.04270.16280.36290.64301.00311.00321.00DEFINITIONS OF SIX SIGMA MANAGEMENT Six Sigma management is the relentless and rigorous pursuit of the reduction of variation in all critical processes to achieve continuous and breakthrough improvements that impact the bottom line and/or top line of the organization and increase customer satisfaction.An ExampleFor example, a bank takes 60 days on average to process a loan with a 10% rework rate in 2000. In a Six Sigma organization, the bank should take no longer than 30 days on average to process a loan with a 1% error rate in 2002 and no more than 15 days on average to process a loan with a 0.10% error rate by 2004.The Normal Distribution. The term Six Sigma is derived from the normal distribution used in statistics.

2 sigmaIn a normal distribution, the interval created by the mean plus or minus 2 standard deviations contains 95.44% of the data points, or 45,600 data points per million (sometimes called parts per million, denoted ppm) are outside of the area created by the mean plus or minus 2 standard deviations [(1.00 0.9544 = 0.0456) 1,000,000 = 45,600]3 sigmaIn a normal distribution, the interval created by the mean plus or minus 3 standard deviations contains 99.73% of the data, or 2,700 ppm are outside of the area created by the mean plus or minus 3 standard deviations [(1.00 0.9973 = 0.0027) 1,000,000 = 2,700]. 6 sigmaIn a normal distribution, the interval created by the mean plus or minus 6 standard deviations contains 99.9999998% of the data, or 2 data points per billion data points (ppb) outside of the area created by the mean plus or minus 6 standard deviations.Relationship Between VoP and VoCSix Sigma promotes the idea that the distribution of output for a stable normally distributed process (Voice of the Process) should be designed to take up no more than half of the tolerance allowed by the specification limits (Voice of the Customer).Relationship Between VoP and VoCIf a process is originally designed to be twice as good as a customer demands (i.e., the specifications representing the customer requirements are 6 standard deviations from the process target), then even with a shift, the customer demands are likely to be met. In fact, even if the process shifted off target by 1.5 standard deviations, there are 4.5 standard deviations between the process mean ( + 1.5) and closest specification ( + 6.0), which results in at worst 3.4 ppm at the time the process has shifted or the variation has increased to have similar impact as a 1.5 standard deviation shift.

The three sigma process"Voice of the Process" for an accounting function with an average of 7 days, a standard deviation of 1 day, and a stable normal distribution. It also shows a nominal value of 7 days, a lower specification limit of 4 days, and an upper specification limit of 10 days.

Three Sigma Process with 0.0 Shift in the Mean

USL = + 3 and LSL 3. This scenario will yield 1,350 defects per million opportunities at either specification limit or one early or late monthly report in 61.73 years [(1/0.00135)/12].

Three Sigma Process with a 1.5 Sigma Shift in the Mean

The 1.5 standard deviation shift in the mean results in 66,807 defects per million opportunities at the nearest specification limit or one early or late monthly report in 1.25 years ([1/0.066807]/12)Six Sigma Process with 0.0 Shift in the Mean

The process mean remains the same as in Figure 1, but the process standard deviation has been reduced to a half-day through application of process improvement. In this case, the resulting output will exhibit 1 defect per billion opportunities at either specification limit or one early or late monthly report in 83,333,333 years ([1/0.000000001]/12).Six Sigma Process with a 1.5 Sigma Shift in the Mean

The 1.5 standard deviation shift in the mean results in 3.4 defects per million at the nearest specification limit or one early or late monthly report in 24,510 years [(1/.0000034/12]. This is the definition of Six Sigma level of quality.