Category: Metrics

Of considerable interest, this concept often mystifies newcomers to field of Six Sigma. As you already surmised, the referenced charts rely upon the assumption of a unilateral specification (single-sided performance requirement). From a defect accounting point-of-view, it should be fairly obvious that a unilateral (one-sided) specification must be treated as a single defect category. However, a bilateral (two-sided) […]

Seems to me that you have described a traditional quality improvement project. Based on the elements of your question, it is my understanding that: 1) Each “drawing feature” constitutes a “defect opportunity.” 2) The customer’s minimum expectation was a quality level of .99, per feature. 3) The pre-project quality was found to .995, per feature […]

To begin, recall that a critical-to-quality characteristic (CTQ) is a vital product design feature (e.g., the strength of a material).  Naturally, we recognize that the product (per se) does not necessarily have to be a piece of hardware – it can be anything (e.g., a software program, a delivered service, a financial transaction, a social […]

Over time, there has been very fine debate (both positive and negative) surrounding the 1.5 sigma shift.  As such, the on-going discussion well serves the need to “keep the idea alive,” so to speak.  To this end, I have recently completed a small book on the subject, soon to be available on iSixSigma.  The title […]

Right up front in our discussion, let us recognize that the 1.5 sigma shift can be attributable solely to the influence of random error. In this context, the 1.5 sigma shift is a statistically based correction for scientifically compensating or otherwise adjusting a postulated model of instantaneous reproducibility (short-term capability) for the inevitable consequences associated […]

To open our discussion, we acknowledge that not all product (or service) opportunities should be Six Sigma. In the total scheme of things, some are not destined to be critical – to anything. For example, in a garden supply store we can find many different types of tools.  More specifically, let us consider an ordinary hand […]

Let us postulate that a certain process is comprised of three progressive steps, say A, B, and C, respectfully. Further, we note the observed defects-per-unit (dpu) at the first step to be dpu.A = .10. At the second step, dpu.B = .05. The third step was found to be dpu.C = .008. Of course, we acknowledge dpu as a […]

To help you better understand the nature of this question; let us consider a very simple example.  Let us suppose that we go to the store – looking for fresh apples.  Once there, we notice a sign that reads “3 apples for $1.00.”  Based on this sign, we ask the storekeeper: “If I want to buy […]

Perhaps you are both in error (as related to your Sigma calculations.) Do not be discouraged by such debate, as it is quite common among those new to Six Sigma. However, do be aware of a phenomenon I call “denominator management.” This colorful term is used to describe the practice of inflating or otherwise distorting the denominator […]

As you likely know, the issue of opportunity counting is somewhat illusive. It is laced with many misconceptions. The seeming intuitive nature of a “defect opportunity” runs wider and deeper than what one would naturally expect. To help us better understand this concept (and some of the related pitfalls), we will discuss the classic quality metric […]

Consider the case where a particular system is comprised of three subordinate elements. In this case, we will say the first-time yield (quality confidence) of each element is known to be .85, .90, and .95, respectively. The cross product would then be given as .85 x .90 x .95 = .612, or about 61.2 percent.  This value […]

To facilitate an answer to your question, consider the following table. The first column is the given measure of process capability (provided in the form of Z).  The second column is the corresponding short-term yield of the first column (based on a one-sided specification). Of course, the third column is the associated long-term yield, also predicated on […]

The capability of a process has two distinct but interrelated dimensions. First, there is short-term capability, or simply Z.st. Second, we have the dimension long-term capability, or just Z.lt. Finally, we note the contrast Z.shift = Z.st – Z.lt. By rearrangement, we assuredly recognize that Z.st = Z.lt + Z.shift and Z.lt = Z.st – Z.shift. So as to better […]

So as to establish a corporate-level sigma value (per se), it is generally advisable to follow an established analytical model. Of course, any such model must be conducive to the hierarchical aggregation (pooling) of capability information and data. Generally speaking, the more common approaches for realizing this aim are inclusive of, but not limited to: 1) the […]

Don’t know, never been there – I’m still striving for 5-sigma (at least on a personal level). Given where the world is right now, many followers of Six Sigma (including myself) would say that a capability of 7-sigma is pessimistically possible, but not pragmatically probable. Maybe when I hit a 5-sigma level of capability, I can […]

Once is a great while, there is a need to estimate or otherwise approximate the tail probability of an extreme standard normal deviate – such as Z = 7, Z = 10, or even higher.  For example, certain types of reliability problems rely on such assessments. But as many already know, most published tables of […]

We must understand the sigma of a process is merely an equivalent unilateral figure-of-merit. As such, it is always regarded (and reported) as a short-term measure of capability. The metric can be directly computed when continuous data is at hand, or it can be statistically synthesized from discrete data. In the latter context, a reported sigma is only […]

Creating a process scorecard is not an easy or straightforward task. It becomes even more difficult when the scorecard is comprised of continuous and discrete performance metrics, each having a unique level of complexity (defect opportunity space). Even more perplexing is when some of the baseline metrics are short-term in nature while others are inherently […]