How Are Defects and Opportunities Determined for CTQs?

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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 event, or intellectual activity).  However, once a particular CTQ has been brought into reality (by way of the process), it is recognized as a “manifest opportunity.”  

For every attempted cycle of a process, only two outcomes are possible – either a manifest opportunity is created or it is not (missed opportunity).  If a manifest opportunity is realized, a value of “1” would be assigned.  Following an unproductive cycle, a value of “0” would be assigned.  Thus, we have the data that is necessary to compute “process yield.”  To illustrate, suppose that 100 process cycles were attempted and only 5 such cycles did not realize an outcome.  Given these facts, we would compute the process yield to be Y = 1 – ( 5 / 100 ) = 1 – .05 = .95, or 95 percent.  This is to say that 95 percent of the attempted process cycles could be expected to yield a “manifest product opportunity.”  At this point, we now turn our attention to the consequential “quality” of each manifest opportunity.

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In the interest of furthering our discussion, let us suppose a certain process cycle actually created its intended outcome – a manifest opportunity.  If the given opportunity “passed” its quality verification test, it would be conventional practice to assign a value of “0” to that observation (meaning a defect was not observed).  In this circumstance, we would recognize the outcome as “quality yield.”  On the other hand, if that manifest opportunity “failed” the verification test, a value of “1” would be assigned (meaning a defect was observed).

To better focus our thinking, let us formulate the previous knowledge into a quality metric called defects per opportunity, or simply DPO.  In doing so, we recognize its computational form as DPO = D / O, where D is the number of observed product defects and O is the number of manifest opportunities created by the process.  Thus, each occurrence of a manifest opportunity is progressively assigned to the denominator.  For each assignment to the denominator, we are forced to recognize a quality opportunity in the numerator.  For example, if a manifest opportunity were realized upon completion of a process cycle, it would then be necessary to evaluate its quality condition.  Owing to this, we must recognize that each manifest opportunity will either prove to be “good” or “bad” in terms of quality. 

Therefore, we indirectly form a “numerator-denominator pair,” with respect to the DPO metric.  In other words, the “pair” is formed once the existence of an opportunity is reflected in the denominator term (and noted as a value of 1) and its corresponding quality condition is reflected in the numerator term (and noted as a value of 0 or 1).  Interestingly, this creates two “slots” for inclusion in the DPO metric – one for the numerator (quality condition) and one slot for the denominator (manifest condition).  In this sense, the two slots are “married” and are, therefore, considered “conjugal.”  However, this is only true for the conditions 1/1 and 0/1.  The combinations 1/0 and 0/0 are not feasible alternatives.  Thus, any CTQ that is actively verified constitutes a “defect opportunity.”