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Calculating defect costs


When trying to calculate the costs associated with the production of defective parts and / or service results, it is pivotal to determine where in the process the defect has arisen. If an error occurs during the very first process step, little more than simple material costs are lost. If it occurs on the very last process step, we have to forfeit the value of an entire flow unit (including profit). The location of the bottleneck is especially important here. This is because defective flow units that are produced before the bottleneck have to be calculated with input prices while defective flow units that are produced after the bottleneck have to be calculated with the opportunity costs of lost sales. This insight drives the location of testing points in the process, who have to be arranged in a way which maximizes the chances of identifying and catching defective flow units before bigger losses occur.

By implementing a buffer between steps who can produce defective parts, the process flow can be protected against errors. However, producing too much inventory through so-called error buffering might conceal the necessity for improvements of the error rate.

These lecture notes were taken during 2013 installment of the MOOC “An Introduction to Operations Management” taught by Prof. Dr. Christian Terwiesch of the Wharton Business School of the University of Pennsylvania at Coursera.org.

The two dimensions of quality


There are two basic dimensions of quality: Performance quality measures to what extent a product or service meets the expectations of the customer. Conformance quality measures if processes are carried out the way they were intended to be carried out.

The root cause for quality problems is process variability. Were it not for process variability, every run through a process would result in the optimal output or in the very same error, which would then be easy to detect. However, due to process variability, some runs through a process result in optimal outcomes while others result in different kinds of errors. With some very basic statistical probability tools, we can assess the chances of such errors and defects occurring during a process. To calculate total error probabilities for an assembly line, one has to look at the error rate of each work step and calculate their yields (the percentage of error-free flow units the work step produces).

The yield of the process is defined as the percentage of error-free parts which are produced by the process – which of course depends on the yields of the various work steps. The total process yield is thereby simply the product of the individual yields:

process yield = yield 1 * …. * yield n

It is noteworthy, that even small defect probabilities can accumulate to a significant error rate, if there are many steps in a process. For example, if a process workflow consists of 10 steps with every step having a low defect probability of only 1%, the chances of an completely error-free product leaving this workflow are only 0,99^10 = 89,5%

The Swiss Cheese model explains, why defects or procedural errors sometimes do not get noticed, even if there are highly efficient quality checks in place: Since every slice of Swiss Cheese has some holes (defects) in it, there is a small probability that holes will line up in a way that creates a hole through a staple of cheese slices. This is then akin to multiple quality checks failing during the production of the same flow unit – though the chances of this happening might be low, it is bound to happen from time to time. This insight is also the main reason behind redundant checks, which means checking a quality attribute more than once to etch out all errors that might occur. With redundancy, a process hat to fail at multiple stations in order for the process yield to be affected.

These lecture notes were taken during 2013 installment of the MOOC “An Introduction to Operations Management” taught by Prof. Dr. Christian Terwiesch of the Wharton Business School of the University of Pennsylvania at Coursera.org.
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