Free Course Work On Normal Distribution And Six Sigma

Published: 2021-06-21 23:49:17
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Normal distribution curve has numerous applications in business processes and provides managers with valuable information on the improvement of quality and efficiency in the organization. According to Weiers (2005), normal probability distribution is very popular amongst operational managers because it follows the concepts of the Central Limit Theorem, which claims that the sampling distribution of the sample mean could be approximated by a normal distribution as the size of the sample grows. Consequently, almost any business process which produces iterating outcomes could be described by the normal distribution curve, as long as the number of iterations is considerably large. As described by Landel (2008), normal distribution may appear in the various cases in business operations. For instance, an average weight of produced products on a factory may be approximated by normal distribution. The delivery and pick-up time, as well as inventory turnover in logistics may be also described by a bell curve. Finally, qualitative characteristics of a product, such as average battery life are also normally distributed.

For a more specific example, let’s analyze some normal distributions of one of the biggest e-commerce companies in the world, A multinational business such as Amazon has various examples of normal distribution in its operations, but we will pay attention to the most common ones: a) shipment time in various geographic regions, b) product storage time in the warehouse and c) down time of the website per month.

As long as abovementioned variables could be described by the normal distribution, we may apply the six sigma principle to these processes. According to the study of Breyfogle & Meadows (2001), sigma quality level is an indication of how often defects are statistically likely to be produced by a process. The higher the sigma quality level of a process, the less likely the process will create defects. The study of Cupello (2011), claims that “If the customer‟s upper specification limit (USL) and lower specification limit (LSL) for the product‟s tolerances happens to be the same as the three sigma level capability of the production process, and the mean of the output of that process is centred on the mid-point between the USL and LSL, then statistically, approximately 2,700 parts per million produced by such a process will fall outside the customer’s specification limits and therefore be considered defective”. This results in 0.2% defective rate. Research of Harry (1988) also shows that a typical business process described above may have shifts from mean by 1.5 standard deviations during the production cycle. Thus, a company has to maintain the variance of the output in the range of 6 sigmas within the USL and LSL limits. This would minimize the amount of defective products in an output.

According to McLellan (2009), typical Six Sigma methodology in improving operations includes 5 phases (DMAIC): 1) Define Phase, 2) Measure Phase, 3) Analysis Phase, 4) Improvement Phase and 5) Control Phase.

We may apply this methodology to the improvement strategy of Amazon’s website, especially its downtime per month:

Define Phase. During this phase we need to identify the problem (downtime) and be able to quantify it (minutes per month the website is down).

Measure Phase. During this stage we need to develop special tools which will help us to measure the downtime of the website, as well as identify reasons for this downtime.
Analysis Phase. Here we need to perform a thorough analysis of website’s operations and identify the factors which affect the functionality of the website. We also need to find out solutions to the existing problems and evaluate the gap between current capabilities of the website and our desired result.

Improvement Phase. During this stage company’s management has to find out the most beneficial solution to the existing problem as well as develop the plan of the improvement procedures.
Control phase is being performed after all the improvements have been implemented. This phase suggests the development of control functions, which will make sure that improvement procedures are working and general variance in the output is reduced as much as possible, resulting in minimization of defective outputs.


Breyfogle, F.W.; Cupello, J. & Meadows, B. 2001, Managing Six Sigma. John Wiley & Sons, New York, NY.
Breyfogle, F.W., Meadows, B. (2001). Bottom Line Success with Six Sigma. Quality Progress, vol. 34, no. 5, Milwaukee.
Harry, M.J. (1998). Six Sigma: a Breakthrough Strategy for Profitability. Quality Progress.
Landel, R. (2008). Six Sigma: A Basic Overview. Darden Case No. UVA-OM-1339. Retrieved from
McLellan, J. D. (2009). Six Sigma and Management Control Systems. International Journal of Business and Management Research, Vol. 2, No. 1, p. 52, 2009. Retrieved from:
Weiers, R. M. (2005). Introduction to Business Statistics. 5th edition. Thomson South-Western.

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