Six Sigma Tools for Testing Statistical Significance

Six Sigma Tools for Testing Statistical Significance

Six Sigma Tools For Testing Statistical Significance




Six Sigma technique has become exceedingly popular recently. This has resulted from the need for companies to achieve the highest quality in their products. In fact, quite a large number of organizations see Six Sigma as a measure of quality that aims at enhancing perfection in production. Six Sigma refers to a data-driven and disciplined methodology and approach that is used for doing away with or eradicating defects in every stage of production of services and products, as well as manufacturing and transactions. Six Sigma’s statistical representation gives a quantitative description as to the performance of a process. It is noteworthy that a process has to produce less than 3.4 defects for every million opportunities so as to attain Six Sigma(Paul 2004).

Six Sigma defects refer to anything that falls outside the specifications of the customer. In essence, a Six Sigma opportunity would refer to the total number of chances that a defect occurs. The Six Sigma Methodology has its fundamental objective as implementing a measurement-based strategy that concentrates on improvement of the process and reducing variations. This is done using two sub-methodologies of Six Sigma, which are DMADV and DMAIC. Six Sigma DMADV strategy, which stands for Define, Measure, Analyze, Design and Verify, refers to a system of improvement that is used to come up with new products or processes at quality levels of Six Sigma. In addition, it may be used in cases where the current processes need than an incremental improvement (Paul 2004).

Six Sigma DMAIC strategy, which is an acronym for Define, Measure, Analyze, Improve and Control, refers to a system of improvement for existing processes that are not in line with the specifications and, therefore, are seeking incremental improvement. The incorporation of Six Sigma strategies easily means an increase in the gross profit of a company as the defects are reduced and variations in production eliminated. In essence, it strives to fulfill the customers’ requirements in a profitable manner, or rather, to improve to the extent which such efforts improve the profits of the company. In manufacturing, the company will define the customers and their requirements, as well as how the manufacturing process should be improved. The performance of the fundamental business process that is involved will be measured and compared to the requirements of customers to determine the shortfall. The data collected will be analyzed, and causes of defects determined so as to come up with opportunities for improvement. An implementation plan is developed and deployed, while the improvements are controlled to ensure that the processes are on course (Stamatis 2003)

LG Six Sigma

LG started using Six Sigma methodologies in 1996. This was in an effort to correct defects in its production and safeguard its profitability in all branches. In 2002, it attained the 3.4 Six Sigma goal. In the Analysis phase of the DMAIC methodology, LG verifies the potential causes of defects through hypothesis testing.

Potential cause of defects in the products: malformed shipping labels

Defects present Defects absent Total

Root Cause present 140 0 140

Root Cause absent 29 101 130

Total 169 101 270

In this case, the hypothesis for the data presented above will take the following form.

H0: no relationship exists between malformed shipping labels and rejections by the packing scanner

H1: there exists a relationship between malformed labels and rejections by the packing scanner

With this data, the intermediate equation would be

Expected = (totals in the column x the totals of the rows)/ overall total

A Chi-Square test equation is used in testing the hypothesis. The equation is

χ2 = ∑3i=1= (Ai-Ei)/Ei

Where χ is the Chi value, A is the value of the data presented E is the expected value.

Suitability of the Chi-Square test

Chi-Square test refers to a statistical hypothesis test that incorporates chi-square distribution in instances where the null hypothesis holds true. It is mostly used in observing the results obtained through comparison of the given data with expected data. In essence, the Chi-test is carried out as proof that there exists no difference between the actual data and the expected data (Forrest 2003).

Underlining the suitability of the Chi-Square test are the two rules under which it operates. The Chi-Square would only be calculated using numerical values rather than ratios and percentages. In addition, it should never be calculated in cases where the expected value falls below 5 in any category (Stamatis 2003)

Chi-Square test, in this case, would be used to test whether two attributes are independent. In essence, it would determine whether the rejection of LG’s products has in any way been caused by the defective shipping label on the products. While the chi-square test assumes that the population from which the sample is derived is normal, it is noteworthy that the rule does not have to hold in the case of goodness of fit and testing for independence of variables. In addition, both tests only depend on the expected and observed frequencies, as well as degrees of freedom rather than any assumption pertaining to the parent population’s distribution (Forrest 2003).


Six sigma methodologies come in handy for many companies as far as safeguarding the quality of their products is concerned. Its incorporation aims at safeguarding the company’s profitability. In LG, Six Sigma was initially integrated in 1996 in an effort to curb defects. In finding out the connection between malformed labels and rejection by the scanner, a chi-square test would be used. This is because the test would not depend on the distribution of the parent population.


Forrest W. B, 1992. Statistical Methods for Testing, Development, and Manufacturing. New York: Wiley

Stamatis D. H, 2003. Statistics and probability. London: St. Lucie Press

Forrest W. B, 2003. Implementing Six Sigma: Smarter Solutions Using Statistical Methods. New York: John Wiley & Sons

Paul A. K, 2004. Six sigma demystified. New York: McGraw-Hill Professional

(Forrest 1992)

(Stamatis 2003)

(Forrest 2003)

(Paul 2004)