# Quality Progress - July 2015 - (Page 64)

BACK TO BASICS BY JOSEPH PAUL MITCHELL Substantiation Test Hypothesis test provides unbiased, statistics-based solutions HYPOTHESIS TESTING IS one of many The process Handbook.1 The p-value is a conditional Six Sigma tools and techniques used for Steel tubing is processed in a tempering probability: In other words, if the UTS of process improvement. Recently, it was part oven. Following the tempering process, tubes processed in January are the same of a manufacturer's define, measure, ana- one tube per load is randomly selected and as February, what is the likelihood of lyze, improve and control (DMAIC) inves- tensile tested. The mechanical property observing this same data versus observing tigation concerning a suspected variance chosen for investigation was ultimate ten- data that are significantly different? of mechanical properties in steel tubing. In sile strength (UTS)-the maximum stress A statistical software program using an this case, the product's population standard the tube can withstand before it fractures. Anderson-Darling test-used to see whether deviation was unknown, and consequently, a two-sample t-test was used. In January, a total of 80 loads were a sample of data came from a population processed without straightening issues. with a specific distribution2-indicated Data showed the mean UTS for January normal data sets for January and February. The problem was 210.7 kilopounds per square inch Statistical software calculations showed The investigation took place at an organi- (KSI) (see Online Figure 1, which can be (see Online Tables 1 and 2): p-value = 0.000. zation that fabricates steel tubing for com- found on this column's webpage at www. mercial or industrial applications. qualityprogress.com). Management was esis was rejected. The result suggested a Manufacturing specifications for steel unsure if the mean UTS for February (see change in UTS had occurred: It increased. tubing ensure the material will form during Online Figure 2) had changed because no the fabrication process. In February, opera- control charts or other statistical process Test results tors of equipment that straighten and form control charts were used for monitoring The results from hypothesis testing tubing complained that the material was the tempering oven. prompted investigation of the tempering difficult to form, resulting in less-efficient The current quality system was pass/ Based on the p-value, the null hypoth- oven, and the inspection confirmed a heat- production due to constant equipment fail-the UTS specification was 200 KSI ing element was failing and needed to be adjustments. (+/- 25). This type of quality practice is replaced. Due to this condition, the oven known as lot-acceptance sampling, and it was unable to reach the correct tempering variation in material properties. During the does not evaluate the quality of the load temperature, and consequently, the tubing measurement phase of DMAIC, a process and only provides a basis for conclud- did not receive proper heat treatment. map was constructed. Based on the steps ing all parts are acceptable for further shown, a key input variable was determined processing. One possible cause of the problem was a to be the tempering process-the last heat Management realized a significant Hypothesis testing is a valuable tool for determining whether the difference between two means is greater than what treatment the material undergoes prior to change in UTS may contribute to straight- straightening and forming operations. ening difficulties. Hypothesis test steps / The claim opposed to emotions and unsubstantiated Based on the changes in UTS, hypoth- presuppositions. QP would be expected from chance. This allows for an unbiased decision based on statistics and probability, as 1. 2. 3. 4. TABLE 1 The claim Null hypothesis: (H0: µ = 211 KSI). H0: After tempering, mean UTS did not change. Alternative hypothesis: (Ha: ≠ 211 KSI). H1: After tempering, mean UTS did change. Level of significance. α = 0.05 p-value. KSI = kilopounds per square inch 64 QP * www.qualityprogress.com esis testing was proposed. Hypothesis testing requires only a few steps: a null hypothesis, alternative hypothesis, level of significance and p-value. Table 1 shows the hypothesis test used in this scenario. "The significance level is the probability of making the mistake of rejecting the null hypothesis when it is in fact true," states The Certified Quality Engineer REFERENCES 1. Connie M. Borror, ed., The Certified Quality Engineer Handbook, third edition, ASQ Quality Press, 2009. 2. "Anderson-Darling Normality Test," iSixSigma.com, http:// tinyurl.com/n34yb22. JOSEPH PAUL MITCHELL is a metallurgist at True Temper Sports Inc. in Amory, MS. He earned his MBA from Lawrence Technological University in Southfield, MI. A member of ASQ, Mitchell is an ASQ-certified quality engineer. http://www.qualityprogress.com http://www.tinyurl.com/n34yb22 http://www.iSixSigma.com http://www.qualityprogress.com

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# Quality Progress - July 2015

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