## 2018

BACK TO BASICS

# Substantiation Test

## Hypothesis test provides unbiased, statistics-based solutions

by Joseph Paul Mitchell

**This article was featured in January 2016’s Best Of Back to Basics edition.**

Hypothesis testing is one of many Six Sigma tools and techniques used for process improvement. Recently, it was part of a manufacturer’s define, measure, analyze, improve and control (DMAIC) investigation concerning a suspected variance of mechanical properties in steel tubing. In this case, the product’s population standard deviation was unknown, and consequently, a two-sample t-test was used.

### The problem

The investigation took place at an organization that fabricates steel tubing for commercial or industrial applications.

Manufacturing specifications for steel tubing ensure the material will form during the fabrication process. In February, operators of equipment that straighten and form tubing complained that the material was difficult to form, resulting in less-efficient production due to constant equipment adjustments.

One possible cause of the problem was a variation in material properties. During the measurement phase of DMAIC, a process map was constructed. Based on the steps shown, a key input variable was determined to be the tempering process—the last heat treatment the material undergoes prior to straightening and forming operations.

### The process

Steel tubing is processed in a tempering oven. Following the tempering process, one tube per load is randomly selected and tensile tested. The mechanical property chosen for investigation was ultimate tensile strength (UTS)—the maximum stress the tube can withstand before it fractures.

In January, a total of 80 loads were processed without straightening issues. Data showed the mean UTS for January was 210.7 kilopounds per square inch (KSI) (see Online Figure 1). Management was unsure if the mean UTS for February (see Online Figure 2) had changed because no control charts or other statistical process control charts were used for monitoring the tempering oven.

The current quality system was pass/fail—the UTS specification was 200 KSI (+/– 25). This type of quality practice is known as lot-acceptance sampling, and it does not evaluate the quality of the load and only provides a basis for concluding all parts are acceptable for further processing.

Management realized a significant change in UTS may contribute to straightening difficulties.

### The claim

Based on the changes in UTS, hypothesis 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 Handbook*.^{1}
The p-value is a conditional probability: In other words, if the UTS of tubes
processed in January are the same as February, what is the likelihood of
observing this same data versus observing data that are significantly
different?

A
statistical software program using an Anderson-Darling test—used to see
whether a sample of data came from a population with a specific distribution^{2}—indicated
normal data sets for January and February. Statistical software calculations
showed (see Online Tables 1 and 2): p-value = 0.000.

Based on the p-value, the null hypothesis was rejected. The result suggested a change in UTS had occurred: It increased.

### Test results

The results from hypothesis testing prompted investigation of the tempering oven, and the inspection confirmed a heating element was failing and needed to be replaced. Due to this condition, the oven was unable to reach the correct tempering temperature, and consequently, the tubing did not receive proper heat treatment.

Hypothesis testing is a valuable tool for determining whether the difference between two means is greater than what would be expected from chance.

This allows for an unbiased decision based on statistics and probability, as opposed to emotions and unsubstantiated presuppositions.

### References

- Connie M. Borror, ed.,
*The Certified Quality Engineer Handbook*, third edition, ASQ Quality Press, 2009. - "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.

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