# Product Quality Improvement TQM/SPC

Certain tyre manufacturer is about to introduce a new line of tyres. The company’s quality control manager has been asked to present the results of a recent test of tires on a hundred racing automobiles. The following table contains a list of how the 100 cars got (to the nearest 100km) before one of the tires failed to meet the minimum EC standards.

- Use appropriate TQM /SPC tools to show the variability and distribution of the data;
- Comment on the distribution of the data and explain how the chosen TQM/SPC tools can be used in the quality improvement process.

The Wheelie Company has presented a table with data of how 100 bicycles got to the nearest 100 km before having one of the tires punctured or faulty. Taking a glance to this table a great range of the product can be detected, from 20 to 77 km. The distribution is quite simetric (see Fig 1) with a peak between 40 and 50 km involving 42% of the samples. From the table, we can deduce that tires have been faulty in a range of 57km. The first one at 20km, and the last one at 77km. The Wheelie Company can say that their average tyre makes 44.45 km. For doing the data more comprehensive, it has been grouped in a frequency distriubution. This provides a better way of appreciating the data (Figure 1)

Once calculated the standard deviation (1σ and 2σ) the measurements and its distribution can be displayed in the charts below as a Gaussian or normal distribution. We can see that the bell curve is not very tall, and it is quite wide. This means that the data is much spread. Logothetis N. (1992)

Based on the previous calculations, we see that The Wheelie Company would be between a 2σ and 3σ, where 99.73% of the values would lie within the limits. In other words, a wheel from TheWhelie has 69% of chances of breaking between 33 and 56 km, and a 97 % of chances of breaking between 21 and 67 km.

This control chart diferenciates between the special and common causes. In this case, for 2σ (for 3σ all the samples would be normal) three of the samples have scaped the control limits. 2 of the wheels have had a long endurance, and another one failed before it was expected. It is important to analyze why this wheels didn’t performed as expected, an “out of control situation of the average performance”. It is important to find out why these errors have happened.

Logothetis mentions the idea that based in the principles of normal distribution (like this case) actions have to be taken over the samples concentrated around the limits, rather than in the ones near the mean. By reducing the range of these points (here near the limits of 2 sigma) the quality would be improved. “The guideline is that action should be taken when at least 2 consecutive points fall out the warning limits” Logothetis, N (1992)

Process control is a function in a manufacturing process, which looks for deviations from the mean output and gathers changes before the product quality is compromised. The use of SPC will involve the use of control charts where the output of a certain process is gathered and charted. When the process produces results outside the limits, it is said to be out of control. Actions must be taken in this point to bring the process under control again. Raisinghani, M.S. (2005)

**References:**

- Logothetis, N. (1992) Managing for total quality. From Deming to Taguchi and SPC.Prentice Hall International, Hertfordshire, UK
- Raisinghani, M.S. (2005) Six Sigma, concept, tools and applications in Industrial Management and Data Systems. Vol 105, nº4. Emerald Group, Texas, U.S.A.