# Case Study: Aluminum on a hot rolling mill ( Multi-Vari Study )

Welcome to Six Lean Sigma Blog, today we are going to discuss a very interesting case study about Hot Rolling Mill. Rolling mill, are machines, which roll aluminum utilizing combination of force and temperature. In this classic example, i will describe scope of Six Sigma ( Mult- Vari Study).

First of all what is Multi-Vari Study?

Let me start with a very simple example from daily life. Say, you have a laptop & you are working on it from past 3 hours. One of you might notice heat produce by your laptop. Thus, measure of heat represent, temperature. We can say temperature is one of the factor associated with Heat. Now, let’s see how temperature can vary:

1. It can vary from one point to other point, across length of laptop.

2. It can vary from time to time. When you switch on, temperature was low and after 3 hour temperature is little high.

3. It can vary from laptop to laptop. HP, is heating up more than Apple.

If we wanna solve problem of laptop heating, we can investigate the stability or consistency of a laptop with Multi Vari Study. Multi Vari chart consists of a series of vertical lines, or other appropriate schematics, along a time scale. The length of each line or schematic shape represents the range of values found in each sample set.  I hope, it’s clear now what is Multi Vari Study. Let’s look at our case study:

Six Sigma Case Study based on Multi Var Study

A manufacturer produced flat sheets of aluminum on a hot rolling mill with a thickness specification was 0.245″ to.005″.  A process capability study indicated that the process spread was 0.0125″ (a Cp of 0.8) versus the requirement of 0.010″. The operation generated a profit of approximately \$200,000 per month even after a scrap loss of \$20,000 per month.

Refitting the mill with a more modern design, featuring automatic gauge control and hydraulic roll bending, would cost \$800,000 and result in 6 weeks of downtime for installation. The department manager requested that a multi-vari study be conducted by a quality engineer before further consideration of the new mill design or other alternatives.

Four positional measurements were made at the corners of each flat sheet in order r to adequately determine within piece variation. Three flat sheets were measured in consecutive order to determine piece to piece variation. Additionally, samples were collected each hour to determine temporal variation.

The results of this short term study were slightly better than the earlier process capability study. The maximum detected variation was 0.010″. Without sophisticated analysis, it appeared that the time to time variation was the largest culprit. A gross change was noted after the 10:00 AM break. During this time, the roll coolant tank was refilled.

Actions taken over the next two weeks included re-leveling the bottom back-up roll (approximately 30% of total variation) and initiating more frequent coolant tank additions, followed by an automatic coolant make-up modification (50% of total variation).

Additional spray nozzles were added to the roll stripper housings to reduce heat build up in the work rolls during the rolling process (10-15% of total variation). The piece to piece variation was ignored. This dimensional variation may have resulted from roll bearing slop or variation in incoming aluminum sheet temperature (or a number of other sources).

The results from this single study indicated that, if all of the modifications were perfect, the resulting measurement spread would be 0.002″ total.In reality, the end result was : +/-0.002″ or 0.004″ total, under conditions similar to that of the initial study. The total cash expenditure was \$8,000 for the described modifications.

All work was completed in two weeks. The specification of 0.245″ +/-0.005″ was easily met. Most multi-vari analysis does not yield results that are this spectacular, but the potential for significant improvement is apparent.