Multi-vari charts are a useful tool for presenting analysis of variance data in graphical form. They can identify patterns of variation, on a single chart, from many causes.
In a multi-vari study, samples are taken systematically from the process in order to capture the effect that various times and location have on variation. It can be an excellent tool to use early in the progressive search for a dominant cause (the Red X).
When confronted with excess variation on a cylindrical shaft, a study was launched using multi-vari charts. Three consecutive shafts were selected each hour for one shift. The shaft diameters were measured at four locations (left and right sides at two different orientations) on each shaft. Plotting the data from left to right measured taper. Top to bottom measured out-of-round condition.
Three charts were produced: within-unit variation (positional); unit-to-unit (cyclical) variation; and time-to-time (temporal) variation. A glance at the charts quickly revealed that the largest variation was time-to-time.
The diameter decreased sharply from the first to the second hour, followed by less drop in the second hour, but then stabilized until mid-day (lunch). Before this study, this variation was thought to be due to tool wear, so operators would routinely adjust the process which added to the variation. For this study, though, it was decided to let the process run without adjustment.
When the next three-piece sample was taken after lunch, the readings increased to a level similar to those at the start of the day. This would indicate tool wear was not the dominant factor as earlier thought, so ‘tweaking’ (for tool wear) only made the variation worse!
The cause for the variation was subsequently determined to be related to temperature change. The machine was ‘cold’ in the morning but as it warmed up, the readings decreased before finally stabilizing. When the machine was shut down for the lunch hour, everything ‘cooled off.’ The cooler condition then resulted in the higher readings immediately after lunch.
The decision was made to keep the machine running during lunch and then repeat the study. With the machine left running during lunch, the time-to-time variation, which had accounted for about 60% of the total variation was reduced to almost zero! This illustrated how the time clue led to the temperature clue that led to the Red X.
Unit-to-unit variation only accounted for about 5% of the total variation, so it was not worth investigating. However, the within-unit or positional variation revealed two other causes of variation. Out of roundness accounted for about 25% and taper about 10% of the total variation.
It was discovered that a worn bearing was the culprit for the out-of-round condition. The taper was caused by the cutting tool not being parallel to the axis of the shaft. Once these two issues were corrected, variation was reduced to about 40% of the allowed variation.
Multi-vari charts provide an excellent visual display of the components of variation.
Frank E. Satterthwaite, a statistician working as a consultant for Rath & Strong, is given credit for creating the pre-control technique in 1954. However, Shainin certainly translated their use into guidance on the factory floor.
Don’t get me wrong, pre-control charts are not statistical process control charts! However, they do have a purpose. The goal of pre-control is to identify the need for adjustment and to control the process so that defective parts are not produced and sent on to the customer.
In the late 1980s I was confronted with a quality issue which led me to convince management that the use of pre-control was the best short-term option to improve out-going quality.
It only took about four hours to develop a one-hour training program for machinists and supervisors. We added three twists to the normal pre-control rules. First, we referred to the pre-control charts as stoplight charts using green, yellow and red zones. Second, we set the red zones just inside the specification limits. Third, we adapted pre-control to unilateral tolerances. The process worked very well for our purpose and prevented us from knowingly producing bad product.
For many who knew him and his work, Shainin was referred to as the world’s foremost quality problem-solver. Keki Bhote, author of “World-Class Quality,” commented about Shainin’s work at Motorola, “Without Deming, the U.S. would not have had a quality philosophy; without Juran, it would not have had a quality direction; without Shainin, it would not have solved quality problems.”