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Robert F. Hart, Ph.D., and Marilyn K. Hart, Ph.D.

Robert F. Hart, Ph.D., and Marilyn K. Hart, Ph.D.’s default image

Quality Insider

Using p-Charts to Improve Steel Mill Quality

How to eliminate manufacturing failures by using control charts

Published: Monday, January 24, 2005 - 23:00

A steel mill had a quality problem in the manufacture of cold-rolled steel for use in applications such as automobile hoods. Several hot-rolled coils were welded end-to-end to form a long continuous band. The band included the welds that were made to join the original coils together. Unfortunately, many of these welds were failing under tension, causing damage and extreme danger as the coils flailed about.A functional test was performed at the weld station to discover why these coils were failing. After removing the long ridge of previously molten metal, the weld was removed in a 12 in. strip of steel from the full width of the coil. This was done four times every 8-hour shift. (In the steel mill an 8-hour shift is called a "turn".) A 1-in. diameter tool steel ball was pressed down into the test piece until a half-in. high bulge was raised on the opposite side. A failed weld bulge was one where a crack appeared, with some portion of that crack running parallel to the direction of the weld. The rationale for this definition was that such a crack implied that the weld had less ductility than the parent metal.

Every two hours, a completed weld was tested using six bulges equally spaced along the weld. Starting at the north edge of the coil, these bulges were numbered one through six, with the odd-numbered bulges toward the top of the sheet and the even-numbered ones toward the bottom. This was done in case there turned out to be a preference for the top or the bottom of the sheet in the welding process.

After establishing standard procedures for the weld and the bulge test, it was time to consider the various methods of subgrouping that could be used to study the test results. To improve the weld process so all welds would have sufficient ductility to prevent fracture, the employees working on this project needed to look at the data in time-order. But first, they needed to address the potential sources of variation in weld quality, based upon their expert knowledge of the process. The next step was to subgroup the same failure data in many different ways for repeated p-Chart analyses. From a long list of possibilities, the following subgrouping methods were considered the easiest to apply:

  • Turn—Determines which shift was worse than the overall average
  • Crew—Consists of both operators and inspectors working together as a single team, with rotating shift assignments
  • Top vs. Bottom—Determines how many failures occur on bulges toward the top or bottom of the strip
  • Position of Bulge—Determines what bulge positions across the weld (numbered one through six) or which combinations of positions have significantly more (or less) than their pro-rata share of defective bulges

If in a given week, the mill had run 18 turns, the number of bulges inspected would have been:

# inspected = 18 turns x 4 welds/turn x 6 bulges/weld = 432 bulges

If 73 bulges failed, the fraction defective for the week would have been p = # failed/ # inspected = 73/432 = 0.17 or 17% defective.

The 17 percentage defective was an intrinsic property of the week, regardless of the subgrouping method. Two-sigma limits were used when using rational subgroups because of the small number of subgroups. After the data on bulge test failures for the first week was gathered, a different p-Chart for each proposed method of subgrouping could be made. Week after week, the employees could compare these charts seeking evidence of assignable causes of excessive variability points outside of the control limits, particularly those that would repeat for more than one week.

Control charts for several potential sources of uncontrolled variation showed no out-of-control points. The first success in identifying an assignable cause for uncontrolled variability in weld quality came when the data was subgrouped by crew.

Figure 1. p-Chart Subgrouped by Crew, Two-Sigma Limits

The first week showed "Crew C" to be above the upper two-sigma control limit, indicating an assignable cause of variation. This was reinforced when the variation occurred two weeks in a row. Crew C was doing something different from crews A and B. This was a significant source of excessive variability that had to be removed. It took several weeks of talking with the crews before the Crew C problem disappeared. Crew C operators had finally started using the specified weld parameters. The employees eliminated a major source of variability in the weld quality, and they saw a decrease in the number of weld fractures reported in the cold-rolling division.

Subgrouping the data by bulge position along the weld showed ample evidence of lack of control but gave little indication of the root cause. The problem was solved by regrouping the data so that positions one, two and three (the north half of the coil) formed one single subgroup; and positions four, five and six (the south half of the coil) formed another. Week after week, workers found the north side to have too many failures and the south side to have too few to be explained by chance. Quality control people asked maintenance personnel to look for an out-of-square condition in the welding equipment. They were looking for something that would allow the two pieces to repeatedly come together cocked toward the same side, rather than butting up squarely, one to another.

Figure 2. p-Chart Subgrouped by North vs. South, Two-Sigma Limits

After considerable effort, it was found that one corner of the leading coil tail, a corner that should have been firmly anchored, was slipping under load when the head end of the trailing coil was forced against it. Repair procedures to ensure that the anchored coil tail was securely fastened in place corrected the problem, but the most impressive result was the effect of the experience upon the maintenance crew. They were suddenly completely convinced of the power of the control chart—it had accurately pinpointed a serious problem that they otherwise wouldn’t have discovered.

It was now possible to detect that there were significantly more failures near the center of the weld than at the two extremities. By then, maintenance personnel were true believers in the control charts, and they were able to quickly find and correct the problem. Following engineering theory, the dies for trimming the coil ends had been designed with a slight bow, but the problem vanished as soon as a simpler square cut was used. Engineering must "listen to the process," rather than just doing it "by the book."

By this time, the cold-rolling mill quality problem had been largely corrected, but the quality control staff continued to study the weld bulge test results. They started looking at the data by order-of-production, setting three-sigma limits based upon the results of the most recent two weeks. They quickly discovered that all points above the upper control limit came from only eight out of the more than 200 grades of steel. These eight grades were subsequently identified by metallurgical consultants as hard-to-weld grades that inherently suffered from low ductility after welding and new weld parameters were established for this family of steels.

The bottom line was clear: Problem-solving through the use of control charts allowed the company to improve weld quality until weld failures in manufacturing were completely eliminated.


About The Author

Robert F. Hart, Ph.D., and Marilyn K. Hart, Ph.D.’s default image

Robert F. Hart, Ph.D., and Marilyn K. Hart, Ph.D.

Robert Hart has a doctorate from Northwestern University in engineering, with a master’s degree in operations research. He worked with General Motors in product design and statistical process control for 20 years. Since 1980, he has been a consultant and is presently adjunct professor in the College of Business Administration, University of Wisconsin, Oshkosh.

Marilyn Hart has an academic background in mathematics and operations research with a doctorate in management sciences from the Illinois Institute of Technology. She has taught extensively in higher education and industry, specializing in the statistical control of quality and productivity. Dr. Marilyn Hart is a full professor in the College of Business Administration, University of Wisconsin, Oshkosh.