Using p Charts to Solve a Steel Mill Quality Problem

Authors: Marilyn & Robert Hart

A steel mill quality problem arose in the manufacture of cold-rolled steel for use in applications such as automobile hoods. In order to form a long continuous band, several hot-rolled coils were welded together end-to-end. The long continuous band then included the welds that were made to join the original coils together. Unfortunately, many of these welds were failing under tension, causing damage as well as extreme danger as these coils then flailed about.

In order to discover why these coils were failing at the welds, a functional test was performed at the weld station. After removing the long ridge of previously molten metal, the weld was removed in a 12" strip of steel from the full width of the coil. This was done four times each 8-hour shift. (In the steel mill an 8-hour shift is called a "turn".) A one-inch diameter tool steel ball was pressed down into the test piece until a "bulge" a half-inch high 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 would be tested using six bulges equally spaced along the weld. Starting at the north edge of the coil, these bulges would be numbered 1 through 6 with odd numbered bulges toward the top of the sheet and even 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 for the bulge test, we were ready to consider the various methods of subgrouping that could be used to study the test results. We needed to improve the weld process so welds would uniformly have sufficient ductility to prevent fracture. To do this we needed to look at the data in time-order but first we wanted to address the potential sources of variation in weld quality, based upon expert knowledge of the process. We would then 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 selected as easiest to apply.

  • TURN: e.g., Was the third shift really worse than the overall average?
  • CREW: Consisting of both operators and inspectors working together as a single team, with rotating shift assignments.
  • OP vs. BOTTOM: e.g., Did significantly more than half of the failures occur on bulges toward the top of the strip?
  • POSITION OF BULGE: Do certain bulge positions across the weld (numbered 1 through 6) or certain combinations of positions have significantly more (or less) than their pro-rata share of defective bulges.

Suppose that for a given week, the mill had run eighteen turns. Then the number of bulges inspected would have been:

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

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

Note that the 17% defective was an intrinsic property of the week regardless of the subgrouping method. We chose to use 2-sigma limits when using rational subgroups because of the small number of subgroups. After we had obtained the data on bulge test failures for the first week, we could make a different p-chart for each proposed method of subgrouping. Week after week, we 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. Our first success in identifying an "assignable cause" for uncontrolled variability in weld quality came when we subgrouped the data by "crew", as seen in Figure 1.

Figure 1. p Chart Subgrouped by Crew, 2-Sigma Limits

The first week showed "Crew C" to be above the upper 2-sigma control limit, indicating an assignable cause of variation. This was reinforced when it happened two weeks in a row. Crew C was doing something different from Crews A and B. We had identified a significant source of excessive variability, which 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. We had eliminated a major source of variability in the weld quality and we saw a decrease in the number of actual weld fractures reported in the cold rolling division.

Subgrouping the data by bulge position along the weld (positions 1 through 6) 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 1, 2 and 3 (the north half of the coil) formed one single subgroup, and positions 4, 5 and 6 (the south half of the coil) formed another. As seen by example in Figure 2, week after week we found the north side to have "too many" failures and the south side to have "too few" to be explained by chance. We asked maintenance personnel to look for an out-of-square condition in the welding equipment. We were looking for something which 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, 2-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 assure that the anchored coil tail was securely fastened in place corrected the problem, but the most impressive result was the impact 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 would not 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 we continued to study the weld bulge test results. Now we looked at the data by order-of-production, setting 3-sigma limits based upon the results of the most recent two weeks. We quickly discovered that all of the points above the upper control limit came from only eight out of the total of over two hundred 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 us to improve weld quality until weld failures in manufacturing were completely eliminated.


Hart, Robert. "Steel by Shewhart." Quality, June 1984, pp. 66 - 69.
Hart, Marilyn and Hart, Robert. Quantitative Methods for Quality and Productivity Improvement, American Society for Quality, ASQ Quality Press, 1982.

For more information, contact Drs. Robert and Marilyn Hart at or (541) 412-0425.

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