# Using process control charts to reduce production times.

In a PVC powder plant where |Mathematical Expression Omitted~ and R charts were used to control and reduce manufacturing times, output was increased by 25% and the loss rate was lowered by 90%.

Industrial engineers and production personnel are generally familiar with the use of |Mathematical Expression Omitted~ and R charts to improve and control product quality. |Mathematical Expression Omitted~ is the average of a set of two or more observed values, and R is the range, that is, the difference between the largest and the smallest values in the set. Production costs can be reduced by applying these techniques to improve and control manufacturing times. This article discusses one such application in which |Mathematical Expression Omitted~ and R charts were used to increase the output of a PVC powder plant.

Each month this plant produced five or six of eighteen possible grades of PVC powder. The process required ten discrete steps; twenty-four reactors were used in a three-shift operation. The plant experienced thousands of elemental production times each month--and the company was losing \$100,000 per month. There was a pressing need for corrective action, yet production analysts had no way of knowing which basic elemental times for any step, shift, grade, and reactor combination were varying normally and which abnormally.

After several years without guidance with respect to locating such hidden production problems, management instituted |Mathematical Expression Omitted~ and R control charting of elemental times. The result after one year was a production increase of 25%, and remedial actions dictated by the control charts cut the loss rate by 90%. The industrial engineers introduced the control concepts in the following steps.

1. Determine which elemental times to chart.

The ten basic steps in the reaction cycles are:

a. Fill a reactor with water.

b. Draw a vacuum.

c. Charge with vinyl chloride monomer.

d. Let the batch react.

e. Degas the reactor.

f. Delay (no place to transfer the completed batch).

g. Transfer the completed batch.

h. Delay (no one available to clean the reactor).

i. Clean the reactor.

j. Delay (water or worker being used elsewhere).

These variables require ten charts, but adding the other variables--three shifts, eighteen grades, and twenty-four reactors--extended to 12,960 the total number of elements that could be charted (10x3x18x24), one for each step, shift, grade, and reactor combination. Because most variables could be combined, the number of charts needed was greatly reduced. For example, the time required to draw a vacuum was independent of product, reactor, or shift, so only one chart was needed.

2. Record the ninety most recent production times for each element, to be charted in thirty subgroups of three.

Ninety, thirty, and three are not absolute requirements but practical guides, especially if the amount of past data is limited. An example for drawing a vacuum:
```Subgroup Date Elapsed time, min
1 4/12 76 63 82
2 4/13 88 59 72
```

3. Calculate the average and the range for each of the thirty subgroups.

Continuing the above example:

TABULAR DATA OMITTED

4. Calculate the average of the averages, |Mathematical Expression Omitted~, and the average of the ranges, |Mathematical Expression Omitted~, for each element of the thirty subgroups.

If, for drawing a vacuum, the thirty |Mathematical Expression Omitted~ totaled 2229 and the thirty Rs totaled 638, then:

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~.

5. Calculate the upper trial control limit for the range chart, |UCL.sub.R~.

|Mathematical Expression Omitted~

|UCL.sub.R~ = (2.57) (21.3) = 54

6. Remove any ranges exceeding |UCL.sub.R~ and calculate a new |Mathematical Expression Omitted~ and |UCL.sub.R~.

Repeat this step until no remaining ranges exceed the last calculated |Mathematical Expression Omitted~ and |UCL.sub.R~ for the R control charts.

For drawing a vacuum, the final |Mathematical Expression Omitted~ came out to be 19 and the final |UCL.sub.R~ to be 48.

7. Calculate the upper and lower trial control limits for the |Mathematical Expression Omitted~ chart, |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~.

|Mathematical Expression Omitted~

The least value of |Mathematical Expression Omitted~ and |A.sub.2~ = 1.02 for a subgroup of three (from any SQC text) are used.

For drawing a vacuum:

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

8. Remove any averages exceeding |Mathematical Expression Omitted~, and calculate a new |Mathematical Expression Omitted~, |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~. Repeat this step until no remaining averages exceed the last calculated |Mathematical Expression Omitted~. Use the last calculated |Mathematical Expression Omitted~, |Mathematical Expression Omitted~, and |Mathematical Expression Omitted~ for the |Mathematical Expression Omitted~ control charts.

For drawing a vacuum, the final |Mathematical Expression Omitted~ came out to be 68, the final |Mathematical Expression Omitted~ to be 87, and final |Mathematical Expression Omitted~ to be 48.

Unlike all the previous steps, this step is not taken for quality control. However, it is a basic and important step in time control that enables the industrial engineers to take step 9.

9. Determine key efficiencies.

The last calculated |Mathematical Expression Omitted~ for each element is its statistically valid standard time. Since the average elapsed time (from step 4) and the actual standard time (from step 8) were now available for every element, the real efficiency of each element, each product, each reactor, each shift, and the plant as a whole could be calculated by:

Efficiency = standard time x 100%/average time

10. Maintain |Mathematical Expression Omitted~ and R charts of subsequent production times on a monthly basis to be submitted in a monthly report to all levels of management. Include key efficiencies and month-to-month improvements.

Everyone could now see precisely where action was needed to alleviate problems. Averages and ranges above UCLs were considered to be the result of specific abnormalities that could be found and removed. Action was not needed for averages and ranges below UCLs because they were considered to be within normal process variations. The Figure shows |Mathematical Expression Omitted~ and R charts for drawing a vacuum for one particular month; arrows point to out-of-control times, requiring investigation and remedial action.

As the monthly reports and charts were issued, control and efficiency improved immediately and continued to improve when actions were taken by plant personnel or management on points exceeding UCLs. After improvements were instituted, time standards and control limits were lowered accordingly.

The control charts clearly showed where to act, and just as clearly, where not to act, to rapidly isolate and remove production problems. |Mathematical Expression Omitted~ and R control charting of production times is a powerful and simple tool that can no doubt be applied in numerous plants across the United States where greater manufacturing time reduction and control are needed, but especially in chemical and plastic batch production involving a mix of products. If this example is at all typical, time reductions of 30% or more and cost reductions of 15% or more could be commonplace--resulting in, for example, a \$15-million profit increase in a \$100-million operation. Certainly this is hypothetical, but the point is that there is a lot of money to be made from using this technique.
COPYRIGHT 1992 Society of Plastics Engineers, Inc.
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