WMBA 6040 Week 4 Pareto Remake Analysis Example

Coating Defects Top the Pareto Chart, but the Waiting Causes Them: A Pareto Analysis of 1,170 Remakes at an Optical Lab, Stratified by How Long Lenses Sat Before Coating

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Walden University

WMBA 6040: Improving Business Performance

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Month Day, Year

Coating Defects Top the Pareto Chart, but the Waiting Causes Them: A Pareto Analysis of 1,170 Remakes at an Optical Lab, Stratified by How Long Lenses Sat Before Coating

The Problem and the Tool

Final inspection at Clearwater, the invented lens lab this course follows, rejects about 9 percent of jobs, and every rejected job is remade from the beginning, adding about six business days to its turnaround. Week 3 proposed first-pass yield as a weekly measure. This paper applies one quality tool, the Pareto chart, to four weeks of reject records to find where remakes come from, and then stratifies the largest category to see what lies beneath it.

The Pareto principle, named by Juran after the economist Vilfredo Pareto, holds that most occurrences of a problem tend to trace back to a handful of causes, so ranking causes by frequency shows where effort will pay most (Juran & De Feo, 2010). The chart itself is simple: categories in descending order of frequency, with a cumulative percentage. Its value depends on the categories being defined consistently, which the lab's reason codes allow.

The Data

Over four weeks, final inspection examined about 13,000 jobs for the first time and rejected 1,170, a first-pass yield of 91 percent. Each reject carries one reason code entered by the inspector.

Table 1

Remakes by Reason Code, Four Weeks

Counts are composite figures for a four-week period.

Figure 1

Remakes by Reason Code, Four Weeks

Bars are ordered by frequency, with Other placed last by convention.

What the Chart Shows at the Surface

The chart shows the expected concentration. Coating defects and axis errors together account for 56 percent of remakes, and the top three categories for 71 percent. A manager reading only the chart would conclude that the coating department has a quality problem and the edging department a calibration problem, and would direct attention to those two departments.

That conclusion is partly right and partly misleading, which is why the largest category needs a second look.

Beneath the Largest Category

Coating defects can arise inside the chamber, from a contaminated chamber or a bad batch of material, or before it, from lenses that are not perfectly clean when they enter. Polishing compound that dries on a lens surface is hard to remove completely, and lenses that wait longer between surfacing and coating have more time for residue to harden. The Week 2 map showed that coated lenses wait an average of 2.4 business days for a run of their formulation. If waiting causes defects, defect rates should rise with waiting time.

The lab's scans record when each lens left surfacing and when it entered coating, so the coating rejects can be stratified by that interval.

Table 2

Coating Defect Rate by Hours Waiting Between Surfacing and Coating

Jobs are grouped by the interval recorded in tray scans; composite figures.

The pattern is strong. Lenses that waited more than 36 hours had a coating defect rate more than three times that of lenses coated within 12 hours. Waiting over 36 hours accounts for 39 percent of coated jobs but 60 percent of coating defects.

This does not prove that waiting causes defects. Lenses that wait longer may differ in other ways; for example, a formulation used mainly for high-index lenses, which are harder to coat, might also be the one run least often. A check by formulation would be the next step. But the stratification changes the likely remedy. If waiting drives defects, the fix is not mainly inside the coating department's process; it is the coating schedule, the same constraint the Week 2 map identified for turnaround.

A Brief Look at the Second Category

Axis errors were also stratified, by edger and shift. Seventy percent came from one of the lab's four edgers, and most of those from the night shift, when the machine's calibration is checked least often. That category appears to have a simpler cause, a single machine's calibration, which the edging lead can test with a daily calibration check.

What the Analysis Finds

The surface finding is that coating defects are the largest source of remakes. The finding underneath is that coating defects concentrate among lenses that wait longest before coating, which links the lab's largest quality problem to its largest flow problem. Shortening the wait at coating could therefore improve yield and turnaround together, and it would shrink the stock of unfinished trays as well, since work in process rises with time in the system (Little, 1961). Ishikawa (1985) taught that quality problems should be traced from their visible effects back to their process causes, and the stratification is a small instance of that discipline.

Limits

Four weeks of data may not capture seasonal changes in mix. Reason codes depend on inspectors' judgment, and "Other" holds 9 percent of remakes that deserve a closer look. Most important, the waiting-time link is a correlation; a small test, coating one formulation more often for two weeks, would show whether defects fall when waits shrink.

What the Lab Should Do Next

The analysis points to two next steps. The first is a short test of the waiting link: for two weeks, the lab should run one coating formulation four times a day instead of once every day and a half, and compare that formulation's defect rate with the other two. If its defect rate falls toward the rate seen for short waits, the case for changing the whole coating schedule becomes much stronger. The second is a daily calibration check on the edger that produced most axis errors, a ten-minute task at the start of each shift. Both steps are cheap, both can begin within a week and both produce data the lab can read within a month. Neither requires new equipment.

References

Ishikawa, K. (1985). What is total quality control? The Japanese way (D. J. Lu, Trans.). Prentice-Hall.

Juran, J. M., & De Feo, J. A. (2010). Juran's quality handbook: The complete guide to performance excellence (6th ed.). McGraw-Hill.

Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383-387. https://doi.org/10.1287/opre.9.3.383