Managing COPQ by Analyzing and Optimizing Thresholds

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By David Lengacher

At the core of Six Sigma lies the continuous drive to reduce the cost of poor quality (COPQ), and it often takes center stage when making the business case for continuous improvement projects. Its components include aspects of operations such as scrap, rework and costly customer returns. In the wake of the current global economic crisis, it has never been more important to minimize the burden COPQ places on the viability of a business.

Unfortunately, one area that has a significant effect on COPQ is often overlooked in continuous improvement projects: the thresholds used to determine whether a product is at an acceptable quality level. When people think of thresholds, they may conjure up images of machinery. Yet thresholds are used either consciously or unconsciously in most every type of decision making, most of which are non-industrial related.

Practitioners often assume that the thresholds in place were set correctly. Yet a routine investigation into the current threshold will often be met with the following results:

• The person who originally chose the threshold level is no longer with the company.
• There is little or no documentation outlining how the level was chosen.
• The threshold is not set at an optimal level.

Therefore, practitioners may find savings by taking a closer look at quality thresholds. The following case study illustrates how changing thresholds can impact COPQ.

Case Study: Bearings Diameter Thresholds

In a facility that manufactures bearings, a new Black Belt was under pressure to present a solution that could reduce the current COPQ. By conducting some intermediate statistical analysis, the Belt identified the optimal threshold setting.

Production

Annual production was 10,000 bearings, with a mean diameter of 100 cm, standard deviation of 2 cm, and customer specification limits of 94 cm (lower) and 106 cm (upper).

Costs

The company faced an internal scrap cost of $9,800 per unit if bearings did not conform to customer specifications. An external cost of $19,950 per unit was lost if a unit was returned by the customer.

Problem

The yield of this process was 99.73 percent, meaning the internal scrap costs equaled:

27 units x $9,800 = $264,600

However, in addition to this internal cost, the facility had experienced approximately 50 units that failed in the field (FIF) and resulted in customer returns equal to:

50 x $19,950 = $997,500

Therefore, total COPQ was $1,262,100.

This pattern of 50 customer returns annually had persisted for several years. In an attempt to identify the root cause behind the failure, all 50 returned units this time were to be sent to the lab for chemical analysis. However, before sending them to the lab, the Belt discovered that these returned bearings had one thing in common: their diameter. Data analysis concluded that the FIF units had a mean diameter of 105 cm, with a standard deviation of 0.5 cm. The Belt depicted this situation using a distribution plot (Figure 1).

Figure 1: Bearings Diameter

Results from the chemical analysis in the lab were not expected for weeks or possibly months. Although the results could provide a root cause, it was possible they would not. The Belt needed to create a more immediate plan of action to reduce the amount of FIFs and the COPQ.

The options for controlling variables in this situation were limited. It was apparent that by conducting some what-if analysis regarding the establishment of a tighter upper specification limit, the Belt might be able to cut off part of the tail of the FIF distribution. However, by implementing a tighter spec, the Belt would also increase internal scrap. To find the net effect on COPQ of altering the specification limit, the Belt needed to conduct some spreadsheet modeling and simulation.

Before performing any calculations on the FIF distribution, the Belt first conducted a t-test to see if it was reasonable to treat the 50 FIF units as a separate distribution. In this case, the t-statistic exceeded 16 (highly significant). This told the Belt that performing calculations on the FIF distribution was reasonable.

Conducting Threshold Analysis

The first step in the threshold analysis was choosing a range, between which the net effect on COPQ could be tested. In this case, the Belt set the range to be 104.9 cm to 106 cm, in 0.1 cm increments. Next, the Belt constructed a table that would capture all of the contributing factors. As the upper specification moved inward toward 104.9, the Belt calculated how much the cost of scrap was increasing and how much the cost of FIFs was decreasing (Table 1).

Table 1: Cost of Scrap and FIFs with Different Thresholds
Threshold	Percent of Product Scrap Due to Internal Threshold	Scrapped Units (Upper Spec)	Upper Spec Scrap Cost (Units x $9,800)	Percent of FIFs Shipped	FIF Units	FIF Cost (Units x $19,950)	Add Scrap Cost from Lower Spec	Cost of Poor Quality
104.9	0.7 percent	71	$699,995	42 percent	22	$442,411	$132,290	$1,274,697
105	0.6 percent	62	$608,547	50 percent	26	$521,473	$132,290	$1,262,310
105.1	0.5 percent	54	$527,842	58 percent	30	$600,535	$132,290	$1,260,667
105.2	0.4 percent	47	$456,796	66 percent	34	$676,506	$132,290	$1,265,593
105.3	0.3 percent	40	$394,410	73 percent	37	$746,656	$132,290	$1,273,355
105.4	0.3 percent	35	$339,763	79 percent	41	$808,897	$132,290	$1,280,951
105.5	0.3 percent	30	$292,017	84 percent	43	$861,964	$132,290	$1,286,271
105.6	0.3 percent	26	$250,403	88 percent	45	$905,441	$132,290	$1,288,134
105.7	0.2 percent	22	$214,224	92 percent	47	$939,668	$132,290	$1,286,183
105.8	0.2 percent	19	$182,850	95 percent	48	$965,561	$132,290	$1,280,700
105.9	0.2 percent	16	$155,709	96 percent	49	$984,383	$132,290	$1,272,382
106	0.1 percent	13	$132,290	98 percent	50	$997,530	$132,290	$1,262,110

The Belt evaluated the results across the range of 106 cm to 104.9 cm and noticed that by slowly moving an internal threshold inward to a value of 105.1 cm, the company could reduce its COPQ by more than $2,000 while at the same time reducing the projected annual customer returns from 50 units to 30 units, a decrease of 40 percent. To get an idea of the entire output space, the Belt graphed the spectrum of COPQ for all threshold levels (Figure 2).

Figure 2: Cost of Poor Quality Based on Threshold

Yielding Results

Threshold investigations should be an integral part of any continuous improvement program. By optimizing thresholds, Belts can yield incredibly significant and immediate results because thresholds directly affect scrap and lost sales. Belts should consider looking around their local areas and inquiring into how the thresholds in their environment were derived– they might just be surprised with what they find.

About the Author: David Lengacher is a Master Black Belt. He holds an MBA from Purdue University and a master’s in operations research from the University of Florida, and is an American Society for Quality-certified reliability engineer. His areas of expertise are modeling and simulation, and the analysis of high-dimensional data for use in optimization. He can be reached at dclengacher@gmail.com.

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