Mr. Qiang is the owner of Fuxing Caster Company Ltd. located in Yantai, China. His company has been in operation since 2010. Fuxing produces vibration-dampening, machine balancing mounts. Customers use mounts to balance and isolate sensitive equipment from floor vibrations.
Last year the company sold 30,000 mounts generating approximately 2.5 million RMB is sales . Nearly all sales were to Chinese original equipment manufacturers (OEMs). While the domestic market is very large, intense price competition has resulted in tight margins. To boost profitability, the company has started selling mounts overseas. The company has an English language website (Figure 1) and contracted with an international distributor. The distributor presently has 15,000 Fuxing mounts in inventory.
The distributor is pleased with the 85 RMB price for mounts and on time delivery. Unfortunately, a few customers have had issues. The problem is wheel swivel. Wheels need to freely swivel, otherwise, it’s difficult to position machine tools prior to balancing. The distributor doubts that 99% of mounts in his inventory, as promised in the purchase order, are of good quality.
The quality engineer at Fuxing suspects that the problem can be traced back to bearing assembly. Too little lubrication could cause mounts to bind. Too much preload on the bearing could cause the same issue. Next week the distributor has scheduled a meeting with Mr. Qiang to discuss wheel swivel. Key questions he expects answers to are, “What percentage of his inventory is potentially defective?” and “What process changes will be implemented to ensure no more than 1% of mounts are nonconforming?”
At Fuxing mounts are assembled on a single production line which operates one shift per day four days per week. One day per week is spent making packages and labels. Three associates work full time on the line. New hires are paid 2 RMB/hr. base pay. Each associate is scheduled to work one, seven hour shift per day. Planned downtime includes a 30 minute break for lunch and two, fifteen minute rest breaks per day. After accounting for plant shut downs, Chinese New Year and national holidays, the plant operates 5 days per week 39 weeks per year.
One mount is assembled on the line every two minutes after taking into account set ups, material handling, scrap, rework and unplanned downtime. Of the five steps involved in making a mount, bearing assembly (as shown in Figure 2) is easily the most time consuming. It involves lubricating each angular contact ball and torque wrench tightening a preload nut to seat the bearing.
Figure 2: Bearing assembly
To distribute the work load evenly, each of the three operators alternate by week time spent on the line assembling bearings. The quality engineer was able to collect 15 batches of mounts traceable back to which operators performed assembly. She was also able to collect a few defective mounts from the distributor. All of these parts were sent to an outside lab for measurement of swivel torque. The lab determined mount quality is binary. They are either good or bad based up swivel torque. For example, if swivel torque, at 95% confidence, exceeded the desired amount by 15 N-cm mounts were bad. Otherwise, mounts were good. Based on this N-cm limit, the average amount of defective mounts by assembly worker across batches are listed in Table 1.
Table 1: Percentage Defective Mounts
Sample Group Operator 1 Operator 2 Operator 3
1 0.37% 0.50% 0.33%
2 0.70% 0.33% 0.33%
3 0.33% 0.43% 0.17%
4 0.50% 0.67% 0.20%
5 1.10% 0.70% 0.33%
6 0.70% 0.40% 0.63%
7 0.73% 0.33% 0.63%
8 0.53% 0.50% 0.67%
9 0.63% 0.67% 0.34%
10 0.70% 0.70% 0.37%
11 0.40% 0.20% 0.25%
12 0.60% 0.50% 0.20%
13 0.70% 0.63% 0.40%
14 0.87% 0.43% 0.33%
15 0.43% 0.40% 0.23%
Upon reviewing this data, the operations manager noted the only difference among the three assembly line workers was their experience. Operator #1 has worked at the factory for less than a year. Operator #2 has 2 years’ experience. Operator #3 has nearly 3 years’ experience. The HR manager explained that Operator #3 would be leaving next month. Her labor contract was expiring.
Per Chinese Labor Law all full time employees work under contracts. The employer has the option of offering 1, 2 or 3-year contracts. Part time workers are not required to have contracts, but they can work no more than 20 hours per week. At Fuxing assembly line workers are offered 3-year contracts. To keep them from quitting over the course of their contracts management provides five percent pay increases per year along with annual bonuses equal to two months’ salary. To control the rise in labor costs Mr. Qiang has been considering use of 2 year contracts.
In addition to operator impact the quality engineer and operations manager also considered other solutions to the caster wheel swivel problem. On the one hand, if bearing lubrication and bearing preload could be controlled within 0.1 grams and 0.1 N-cm respectively perhaps swivel torque could be controlled without actually measuring it. To test this hypothesis the quality engineer recorded lubrication amounts and bearing preload settings for 14 mounts. Mounts were then sent out for swivel torque measurement. Results are summarized in Table 2.
Table 2: Swivel Torque by Lubrication and Preload Setting
Assembly Grease (grams) Preload (N-cm) Measured Torque (N-cm)
1 1 20 20
2 1.1 21 22
3 1.2 20.9 20.8
4 1.3 20.2 20.3
5 1.5 20.9 20.9
6 1 21 21
7 0.9 22 22
8 0.9 22.3 22.3
9 0.8 23 23
10 1 23.3 22
11 1.3 22 22
12 1.5 22.4 22.3
13 1 22 21
14 1 22 22
Another option the quality engineer and operations manager discussed is spending 600,000 RMB on a machine capable of directly measuring swivel torque. The machine requires 2.2 minutes to load a part, calibrate, conduct measurement and unload. The machine is 91% efficient after taking into account planned and unplanned downtime. Given the high machine price Mr. Qiang would only consider purchasing a single unit. Fuxing produces all its products to a single quality standard. That said, Mr. Qiang would only approve machine purchase if it’s capable of ensuring at 99% probability all 30,000 mounts made per year are good. A proponent of The Fallacy of 100% Inspection (Gunter, 1983), Mr. Qiang is adamant that he will not approve making mounts for inventory to be sorted at a later time. He is, however, agreeable to hiring a full time or part time inspector at 2 RMB/hr. to operate a measurement machine so long as the inspector is at least 60% utilized. In light of these constraints the quality engineer met with the operations manager and HR manager to put together a plan.
1. At 95% probability how many defective mounts are in inventory at the distributor?
2. At 95% probability what is the potential replacement cost of these mounts?
3. What is the recommended process at Fuxing to ensure no more than 1% of mounts are nonconforming?
4. At 95% confidence what is the potential scrap and labor cost of implementing your new process?
Gunter, B. (1983). The Fallacy of 100% Percent Inspection. ASQ Statistics Division, Newsletter 5,1. Retrieved from: http://asq.org/statistics/2011/11/quality-control/the-fallacy-of-100-inspection.pdf
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