Question

The Operations manager at a large widget factory is complaining that since the company has changed to a cheaper supplier for one of the raw materials used for widgets, the quality of their widget has changed. In fact, he has one of the final widgets that has a strength testing below their spec. The new operations employee had previously taken 5 samples each week over a 10-week period, and logged the data in the chart below.

Calculate upper and lower control limits for an Xbar chart using this data.

Sample data:	1	2	3	4	5	6	7	8	9	10
Mean	27.4	28.6	28.4	27.8	29.3	28.0	27.2	28.5	28.0	27.5
Range	1.5	1.9	0.9	2.0	1.6	1.6	2.0	1.9	2.1	1.9

Multiple Choice

• UCL = 29.08

  LCL = 3.67

• UCL = 28.61

  LCL = 27.53

• UCL = 29.3

  LCL = 27.2

• UCL = 28.07

  LCL = 1.74

Using the data from Question #4, calculate upper and lower control limits for a range chart

Multiple Choice

• UCL = 3.67

  LCL = 0

• UCL = 3.10

  LCL = .38

• UCL = 2.1

  LCL = 0.9

• UCL = 3.99

  LCL = 0

c.) Continuing on from question #4, the employee continues to track the same data for 10 weeks after the supplier change, and gets the following data:

Sample data:	1	2	3	4	5	6	7	8	9	10
Mean	27.8	28.9	27.4	28.7	28.0	27.1	27.2	27.3	28.0	27.4
Range	2.3	1.5	3.0	2.1	3.2	2.2	3.6	2.0	3.4	1.7

The Operations manager looks at the data and points out that the strength has gone down as he claims, as the average of these new readings is below the previous average, and the average range of the samples is also higher, which he claims proves there is more variability. Should the company change back to the original supplier? Why or why not?

Multiple Choice

• All the new sample means fall within control limits, as do all the new sample ranges. Therefore, the process is “under control”, which means there has been no assignable variation. The supplier change therefore did not have an impact and they should not change back.

• The operations manager is correct, and there the new supplier has added additional variability to the process. They should therefore change back to the original supplier.

• Calculating new control limits for the new data, shows that the process is in control, so they should not change back.

• Calculating new control limits for the new data gives clearly different control limits. There therefore has been an assignable change in variation, so they should change back to the original supplier.

Answer 1

upper and lower control limits for an Xbar chart

Ans:

UCL = 28.61

LCL = 27.53

upper and lower control limits for a range chart

UCL = 3.10

LCL = .38

Number of samples	5
Sample size	10
Data				Results
	Mean	Range			Xbar	Range
1 1	27.4	1.50	Below LCL	x-bar value	28.07
1 2	28.6	1.90
1 3	28.4	0.90		R bar		1.74
1 4	27.8	2.00
1 5	29.3	1.60	Above UCL	Upper control limit	28.61	3.1
1 6	28	1.60		Centerline	28.07	1.74
1 7	27.2	2.00	Below LCL	Lower control limit	27.53	0.388
1 8	28.5	1.90
1 9	28	2.10
1 10	27.5	1.90	Below LCL
Average	28.07	1.74

The calculation after changing the supplier:

Number of samples	5
Sample size	10
Data				Results
	Mean	Range			Xbar	Range
1 1	27.80	2.30		x-bar value	27.78
1 2	28.90	1.50	Above UCL
1 3	27.40	3.00		R bar		2.5
1 4	28.70	2.10	Above UCL
1 5	28.00	3.20		Upper control limit	28.55	4.4
1 6	27.10	2.20		Centerline	27.78	2.50
1 7	27.20	3.60		Lower control limit	27.01	0.558
1 8	27.30	2.00
1 9	28.00	3.40
1 10	27.40	1.70
Average	27.78	2.50

Answer:

The operations manager is correct, and there the new supplier has added additional variability to the process. They should, therefore, change back to the original supplier.

Explanation: We see the variation has crossed the control limits. This indicates the variation is more and has crossed the UCL at two points and going back to the old supplier is recommended. The range of variability is also high which might mean that quality and product specifications are not as desired.