An expert in business math

Problem 10-2

An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approximately normal with a mean of .97 liter and a standard deviation of .04 liter. Output is monitored using means of samples of 29 observations. Use Table-A.

a.	Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. (Do not round intermediate calculations. Round your answers to 4 decimal places.)


Upper control limits:	liter
Lower control limits:	liter

Given these sample means: 1.005, 1.001, .998, 1.002, .995, and .999, is the process in control?

	Yes
	No

rev: 11_21_2014_QC_59337

Problem 10-17

The process specs are 9.5 and 10.5 minutes. Based on the data given.

	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5
	10.3	10.2	9.8	9.8	9.7
	9.8	10.0	9.5	10.1	9.9
	10.2	9.6	10.2	10.4	10.4
	9.5	9.5	9.5	9.7	10.0

Totals	39.8	39.3	39.0	40.0	40.0

Does it appear that the specs are being met?

	No
	Yes

Problem 10-21

A process that produces computer chips has a mean of .04 defective chip and a standard deviation of .003 chip. The allowable variation is from .036 to .044 defective.

a.	Compute the capability index (Cp) for the process. (Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places.)

Capability index

Is the process capable?

	No
	Yes

Problem 10-23

Suppose your manager presents you with the following information about machines that could be used for a job, and wants your recommendation on which one to choose. The specification width is .48 mm. In this instance, you can narrow the set of choices, but you probably wouldn’t make a recommendation without an additional piece of information. (Round your answers to 3 decimal places.)

Machine	Cost per Unit ($)	Standard Deviation (mm)
A	12	.065
B	12	.060
C	19	.056
D	10	.063

Process	Cp
A
B
C
D

We can narrow the choices to processes .

References

eBook & Resources

Problem 10-25

An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis. The company has set an acceptable range of repair time of 50 minutes to 90 minutes. Two firms have submitted bids for the work. In test trials, one firm had a mean repair time of 74 minutes with a standard deviation of 4.0 minutes and the other firm had a mean repair time of 72 minutes with a standard deviation of 5.1 minutes. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Firm	Cpk
1
2

Which firm would you choose?

	Firm 1
	Firm 2
	None

References

eBook & Resources

Problem 10-28

The following is a control chart for the average number of minor errors in 22 service reports.

a.	Calculate the observed mean, expected mean, standard deviation and z value for the median and up/down test. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)