15-8 Shader Storage Technologies produces refrigeration units for food producers and retail food establishments. The overall average temperature that these units maintain is 46° Fahrenheit. The average range is 2° Fahrenheit. Samples of six are taken to monitor the process. Determine the upper and lower control chart limits for averages and ranges for these refrigeration units.

15-9 When set at the standard position, Autopitch can throw baseballs toward a batter at an average speed of 60 mph. Autopitch devices are made for both major- and minor-league teams to help them improve their batting averages. Autopitch executives take samples of 10 Autopitch devices at a time to monitor these devices and to maintain the highest quality. The average range is 3 mph. Using control-chart techniques, determine control-chart limits for averages and ranges for Autopitch.

15-10 Zipper Products, Inc., produces granola cereal, granola bars, and other natural food products. Its natural granola cereal is sampled to ensure proper weight. Each sample contains eight boxes of cereal. The overall average for the samples is 17 ounces. The range is only 0.5 ounce. Determine the upper and lower control-chart limits for averages for the boxes of cereal.

15-11 Small boxes of NutraFlakes cereal are labeled “net weight 10 ounces.” Each hour, random samples of size $n=4$ boxes are weighed to check process control. Five hours of observations yielded the following:

Using these data, construct limits for $\overline{x}$- and R-charts. Is the process in control? What other stpng should the QC department follow at this point?

15-12 Sampling four pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results:

Develop appropriate control limits and determine whether there is any cause for concern in the cutting process.

15-13 Due to the poor quality of various semiconductor products used in their manufacturing process, Microlaboratories has decided to develop a QC program. Because the semiconductor parts they get from suppliers are either good or defective, Milton Fisher has decided to develop control charts for attributes. The total number of semiconductors in every sample is 200. Furthermore, Milton would like to determine the upper and the lower control-chart limits for various values of the fraction defective ($\overline{p}$) in the sample taken. To allow more flexibility, he has decided to develop a table that lists values for $\overline{p}$, UCL, and LCL. The values for $\overline{p}$ should range from 0.01 to 0.10, incrementing by 0.01 each time. What are the 10 UCLs and the LCLs for 99.7% confidence?

15-14 For the past two months, Suzan Shader has been concerned about machine number 5 at the West Factory. To make sure that the machine is operating correctly, samples are taken, and the average and range for each sample are is computed. Each sample consists of 12 items produced from the machine. Recently, 12 samples were taken, and for each, the sample range and average were computed. The sample range and sample average were 1.1 and 46 for the first sample, 1.31 and 45 for the second sample, 0.91 and 46 for the third sample, and 1.1 and 47 for the fourth sample. After the fourth sample, the sample averages increased. For the fifth sample, the range was 1.21, and the average was 48; for sample number 6, it was 0.82 and 47; for sample number 7, it was 0.86 and 50; and for the eighth sample, it was 1.11 and 49. After the eighth sample, the sample average continued to increase, never getting below 50. For sample number 9, the range and average were 1.12 and 51; for sample number 10, they were 0.99 and 52; for sample number 11, they were 0.86 and 50; and for sample number 12, they were 1.2 and 52.

Although Suzan’s boss wasn’t overly concerned about the process, Suzan was. During installation, the supplier set a value of 47 for the process average, with an average range of 1.0. It was Suzan’s feeling that something was definitely wrong with machine number 5. Do you agree?

15-15 Kitty Products caters to the growing market for cat supplies, with a full line of products, ranging from litter to toys to flea powder. One of its newer products, a tube of fluid that prevents hair balls in long-haired cats, is produced by an automated machine that is set to fill each tube with 63.5 grams of paste.

To keep this filling process under control, four tubes are pulled randomly from the assembly line every 4 hours. After several days, the data shown in the following table resulted.

Set control limits for this process and graph the sample data for both the $\overline{x}$- and R-charts.

15-16 Colonel Electric is a large company that produces lightbulbs and other electrical products. One particular lightbulb is supposed to have an average life of about 1,000 hours before it burns out. Periodically, the company will test five of these and measure the average time before these burn out. The following table gives the results of 10 such samples:

1. What is the overall average of these means? What is the average range?

2. What are the upper and lower control limits for a 99.7% control chart for the mean?

3. Does this process appear to be in control? Explain.

15-17 For Problem 15-16, develop upper and lower control limits for the range. Do these samples indicate that the process is in control?

15-18 Kate Drew has been hand-painting wooden Christmas ornaments for several years. Recently, she has hired some friends to help her increase the volume of her business. In checking the quality of the work, she notices that some slight blemishes occasionally are apparent. A sample of 20 pieces of work resulted in the following number of blemishes on each piece: 0, 2, 1, 0, 0, 3, 2, 0, 4, 1, 2, 0, 0, 1, 2, 1, 0, 0, 0, 1. Develop upper and lower control limits for the number of blemishes on each piece.

15-19 A new president at Big State University has made student satisfaction with the enrollment and registration process one of her highest priorities. Students must see an advisor, sign up for classes, obtain a parking permit, pay tuition and fees, and buy textbooks and other supplies. During one registration period, 10 students every hour are sampled and asked about satisfaction with each of these areas. Twelve different groups of students were sampled, and the number in each group who had at least one complaint is as follows: 0, 2, 1, 0, 0, 1, 3, 0, 1, 2, 2, 0.

Develop upper and lower control limits (99.7%) for the proportion of students with complaints.

15-20 Cybersecurity is an area of increasing concern. The National Security Agency (NSA) monitors the number of hits at sensitive websites. When the number of hits is much larger than normal, there is cause for concern, and further investigation is warranted. For each of the past 12 months, the number of hits at one such website has been 181, 162, 172, 169, 185, 212, 190, 168, 190, 191, 197, and 204. Determine the upper and lower control limits (99.7%) for the associated c-chart. Using the upper control limit as your reference, at what point should the NSA take action?

15-21 V. S. Industries in Parkersburg, West Virginia, is a small manufacturer of military-grade hybrid microcircuits. One of the many quality assurance procedures required by Military Standard 883 (MIL-STD-883) for hybrid microcircuits is known as nondestructive bond pull (method number 2023.7 in MIL-STD-883). The procedure involves pulling on a random sample of wires within the hybrid microcircuit with a prespecified amount of force. If the wire tears, breaks, or separates in any way from the circuit, it fails the test and is considered defective and scrapped. In a recent batch of 1,000 devices, 13 failed the pull test. Determine upper and lower control limits for the associated p-chart.

15-22 As noted in Problem 15-21, wire bond pull strengths for U.S. defense contractors are tested according to MIL-STD-883. In addition to nondestructive testing, destructive testing is also employed. A small potentiometer measures the grams of force necessary to either shear the wire in two or separate one of the two bonds from the underlying substrate. Ten samples ($n=5$) of V. S. Industries’ 1 mil diameter Au wire have shown these results for force: 2.1, 2.2, 2.6, 2.1, 2.5, 2.4, 2.3, 2.1, 2.4, and 2.6 grams. Determine 99.7% control limits for the associated x-bar and R-charts.

15-23 Every commercial airline pilot visually inspects his/her airplane before flying. If the number of visible defects (known as marks) exceeds a certain prescribed limit, the pilot can call for maintenance, causing flight delays or even flight cancellations. Explain what kind of control chart could be used by the airline companies to monitor and control the number of marks on the plane.