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Attached - 10 questions.

1Design specifications require that a key dimension on a product measure 102 ± 15 units. A process being considered for producing this product has a standard deviation of 6 units.(Format answers rounded to 4 decimal places when entering answers in the quiz, Leave the probabilty as decimal numbers, not %.) a) Find the process capability index, Cpk, and the probability of defective output. Assume that the process is centered with respect to specifications, i.e., process mean is 102.b) Suppose the process mean shifts to 96. Calculate the new process capability index. c) What is the probability of defective output after the process shift? Did it increase or decrease? (For this question and the next, a relevant reference is Example 13.1 in the textbook, pp. 370-371. The Excel calculation of that example is shown in sheet Ex 13.1 of Excel SPC workbook. )2Thickness (mm)1.91.82.12.122.22.421.92.12.22.41.82.22.11.72.21.92.12.21.71.82222.11.81.61.91.61.721.71.81.92.11.81.61.92.2To the right is a picture of a washer that is supposed to be 1.9 mm thick. The tolerances on the thickness are 0.5 mm, so the thickness should be between 1.4 mm and 2.4 mm. You are given here the thickness in mm for a sample of 40 washers. Assume the thickness is distributed normally.Format your answers with 4 decimal places except where otherwise specified.a) Verify that the mean = 1.9625 and the standard deviation from this data is 0.2096. (Recall STDEV.S is the function for computing the sample standard deviation.)b) What is the Cpk for the process?c) What % of the output is expected to be out of tolerance (outside the specification limits = defective)? (Express the probability as % with 2 decimal digits, e.g., 12.34%.)d) If the process were centered, i.e., sample mean were equal to 1.9 mm (with the standard deviation unchanged), what would be the Cpk? e) If the process were centered as in (d), what percentage of output would be expected to be out of tolerance? f) If the process were centered AND the standard deviation was only about .10 millimeter, what would be the Cpk and percent defective?(This percent defective is very close to 0. Increase decimal digits until you can see 2 significant figures (e.g., 0.0000012%))g) Out of situations in (b), (d), and (f) which had the process considered capable?3SamplenNumber of Defective Items11512152315341525151615271518153915210151Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart. The samples and the number of defectives in each are shown in the following table.a) Determine the p-bar, Sp, UCL and LCL for a p-chart with z = 3 (Format your answers with 4 decimal places.) b) Plot the p-chart.c) Based on the plotted data points, what comments can you make? (i.e., is the process in control or out of control?) Decide based on whether at least one point is outside the control limits. Recall a point is outside the control limits if it is < LCL or > UCL.4Sample# Defects1625304154627583931021161211381471551641711183190204At Data Systems Services company owned by Donna, she wants to see if the data entry process is in control. She collected 100 records entered by each of the 20 clerks. She counted the number of incorrectly entered records out of each sample. Below, you are given this data. Determine whether this process is in control. (Remember the sample size is not number of rows, but the number of items in each sample.)5AreaNumber of CrimesSample Size110910219103159104149105109106229107169108159109891010591011129101211910131491014109101513910161891017491018129101969102018910A city has 20 police precincts (geographical areas in the city served by different units). Some citizens in the city complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence. The police recognize that not all crimes and offenses are reported. Because of this, the police have contacted by phone a random sample of 910 residences for data on crime in each area. (Respondents are guaranteed anonymity.) The 910 sampled from each area showed the following incidence of crime during the past month.a) Determine the p-bar, Sp, UCL and LCL for a p-chart of 99.7 percent confidence (at Z = 3). (Round your answers to 4 decimal places in the quiz.)b) Is the process in control? If not, are there certain areas that warrant further investigation into their relative high or low crime rates? 6Factors forX-barLCLUCLSample Size, nJanice Winch: Same as Exhibit 13.7 on p. 377 of textbookA2D3D421.8803.26731.02302.57440.72902.28250.57702.11460.48302.00470.4190.0761.92480.3730.1361.86490.3370.1841.816Sample Mean, X-barRange, R100.3080.2231.777110.0020.011110.2850.2561.744210.0020.014120.2660.2831.71739.9910.007130.2490.3071.693410.0060.018140.2350.3281.67259.9970.013150.2230.3471.65369.9990.012710.0010.008810.0050.01399.9950.0041010.0010.0111110.0010.0141210.0060.009Twelve samples, each containing five parts, were taken from a process that produces steel rods at a factory. The length of each rod (in inches) in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were are shown below. Notice X-bar and R values are already given, so you don't need to compute them. To the right is the table containing A2, D3, and D4.Do not round the intermediate results, but when entering answers, round them to 3 decimal places.In problems involving X-bar and R charts, remember sample size n should be the number of items in each sample, not number of rows.a) Determine the UCL and LCL for X-bar chart, and plot the X-bar chart.b) Determine the UCL and LCL for R chart, and plot the R chart.c) Both X-bar and R should be in control to conclude the process is in control. Based on your results, is the process in control? 7READINGS (IN OHMS)SAMPLE12341101398699497729771027982102431027990998101741023102510161006510051026975991698399899098879919991001985810251023101410239101910049829791099999599110101197099210061012121010985983103013103010021016982149799861016988151028100610191002Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows. Use three-sigma control limits.a) Calculate the mean and range for the samples. (Round "Mean" to 2 decimal places and "Range" to the nearest whole number in the quiz.)b) Determine the UCL and LCL for an X-bar chart. (Round your answers to 2 decimal places.)c) Determine the UCL and LCL for an R chart. (Round your answers to 2 decimal places.)d) Create an X-bar chart and an R chart. Is the process in control?8ObservationsSample12345120.220.119.819.919.7219.919.819.720.120.1319.819.92020.119.7420.119.919.519.819.7519.820.120.119.919.4620.119.619.719.420.2720.220.119.919.919.8820.120.120.319.719.9919.719.920.119.819.81019.919.820.119.920.21120.120.119.919.919.91219.919.519.719.820Each bottle of iced tea is supposed to have 20 fluid ounces, but it is normal for the amount to vary slightly from bottle to bottle. Twelve samples were taken from the bottle-filling process in order to determine whether it is in control. Each sample consists of 5 bottles, so the sample size is 5. Round your answers to 3 decimal places.a) What are the control limits for the mean chart?b) What are the control limits for the range chart?c) Create an X-bar chart and an R chart. Is the process in control?9SampleIrregularities132536435466758493105A shirt manufacturer buys cloth by the 100-yard roll from a supplier. For setting up a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier. a) Determine the c_bar, UCL and LCL for a c -chart with z = 3. (format example: 12.34)b) Suppose the next five rolls from the supplier had two, four, four, three, and seven irregularities. Is the supplier process under control? (Hint: Use the UCL and LCL already established and check if these new values are still between them.)10For each situation below, determine which chart is appropriate and find the control chart limits. For variable measurements, you must find control limits for both the X-bar chart and R chart.(Round your answers to 3 decimal places when entering them in the quiz.)a) An inspector looked at 20 automobiles being prepared for shipment and found an average of 3.9 scratches per unit in the exterior paint.b) An Accounts Receivable department decided to implement SPC in its billing process due to complaints from customers that the bills are inaccurate. Ten samples of 50 bills each were taken over a month's time and checked. The mean proportion of incorrect bills was 0.094 (i.e., 9.4%). c) To make sure the filling process for M&M bags are in control, each hour, a sample of 5 M&M bags were weighed. After 20 samples of 5 weights were collected, averaging the 20 sample means yielded 51.2 grams, and averaging the 20 sample ranges resulted in 0.78 grams.

1Design specifications require that a key dimension on a product measure 102 ± 15 units. A process being considered for producing this product has a standard deviation of 6 units.(Format answers rounded to 4 decimal places when entering answers in the quiz, Leave the probabilty as decimal numbers, not %.) a) Find the process capability index, Cpk, and the probability of defective output. Assume that the process is centered with respect to specifications, i.e., process mean is 102.b) Suppose the process mean shifts to 96. Calculate the new process capability index. c) What is the probability of defective output after the process shift? Did it increase or decrease? (For this question and the next, a relevant reference is Example 13.1 in the textbook, pp. 370-371. The Excel calculation of that example is shown in sheet Ex 13.1 of Excel SPC workbook. )2Thickness (mm)1.91.82.12.122.22.421.92.12.22.41.82.22.11.72.21.92.12.21.71.82222.11.81.61.91.61.721.71.81.92.11.81.61.92.2To the right is a picture of a washer that is supposed to be 1.9 mm thick. The tolerances on the thickness are 0.5 mm, so the thickness should be between 1.4 mm and 2.4 mm. You are given here the thickness in mm for a sample of 40 washers. Assume the thickness is distributed normally.Format your answers with 4 decimal places except where otherwise specified.a) Verify that the mean = 1.9625 and the standard deviation from this data is 0.2096. (Recall STDEV.S is the function for computing the sample standard deviation.)b) What is the Cpk for the process?c) What % of the output is expected to be out of tolerance (outside the specification limits = defective)? (Express the probability as % with 2 decimal digits, e.g., 12.34%.)d) If the process were centered, i.e., sample mean were equal to 1.9 mm (with the standard deviation unchanged), what would be the Cpk? e) If the process were centered as in (d), what percentage of output would be expected to be out of tolerance? f) If the process were centered AND the standard deviation was only about .10 millimeter, what would be the Cpk and percent defective?(This percent defective is very close to 0. Increase decimal digits until you can see 2 significant figures (e.g., 0.0000012%))g) Out of situations in (b), (d), and (f) which had the process considered capable?3SamplenNumber of Defective Items11512152315341525151615271518153915210151Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart. The samples and the number of defectives in each are shown in the following table.a) Determine the p-bar, Sp, UCL and LCL for a p-chart with z = 3 (Format your answers with 4 decimal places.) b) Plot the p-chart.c) Based on the plotted data points, what comments can you make? (i.e., is the process in control or out of control?) Decide based on whether at least one point is outside the control limits. Recall a point is outside the control limits if it is < LCL or > UCL.4Sample# Defects1625304154627583931021161211381471551641711183190204At Data Systems Services company owned by Donna, she wants to see if the data entry process is in control. She collected 100 records entered by each of the 20 clerks. She counted the number of incorrectly entered records out of each sample. Below, you are given this data. Determine whether this process is in control. (Remember the sample size is not number of rows, but the number of items in each sample.)5AreaNumber of CrimesSample Size110910219103159104149105109106229107169108159109891010591011129101211910131491014109101513910161891017491018129101969102018910A city has 20 police precincts (geographical areas in the city served by different units). Some citizens in the city complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence. The police recognize that not all crimes and offenses are reported. Because of this, the police have contacted by phone a random sample of 910 residences for data on crime in each area. (Respondents are guaranteed anonymity.) The 910 sampled from each area showed the following incidence of crime during the past month.a) Determine the p-bar, Sp, UCL and LCL for a p-chart of 99.7 percent confidence (at Z = 3). (Round your answers to 4 decimal places in the quiz.)b) Is the process in control? If not, are there certain areas that warrant further investigation into their relative high or low crime rates? 6Factors forX-barLCLUCLSample Size, nJanice Winch: Same as Exhibit 13.7 on p. 377 of textbookA2D3D421.8803.26731.02302.57440.72902.28250.57702.11460.48302.00470.4190.0761.92480.3730.1361.86490.3370.1841.816Sample Mean, X-barRange, R100.3080.2231.777110.0020.011110.2850.2561.744210.0020.014120.2660.2831.71739.9910.007130.2490.3071.693410.0060.018140.2350.3281.67259.9970.013150.2230.3471.65369.9990.012710.0010.008810.0050.01399.9950.0041010.0010.0111110.0010.0141210.0060.009Twelve samples, each containing five parts, were taken from a process that produces steel rods at a factory. The length of each rod (in inches) in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were are shown below. Notice X-bar and R values are already given, so you don't need to compute them. To the right is the table containing A2, D3, and D4.Do not round the intermediate results, but when entering answers, round them to 3 decimal places.In problems involving X-bar and R charts, remember sample size n should be the number of items in each sample, not number of rows.a) Determine the UCL and LCL for X-bar chart, and plot the X-bar chart.b) Determine the UCL and LCL for R chart, and plot the R chart.c) Both X-bar and R should be in control to conclude the process is in control. Based on your results, is the process in control? 7READINGS (IN OHMS)SAMPLE12341101398699497729771027982102431027990998101741023102510161006510051026975991698399899098879919991001985810251023101410239101910049829791099999599110101197099210061012121010985983103013103010021016982149799861016988151028100610191002Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows. Use three-sigma control limits.a) Calculate the mean and range for the samples. (Round "Mean" to 2 decimal places and "Range" to the nearest whole number in the quiz.)b) Determine the UCL and LCL for an X-bar chart. (Round your answers to 2 decimal places.)c) Determine the UCL and LCL for an R chart. (Round your answers to 2 decimal places.)d) Create an X-bar chart and an R chart. Is the process in control?8ObservationsSample12345120.220.119.819.919.7219.919.819.720.120.1319.819.92020.119.7420.119.919.519.819.7519.820.120.119.919.4620.119.619.719.420.2720.220.119.919.919.8820.120.120.319.719.9919.719.920.119.819.81019.919.820.119.920.21120.120.119.919.919.91219.919.519.719.820Each bottle of iced tea is supposed to have 20 fluid ounces, but it is normal for the amount to vary slightly from bottle to bottle. Twelve samples were taken from the bottle-filling process in order to determine whether it is in control. Each sample consists of 5 bottles, so the sample size is 5. Round your answers to 3 decimal places.a) What are the control limits for the mean chart?b) What are the control limits for the range chart?c) Create an X-bar chart and an R chart. Is the process in control?9SampleIrregularities132536435466758493105A shirt manufacturer buys cloth by the 100-yard roll from a supplier. For setting up a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier. a) Determine the c_bar, UCL and LCL for a c -chart with z = 3. (format example: 12.34)b) Suppose the next five rolls from the supplier had two, four, four, three, and seven irregularities. Is the supplier process under control? (Hint: Use the UCL and LCL already established and check if these new values are still between them.)10For each situation below, determine which chart is appropriate and find the control chart limits. For variable measurements, you must find control limits for both the X-bar chart and R chart.(Round your answers to 3 decimal places when entering them in the quiz.)a) An inspector looked at 20 automobiles being prepared for shipment and found an average of 3.9 scratches per unit in the exterior paint.b) An Accounts Receivable department decided to implement SPC in its billing process due to complaints from customers that the bills are inaccurate. Ten samples of 50 bills each were taken over a month's time and checked. The mean proportion of incorrect bills was 0.094 (i.e., 9.4%). c) To make sure the filling process for M&M bags are in control, each hour, a sample of 5 M&M bags were weighed. After 20 samples of 5 weights were collected, averaging the 20 sample means yielded 51.2 grams, and averaging the 20 sample ranges resulted in 0.78 grams.

Answered 2 days AfterJun 16, 2022

a.

Upper Specification Limit 117

Lower Specification Limit 87

Mean 102

Standard Dev 6

Cpk 0.8333333333

As Cpk < 1.33 the process is not expected to meet its desired specifications 13

Now, in order to find the proportion or probability of defective units, we would find the z values for USL and LSL

Z_USL 2.5 0.9937903347

Z_LSL 2.5

% of units above USL = Probability value derived from z-statistic table for Z 2.5 = 0.0062

% of Units Below LSL = Probability value derived from z-statistic table for Z 2.5 = 0.0062

% of total units out of the desired specification limits = 0.0062 + 0.0062 = 0.0124

b.

Upper Specification Limit 117

Lower Specification Limit 87

Mean 96

Standard Dev 6

Cpk 0.5

As Cpk < 1.33 the process is not expected to meet its desired specifications

c.

Now, in order to find the proportion or probability of defective units, we would find the z values for USL and LSL

Z_USL 3.5

Z_LSL = (µ-L) / σ 1.5

% of units above USL = Probability value derived from z-statistic table for Z 3.5 = 0.0002

% of Units Below LSL = Probability value derived from z-statistic table for Z 1.5 = 0.0668

% of total units out of the desired specification limits = 0.0002 + 0.0668 = 0.0670

Thus, the total probability of defective units is increased by the shift of mean, by 0.0670 - 0.0124 = 0.0546

Design specifications require that a key dimension on a product measure 102 ± 15 units. A process being considered for producing this product has a standard deviation of 6 units.

(Format answers rounded to 4 decimal places when entering answers in the quiz, Leave the probabilty as decimal numbers, not %.)

a) Find the process capability index, Cpk, and the probability of defective output. Assume that the process is centered with respect to specifications, i.e., process mean is 102.

) Suppose the process mean shifts to 96. Calculate the new process capability index.

c) What is the probability of defective output after the process shift? Did it increase or decrease?

(For this question and the next, a relevant reference is Example 13.1 in the textbook, pp. 370-371. The Excel calculation of that example is shown in sheet Ex 13.1 of Excel SPC workbook. )

2

Thickness (mm)

1.9

1.8

2.1

2.1

2

2.2

2.4

2

1.9

2.1

2.2

2.4

1.8

2.2

2.1

1.7

2.2

1.9

2.1

2.2

1.7

1.8

2

2

2

2.1 a Mean 1.9625

1.8 Stand Dev. 0.2096

1.6

1.9 b Cpk 0.6957

1.6

1.7 c z-score 2.0873091603

2 Probability of thickness of washer to be 2.4 mm, P(X = 2.4) = NORMSDIST(z-score) = NORMSDIST(2.0871) = 0.9816

1.7 Probability of thickness of washer greater outside tolerance limit, i.e. greater than 2.4 mm = 1-0.9816 = 0.0184 = 1.84%

1.8 Hence, 1.84% of output is expected to be greater than 2.4 mm.

1.9

2.1 d Mean 1.9

1.8 Cpk 0.7951

1.6

1.9 e z-score 2.3855

2.2 Probability of thickness of washer to be 2.4 mm, P(X = 2.4) = NORMSDIST(z-score) = NORMSDIST(2.3855) = 0.9915

Probability of thickness of washer greater outside tolerance limit, i.e. greater than 2.4 mm = 1-0.9915= 0.0085 = 0.85%

Hence, 0.85% of output is expected to be greater than 2.4 mm.

f Mean 1.9

Stand Dev. 0.1000

Cpk 1.6667

g The process with Cpk >= 1.33 is highly capable, hence we should select the situation mentioned in part (f).

To the right is a picture of a washer that is supposed to be 1.9 mm thick.

The tolerances on the thickness are 0.5 mm, so the thickness should be between 1.4 mm and 2.4 mm.

You are given here the thickness in mm for a sample of 40 washers. Assume the thickness is distributed normally.

Format your answers with 4 decimal places except where otherwise specified.

a) Verify that the mean = 1.9625 and the standard deviation from this data is 0.2096. (Recall STDEV.S is the function for computing the sample standard deviation.)

) What is the Cpk for the process?

c) What % of the output is expected to be out of tolerance (outside the specification limits = defective)? (Express the probability as % with 2 decimal digits, e.g., 12.34%.)

d) If the process were centered, i.e., sample mean were equal to 1.9 mm (with the standard deviation unchanged), what would be the Cpk?

e) If the process were centered as in (d), what percentage of output would be expected to be out of tolerance?

f) If the process were centered AND the standard deviation was only about .10 millimeter, what would be the Cpk and percent defective?

(This percent defective is very close to 0. Increase decimal digits until you can see 2 significant figures (e.g., 0.0000012%))

g) Out of situations in (b), (d), and (f) which had the process considered capable?

3

Sample n Number of Defective Items Fraction Defects UCL LCL

1 15 1 0.0666666667 0.3717141236 -0.1317141236

2 15 2 0.1333333333 0.3717141236 -0.1317141236

3 15 3 0.2 0.3717141236 -0.1317141236

4 15 2 0.1333333333 0.3717141236 -0.1317141236

5 15 1 0.0666666667 0.3717141236 -0.1317141236

6 15 2 0.1333333333 0.3717141236 -0.1317141236

7 15 1 0.0666666667 0.3717141236 -0.1317141236

8 15 3 0.2 0.3717141236 -0.1317141236

9 15 2 0.1333333333 0.3717141236 -0.1317141236

10 15 1 0.0666666667 0.3717141236 -0.1317141236

18 1.2

a p-Bar 0.1200

stand.dev 0.0839

UCL 0.3717141236

LCL -0.1317141236

c Since, all points are within UCL and LCL, process is under Control

Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart. The samples and the number of defectives in each are shown in the following table.

a) Determine the p-bar, Sp, UCL and LCL for a p-chart with z = 3 (Format your answers with 4 decimal places.)

) Plot the p-chart.

c) Based on the plotted data points, what comments can you make? (i.e., is the process in control or out of control?) Decide based on whether at least one point is outside the control limits. Recall a point is outside the control limits if it is < LCL or > UCL.

p Chart

Fraction Defects 6.6666666666666666E-2 0.13333333333333333 0.2 0.13333333333333333 6.6666666666666666E-2 0.13333333333333333 6.6666666666666666E-2 0.2 0.13333333333333333 6.6666666666666666E-2 UCL 0.37171412356083633 0.37171412356083633 0.37171412356083633 0.37171412356083633 0.37171412356083633 0.37171412356083633 0.37171412356083633 0.37171412356083633 0.37171412356083633 0.37171412356083633 LCL -0.13171412356083634 -0.13171412356083634 -0.13171412356083634 -0.13171412356083634 -0.13171412356083634 -0.13171412356083634 -0.13171412356083634 -0.13171412356083634 -0.13171412356083634 -0.13171412356083634

4

Sample # Defects Cbar UCL LCL

1 6 4 10 -2

2 5 4 10 -2

3 0 4 10 -2

4 1 4 10 -2

5 4 4 10 -2

6 2 4 10 -2

7 5 4 10 -2

8 3 4 10 -2

9 3 4 10 -2

10 2 4 10 -2

11 6 4 10 -2

12 1 4 10 -2

13 8 4 10 -2

14 7 4 10 -2

15 5 4 10 -2

16 4 4 10 -2

17 11 4 10 -2

18 3 4 10 -2

19 0 4 10 -2

20 4 4 10 -2

80

C-Bar 4 Here the problem is out of control because 17th sample is out of control having more than UCL value ie 10

UCL 10 So the process is out of control

LCL -2

At Data Systems Services company owned by Donna, she wants to see if the data entry process is in control. She collected 100 records entered by each of the 20 clerks. She counted the number of inco

ectly entered records...

SOLUTION.PDF## Answer To This Question Is Available To Download

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