Empire Beauty School Pittsburgh CH10 P Chart Fraction Defective Chart Worksheet

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zbnu196

Engineering

Empire Beauty School - Pittsburgh

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Please, read the question carefully and answer the questions follow the description

Chapter 6

Problems 5, 6, 12 & 13.


Chapter 10

Problems 4, 7 & 13.

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208 CHAPTER SIX m FORMULAS S - Sd So = Snew = AVERAGE AND RANGE CHARTS m - md X chart: and m ΣΧ; = m 00= : so/ca UCLX = Xo + Ago LCLX = Xo - Ago UCL, = B600 LCL, = B500 UCLX = X + AUR LCLy = X - AZR R chart: m R; CHAPTER PROBLEMS R m 1. Describe the difference between chance and assignable causes. UCLR = DAR LCLR = D3R Revising the charts: ΣΧ - Χε m 2. How would you use variation to manage a group of people? Why should a manager be aware of assignable and chance causes? 3. Select one of the tools taught in this chapter and describe why applying it to problems in your future will enhance your ability to solve those problems. X = Xnew = m - md UCLX = X. + Ago LCLy = X. – Ago 0o = Ro/d2 ŹR - Rd m Rnew m - md UCLR = 1200 LCLR D100 - AVERAGE AND STANDARD DEVIATION CHARTS X AND R CHARTS 4. A large bank establishes X and R charts for the time required to process applications for its charge cards. A sample of five applications is taken each day. The first four weeks (20 days) of data give X = 16 min 5 = 3min R = 7 min Based on the values given, calculate the centerline and control limits for the X and R charts. 5. Steering wheels in many vehicles are outfitted with an airbag and horn as well as switches for controlling radio volume, cruise control, and other devices. Con- necting these devices and switches to a steering wheel requires excellent positioning control during assembly. For this reason, hole location is closely monitored in the X, Y, and Z directions. The data below are X and R values for 25 samples of size n = 4 for hole location data for the X-axis dimension. X chart: m m X; X = UCLy = X + Azs LCLy = X – Az5 s chart: Subgroup Number X Range 5= 1 50.3 0.73 וח 2 49.6 0.75 = B45 3 50.8 0.79 UCL LCL, = B35 Revising the charts: 4 50.9 0.74 0.72 5 49.8 m X - Xd 6 50.5 0.73 Xo = #new 7 50.2 0.71 m - md Variables Control Charts 209 Subgroup Number X Range 8 0.70 0.65 9 49.9 50.0 50.1 50.2 10 0.67 11 0.65 12 50.5 0.67 13 50.4 0.68 14 50.8 0.70 15 50.0 0.65 16 49.9 0.66 17 50.4 0.67 18 50.5 0.68 Set up the X and R charts on this process. Does the process seem to be in control? Why or why not? If necessary, assume assignable causes and revise the trial control limits. 7. When studying a process control chart tracking one variable, what is meant by the statement, “The process is in a state of statistical control”? 8. Describe how both an X and R or s chart would look if they were under normal statistical control. 9. X charts describe the accuracy of a process, and R and s charts describe the precision. How would accuracy be recognized on an X chart? How would precision be recognized on either an R or s chart? 10. Why is the use and interpretation of an R or s chart so critical when examining an X chart? 11. Create an X and R chart for the clutch plate informa- tion in Table 6.1. You will need to calculate the range values for each subgroup. Calculate the control limits and centerline for each chart. Graph the data with the calculated values. Beginning with the R chart, how does the process look? 12. RM Manufacturing makes thermometers for use in the medical field. These thermometers, which read in degrees Celsius, are able to measure temperatures to a level of precision of two decimal places. Each hour, RM Manufacturing tests eight randomly selected thermometers in a solution that is known to be at a temperature of 3°C. Use the following data to create and interpret an X and R chart. Based on the desired thermometer reading of 3º, interpret the results of your plotted averages and ranges. 19 50.7 0.70 20 50.2 0.65 21 49.9 0.60 22 50.1 0.64 23 49.5 0.60 24 50.0 0.62 25 50.3 0.60 Set up an X and R chart on this process. Interpret the chart. Does the process seem to be in control? If nec- essary, assume assignable causes and revise the trial control limits. If the hole location is to be centered at 50.0, how does this process compare? 6. The data below are X and R values for 12 samples of size n = 5. They were taken from a process pro- ducing bearings. The measurements are made on the inside diameter of the bearing. The data have been coded from 0.50; in other words, a measurement of 0.50345 has been recorded as 345. Range values are coded from 0.000; that is, 0.00013 is recorded as 13. Subgroup Average Temperature 3.06 Range 0.10 1 2 3.03 0.09 3 3.10 0.12 Subgroup Number X Range 4 st 3.05 0.07 1 5 345 13 2.98 0.08 6 2 347 14 3.00 0.10 7 3.01 3 0.15 350 12 346 8 4 11 3.04 0.09 9 5 350 15 3.00 0.09 6 3.03 345 16 10 0.14 11 7 349 14 2.96 0.07 12 8 348 13 2.99 0.11 13 3.01 9 348 12 0.09 10 354 15 14 2.98 0.13 11 352 13 15 3.02 0.08 12 355 16 210 CHAPTER SIX Month Average Number Leaving Range January February 13. Interpret the X and R charts in Figure P6.1. 14. Interpret the X and R charts in Figure P6.2. 15. The variables control chart seen in Figure P6.3 is monitoring the main score residual for a peanut canister pull top. The data are coded from 0.00 (in other words, a value of 26 in the chart is actu- ally 0.0026). Finish the calculations for the sum, averages, and range. Create an X and R chart, cal- culate the limits, plot the points, and interpret the chart. 16. Working at a call center isn't an easy job. As custom- ers contact the center, the employee must access a variety of computer screens in order to answer cus- tomer questions. Many employees don't stay with the job very long. One call center uses X and R charts to track voluntary quits over time. The averages compiled below are from three call centers. Use the data below to create an X and R chart. Describe how the process is performing March April May June July August September October November December January February March April May June 29 29 30 32 33 34 40 39 38 32 34 31 31 32 42 41 49 50 NWNWNNWN ONWNW Capability Data Set X-bar UCL = 45.86, Mean = 45.25, LCL = 44.65 (n = 5) 46.0 UCL UCLX 45.5 Mean ܛܓ 45.0 LCL LCLX Range UCL = 2.22, Mean = 1.05, LCL = 0 (n = 5) AM M - ਭਾਈ UCL UCLR 2.0 1.5 Mean 1.0 الما 0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 FIGURE P6.1 Problem 12 354 CHAPTER TEN 16 150 7 0.047 17 150 4 0.027 18 150 3 0.020 6. The following table gives the number of nonconform- ing product found while inspecting a series of 12 con- secutive lots of galvanized washers for finish defects such as exposed steel, rough galvanizing, and discol- oration. A sample size of n = 200 was used for each lot. Find the centerline and control limits for a fraction nonconforming chart. If the manufacturer wishes to have a process capability of p = 0.005, is the process capable? 19 150 9 0.060 20 150 8 0.053 21 150 8 0.053 22 150 6 0.040 23 150 2 0.013 Sample Size Sample Size 24 150 9 0.060 Nonconforming Nonconforming 25 150 7 0.047 200 0 200 0 26 150 3 0.020 200 1 200 0 27 150 4 0.027 200 2 200 1 28 150 6 0.040 200 0 200 0 29 150 5 0.033 200 1 200 3 30 150 4 0.027 200 1 200 1 Total 4,500 173 7. Thirst-Quench, Inc. has been in business for more than 50 years. Recently Thirst-Quench updated their machinery and processes, acknowledging their out-of- date style. They have decided to evaluate these changes. The engineer is to record data, evaluate those data, and implement strategy to keep quality at a maximum. The plant operates eight hours a day, five days a week, and produces 25,000 bottles of Thirst-Quench each day. Problems that have arisen in the past include partially filled bottles, crooked labels, upside down labels, and no labels. Samples of size 150 are taken each hour. Create a p chart. 8. Nearly everyone who visits a doctor's office is covered by some form of insurance. For a doctor, the process- ing of forms in order to receive payment from an insur- ance company is a necessary part of doing business. If a form is filled out incorrectly, the form cannot be processed and is considered nonconforming (defec- tive). Within each office, an individual is responsible for inspecting and correcting the forms before filing them with the appropriate insurance company. A local doctor's office is interested in determining whether errors on insurance forms are a major problem. Every week they take a sample of 20 forms to use in creating a p chart. Use the following information to create a p chart. How are they doing? Number Subgroup Inspected Number Number Non- conforming np Proportion Noncon- forming p n 1 150 6 0.040 Nonconforming 2 150 3 0.020 1 2 3 150 9 0.060 2 5 4 150 7 0.047 3 8 5 150 9 0.060 4 6 150 2 0.013 5 7 150 3 0.020 6 8 150 5 0.033 7 9 150 6 0.040 8 10 150 8 0.053 9 aw sa vw a v A5 11 150 9 0.060 10 12 150 7 0.047 11 13 150 7 0.047 12 14 150 2 0.013 13 15 150 5 0.033 14 Quality Control Charts for Attributes 353 CHAPTER PROBLEMS 60 3 60 6 60 2 60 5 1. Review the control charts covered in this chapter. Describe and discuss how one of these charts could be applied to a situation you face at work or in your personal life. 2. How would you determine that a process is under con- trol? How is the interpretation of a p, u, or c chart different from that of an X and R chart? 60 7 60 4 60 3 60 4 60 1 60 0 60 5 60 3 60 4. 60 3 60 7 CHARTS FOR FRACTION NONCONFORMING 3. Bottled water is very popular with consumers. Manu- facturers recognize that customers don't want bottles with caps that aren't sealed correctly. Faulty seals make the consumer wonder about the purity of the water within, which creates an immediate lost sale and affects the decision to purchase a similar product in the future. For this reason, Local Water Bottling Co. inspects 250 water bottles per hour (out of a total pro- duction of 5,000 bottles per hour) to check the caps. Any bottle inappropriately capped is unusable and will be destroyed. Use the following production informa- tion to create the centerline and control limits for a fraction nonconforming control chart to monitor their recent process. Graph and interpret this chart. What level of performance is their process capable of? 60 4 60 6 60 8 60 4. 60 2 60 3 60 6 n Defectives 250 1 5. Given the following information about mistakes made on tax forms, make and interpret a fraction noncon- forming chart. 250 1 250 0 250 Sample Size Sample Size 250 0 Nonconforming Nonconforming 250 0 20 0 20 10 250 1 20 0 20 2 250 0 0 20 1 250 0 2 20 0 250 1 0 1 1 0 ô ô ô ô ô ô ô ô ô 6 0 0 4. When producing IC chips, the quality inspectors check the functionality of the chip, enabling them to determine whether the chip works or doesn't work. Create the centerline and control limits for today's fraction defec- tive chart. Graph and interpret the chart. How should they expect the process to perform in the near future? 1 0 1 ô ô ô ô ô ô ô ô ô ô ô ô 2 0 3 2 n np 20 1 0 60 2 20 1 4 60 4 20 0 1 60 5 20 2 20 0
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Explanation & Answer

These are the solutions of chapter 6. Have a look and contact me if you have any doubts.will send the solution of chapter 10 within next 12 hours.

Answer 5.
Step 1 – Tabulate the data for a center line for X-bar chart and R Chart
Subgroup
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

Average (X-bar)
50.3
49.6
50.8
50.9
49.8
50.5
50.2
49.9
50.0
50.1
50.2
50.5
50.4
50.8
50.0
49.9
50.4
50.5
50.7
50.2
49.9
50.1
49.5
50.0
50.3

Range
0.73
0.75
0.79
0.74
0.72
0.73
0.71
0.70
0.65
0.67
0.65
0.67
0.68
0.70
0.65
0.66
0.67
0.68
0.70
0.65
0.60
0.64
0.60
0.62
0.60

Step 2 – Compute the UCL and LCL for X-bar and R charts

𝑋̿ =

̅
∑25
𝑖=1 𝑋
25

𝑋̿ = 50.22
𝑅̅ =

∑25
𝑖=1 𝑅
25

𝑅̅ = 0.6784
Now, for sample size 4, A2 = 0.729, D3 = 0, D4 = 2.282
UCLX = 𝑋̿ + A2 𝑅̅
= 50.22 + (0.729*0.6784)
= 50.71

LCLX = 𝑋̿ - A2 𝑅̅
= 50.22 - (0.729*0.6784)
= 49.72
UCLR = D4 𝑅̅
= 2.228*0.6784
= 1.55
LCLR = D3 𝑅̅
= 0*0.6784
=0
Step 4 – Draw the control chart and plot the points

X-bar Chart
51.5
51
50.5
50
49.5
49
48.5
1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Average (X-bar)

Mean

UCL

LCL

R Chart
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2

0
1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Range

R bar

UCL

LCL

The process is out of control as the value of X-bar does not satisfy subgroup 3, 4, 14 and 23. So, eliminating
these four subgroups, revised control limits will be-

𝑋̿ =

̅
∑21
𝑖=1 𝑋
21

𝑋̿ = 50.17
𝑅̅ =

∑21
𝑖=1 𝑅
21

𝑅̅ ...


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