Submitted in PDF format only. Do not submit Excel spreadsheets or datasets. Please copy and paste ALL prompts in

12 Sep Submitted in PDF format only. Do not submit Excel spreadsheets or datasets. Please copy and paste ALL prompts in

Posted at 09:45h in Uncategorized by admin

Submitted in PDF format only. Do not submit Excel spreadsheets or datasets. Please copy and paste ALL prompts in your write up with your response presented beneath. Respond in complete sentences. Respond to ALL requested actions. Please format to class expectations all charts and tables that you generate

Directions: Examine the dataset for this assignment and then respond to the prompts below. The prompts are open-ended so please take the time to provide a complete detailed and statistically justified response using concepts introduced in this class..

1). On visual inspection of the dataset file only, which of the following 3 statistical tools, explored in class, may be possible candidates to use to perform an analysis of this dataset ? Reference specific variables , and variable characteristics, as you explain your choice(s).

Simple Regression

One-way ANOVA

Time Series Analysis

2) Select ONLY one of your analysis choices from #1. State your selection.

3) Perform all needed analysis steps on the dataset using your choice technique stated in #2. When performing your analysis, you are not permitted to use exact variable assignment combinations that have been assigned in previous homework assignments using this dataset. Report all charts, tables, and interpretations used in your analysis..

4) Report the conclusion from your analysis

intro

Control charts

To create a control chart

are used to monitor and improve processes

collect subgroups (samples) of process output over time

data is collected over time

calculate sample statistics for each subgroup

past performances are use to predict future outcomes

plot the statistics over time

add control limits (ususally within +- 3 standard deviations of the statistic of measure

Phase 1 control charts

Goals are to find patterns over time and points that fall outside limits

analyzed at the start of a process to determine where improvements are needed

Phase 2 control charts

analyed after improvements have been imposed

Causes of variation

special and common

special causes are correctable without changing the process

common cause variation is inherit in the process (random)

common cause variation (no points outside limits) – stable process – in control – predictable

A rule of thumb is 8 or more consecutive points

above or below the center line may indicate a trend

special cause variation (point outside limit) – out of control process

unpredictable

p chart

used for categorical variables
				ni = Number of observations
					to find p-bar (mean) divide sum of pi by the number of observations
number of Days	10
subgroup size	100							Generate the plot
				p-bar	(p-bar(1-p-bar))/ni	UCL	LCL	pi	LCL	UCL
	Day	defects	proportion (pi) defects per day	0.147	0.00125391	0.2532317749	0.0407682251	0.12	0.041	0.253
	1	12	0.12					0.14	0.041	0.253
	2	14	0.14					0.1	0.041	0.253
	3	10	0.1					0.18	0.041	0.253
	4	18	0.18					0.21	0.041	0.253
	5	21	0.21					0.14	0.041	0.253
	6	14	0.14					0.15	0.041	0.253
	7	15	0.15					0.12	0.041	0.253
	8	12	0.12					0.15	0.041	0.253
	9	15	0.15					0.16	0.041	0.253
	10	16	0.16
sum of pi			1.47
p-bar (mean)			0.147

pi 0.12 0.14000000000000001 0.1 0.18 0.21 0.14000000000000001 0.15 0.12 0.15 0.16 LCL 4.0768225092489396E-2 4.0768225092489396E-2 4.0768225092489396E-2 4.0768225092489396E-2 4.0768225092489396E-2 4.0768225092489396E-2 4.0768225092489396E-2 4.0768225092489396E-2 4.0768225092489396E-2 4.0768225092489396E-2 UCL 0.25323177490751059 0.25323177490751059 0.25323177490751059 0.25323177490751059 0.25323177490751059 0.25323177490751059 0.25323177490751059 0.25323177490751059 0.25323177490751059 0.25323177490751059

Number of Days

Probability

c chart

monitors errors in an area of opportunity (space, time, etc)
number of areas(time) sampled (n)			10				ci is the number of errors in area i
				Graph the chart
	Day	errors (ci)		Ci	UCL	LCL
	1	7
	2	3
	3	6
	4	3
	5	4
	6	5
	7	3
	8	5					SQRT is the square root feature in Excel
	9	2
	10	0
sum ci
c-bar (Mean)

r chart

Use when observation size is 10 or less
	Is the process range in control?
	number of days collection occurs (k)			10
	observation size (use in control constants table)			5				Graph the process
									From Control table
	Day	5 delivery times collected each day (Xi)					Ri	R-bar	D3	D4	UCL	LCL
	1	6.7	11.7	9.7	7.5	7.8
	2	7.6	11.4	9	8.4	9.2
	3	9.5	8.9	9.9	8.7	10.7
	4	11	9.9	11.3	11.6	8.5
	5	8.3	8.4	9.7	9.8	7.1							D3 and D4 are control group constants
	6	9.4	9.3	8.2	7.1	6.1								they represent relations between variation and mean for a given sample size
	7	10	10.7	9	8.2	11								values are found in tables
	8	9.5	10.5	7	8.6	10.1
	9	7.8	9	12	9.1	11.7
	10	9.9	10.1	8.9	9.6	7.1
sum Ri
R-bar

Table of Control Chart Constants X-bar Chart for sigma R Chart Constants S Chart Constants Constants estimate Sample Size = m

A2 A3 d2 D3 D4 B3 B4 2 1.880 2.659 1.128 0 3.267 0 3.267 3 1.023 1.954 1.693 0 2.574 0 2.568 4 0.729 1.628 2.059 0 2.282 0 2.266 5 0.577 1.427 2.326 0 2.114 0 2.089 6 0.483 1.287 2.534 0 2.004 0.030 1.970 7 0.419 1.182 2.704 0.076 1.924 0.118 1.882 8 0.373 1.099 2.847 0.136 1.864 0.185 1.815 9 0.337 1.032 2.970 0.184 1.816 0.239 1.761 10 0.308 0.975 3.078 0.223 1.777 0.284 1.716 11 0.285 0.927 3.173 0.256 1.744 0.321 1.679 12 0.266 0.886 3.258 0.283 1.717 0.354 1.646 13 0.249 0.850 3.336 0.307 1.693 0.382 1.618 14 0.235 0.817 3.407 0.328 1.672 0.406 1.594 15 0.223 0.789 3.472 0.347 1.653 0.428 1.572 16 0.212 0.763 3.532 0.363 1.637 0.448 1.552 17 0.203 0.739 3.588 0.378 1.622 0.466 1.534 18 0.194 0.718 3.640 0.391 1.608 0.482 1.518 19 0.187 0.698 3.689 0.403 1.597 0.497 1.503 20 0.180 0.680 3.735 0.415 1.585 0.510 1.490 21 0.173 0.663 3.778 0.425 1.575 0.523 1.477 22 0.167 0.647 3.819 0.434 1.566 0.534 1.466 23 0.162 0.633 3.858 0.443 1.557 0.545 1.455 24 0.157 0.619 3.895 0.451 1.548 0.555 1.445 25 0.153 0.606 3.931 0.459 1.541 0.565 1.435 Control chart constants for X-bar, R, S, Individuals (called "X" or "I" charts), and MR (Moving Range) Charts.

NOTES: To construct the "X" and "MR" charts (these are companions) we compute the Moving Ranges as:

R2 = range of 1st and 2nd observations, R3 = range of 2nd and 3rd observations, R4 = range of 3rd and 4th observations, etc. with the "average" moving range or "MR-bar" being the average of these ranges with the "sample size" for each of these ranges being n = 2 since each is based on consecutive observations … this should provide an estimated standard deviation (needed for the "I" chart) of σ = (MR-bar)/d2 where the value of d2 is based on, as just stated, m = 2.

Similarly, the UCL and LCL for the MR chart will be: UCL = D4(MR-bar) and LCL = D3(MR-bar)

but, since D3 = 0 when n = 0 (or, more accurately, is "not applicable") there will be no LCL for the MR chart, just a UCL.

Statistical Quality Control

• Quality is when a product delivers what is stipulated for in its specifications

• Crosby: “quality is conformance to requirements”

• Feigenbaum: “quality is a customer determination”

• Garvin: five dimensions of quality

Quality

• Transcendent quality: “innate excellence” • Product quality: quality is measurable • User quality: quality is determined by the consumer • Manufacturing quality: quality is measured by the

manufacturer's ability to target the product specifications with little variability

• Value Quality: Has to do with the price and cost

Garvin’s Five Dimensions of Quality

Quality Control

• Quality control – the collection of strategies, techniques, and actions taken by an organization to assure themselves of a quality product.

• After-process quality control – involves inspecting the attributes of a finished product to determine whether the product is acceptable • reporting of the number of defects per time period • screening defective products from consumers

• In-process quality control – techniques measure product attributes at various intervals throughout the manufacturing process in an effort to pinpoint problem areas.

Total Quality Management

• W. Edwards Deming – the “father of the quality movement” said that the achievement of quality begins with top managers’ commitment and extends all the way to suppliers and consumers. • He believed that quality control is a long-term total company

effort that he entitled “total quality management (TQM)”. • Deming presented a cause-and-effect explanation of the

impact of TQM on a company, known as the Deming chain reaction. • The chain reaction begins with improving quality, which

decreases costs and improves productivity: • Productivity =

Deming's 14 Points to Improved TQM

1. Create constancy of purpose for improvement of product and service.

2. Adopt the new philosophy. 3. Cease dependence on mass inspection. 4. End the practice of awarding business on price tag

alone. 5. Improve constantly and forever the system of

production and service. 6. Institute training. 7. Institute leadership.

Deming's 14 Points to Improved TQM

8. Drive out fear. 9. Break down barriers between staff areas.

10. Eliminate slogans. 11. Eliminate numerical quotas. 12. Remove barriers to pride of workmanship. 13. Institute a vigorous program of education and

retraining. 14. Take action to accomplish the transformation.

Six Sigma

• Six sigma – total quality approach that measures the capacity of a process to perform defect free work.

• Requires that there be no more than 3.4 incorrectly filled prescriptions of 3.4 unsatisfactory landings per million, with a goal of approaching zero.

• Forces companies that adopt it to work much harder and more quickly to discover and reduce sources of variation in processes.

• May be required to attain world-class status and be a top competitor in the international market.

Six Sigma

• Contains a formalized problem-solving approach called the DMAIC process (Define, Measure, Analyze, Improve, and Control).

• Strong focus on the customer, both internal and external, that is often referred to as Critical to Quality (CTQ).

• Most members of an organization are trained in the methodology.

• Companies using Six Sigma discovered that so many problems existed that required a complete redesign.

• History shows that most companies can only achieve about a 5.0 sigma status.

Lean Manufacturing • A quality-management philosophy that focuses on

the reduction of wastes and the elimination of unnecessary steps in an operation or process.

• The Toyota Production System is generally credited with developing the notion of lean manufacturing.

• Focuses on 7 wastes: 1. Overproduction 2. Waiting time 3. Transportation 4. Processing 5. Inventory 6. Motion 7. Scrap

Important Quality Concepts

• Benchmarking – examine and emulate the best practices and techniques used in the industry. • a positive, proactive process to make changes that will

effect superior performance.

• Just-In-Time Inventory Systems – necessary parts for production arrive “just in time”. • reduced holding costs, personnel, and space needed for

inventory. • no extra raw materials or inventory of parts for production

are stored.

• Reengineering – complete redesign of the core business process in a company.

Other Quality Control Concepts

• Failure Mode and Effects Analysis: • A systematic way for identifying the effects of a potential

product or process failure and includes methodology for eliminating or reducing the chance of a failure occurring.

• Used for analyzing potential reliability problems early in the development cycle.

• Poka-Yoke: • “mistake proofing” • Uses devices, methods, or inspections in order to avoid

machine error or human error. • Two main types:

• Prevention-based • Detection-based

Other Quality Control Concepts

• Team Building: • Occurs when a group of employees are organized to

undertake management tasks and perform other functions such as organizing, developing, and overseeing projects.

• More workers take over managerial responsibilities. • A quality circle is a small group of workers and their

supervisor who meet regularly to consider quality issues.

Process Analysis

A process is a series of actions, changes or functions that bring about a result – examined through flow charts and diagrams.

The seven basic tools are as follows: 1. Flowchart or process map 2. Pareto chart 3. Cause-and-effect diagram (Ishikawa or fishbone chart) 4. Control chart 5. Check sheet or checklist 6. Histogram 7. Scatter chart or scatter diagram

Flowcharts A flowchart is a schematic representation of all the activities and interactions that occur in a process.

Flow Charts – schematic representation of all the activities and interactions that occur in a process.

Pareto Analysis • Pareto Analysis – quantitative tallying of the number and

types of defects that occur with a product. • Pareto Chart – ranked vertical bar chart with most frequently occurring

on the left.

Fishbone

Fishbone Diagram – display of potential cause-and-effect relationships.

Check Sheets

Check Sheets or Checklists – Display the frequency of outcomes for some quality-related event or activity under study.

Other Process Analysis

• Histograms – Depicts a frequency distribution of quantitative data.

• Scatter Chart or Scatter Diagram – for examining the relationship between two variables.

• Control chart – graphical method for evaluating whether a process is or is not in a “state of statistical control .

• Types of control charts: • Control charts for measurement: x-bar and R charts • Control charts for attribute compliance: p and c charts

• Elements of a control chart: • Centerline • Upper control limit (UCL) • Lower control limit (LCL)

Control Charts

• Chart of sample means computed for a series of small random samples over a period of time.

• The centerline is the average of the sample means,

• The upper control limit (UCL) is 3 standard deviations of means above the centerline.

• The lower control limit (LCL) is 3 standard deviations below the center line.

Control Chart

Steps to Creating an Control Chart

Monitor process location (center):

1. Decide on the quality to be measured. 2. Determine a sample size. 3. Gather 20 to 30 samples. 4. Compute the sample average for each sample. 5. Compute the sample range for each sample. 6. Determine the average sample mean for all

samples. 7. Determine the average sample range (or sample

standard deviation) for all samples. 8. Using the size of the samples, determine the value

of A2 or A3. 9. Compute the UCL and the LCL

R Control Chart

Monitor process variation:

1. Decide on the quality to be measured.

2. Determine a sample size.

3. Gather 20 to 30 samples.

4. Compute the sample range for each sample.

5. Determine the average sample mean for all samples.

6. Using the size of the samples, determine the values of D

3 and D

4 .

7. Compute the UCL and the LCL

R Chart Formulas

Control Chart: Formulas

A manufacturing facility produces bearings. The

diameter specified for the bearings is 5 millimeters.

Every 10 minutes, six bearings are sampled and their

diameters are measured and recorded. Twenty of

these samples of six bearings are gathered. Use the

resulting data and construct an chart.

Data for Demonstration Problem 18.1: Samples 1 – 10

1 2 3 4 5 6 7 8 9 10 5.13 4.96 5.21 5.02 5.12 4.98 4.99 4.96 4.96 5.03 4.92 4.98 4.87 5.09 5.08 5.02 5.00 5.01 5.00 4.99 5.01 4.95 5.02 4.99 5.09 4.97 5.00 5.02 4.91 4.96 4.88 4.96 5.08 5.02 5.13 4.99 5.02 5.05 4.87 5.14 5.05 5.01 5.12 5.03 5.06 4.98 5.01 5.04 4.96 5.11 4.97 4.89 5.04 5.01 5.13 4.99 5.01 5.02 5.01 5.04

4.9933 4.9583 5.0567 5.0267 5.1017 4.9883 5.0050 5.0167 4.9517 5.0450 0.25 0.12 0.34 0.10 0.07 0.05 0.03 0.09 0.14 0.18

X R

Data for Demonstration Problem 18.1: Samples 1 – 10

Data for Demonstration Problem 18.1: Samples 11 – 20

11 12 13 14 15 16 17 18 19 20 4.91 4.97 5.09 4.96 4.99 5.01 5.05 4.96 4.90 5.04 4.93 4.91 4.96 4.99 4.97 5.04 4.97 4.93 4.85 5.03 5.04 5.02 5.05 4.82 5.01 5.09 5.04 4.97 5.02 4.97 5.00 4.93 5.12 5.03 4.98 5.07 5.03 5.01 5.01 4.99 4.90 4.95 5.06 5.00 4.96 5.12 5.09 4.98 4.88 5.05 4.82 4.96 5.01 4.96 5.02 5.13 5.01 4.92 4.86 5.06

4.9333 4.9567 5.0483 4.9600 4.9883 5.0767 5.0317 4.9617 4.9200 5.0233 0.22 0.11 0.16 0.21 0.06 0.12 0.12 0.09 0.17 0.09

X R

Demonstration Problem 18.1: Control Chart Computations

Sigma level: 3

20 19

18 17

16 15

14 13

12 11

10 9

8 7

6 5

4 3

2 1

Bearing Diameter

UCL = 5.0679

Average = 5.0022

LCL = 4.9364

Control Chart: Bearing Diameter

Mean

5.10963

5.05590

5.00217

4.94844

4.89471

X Demonstration Problem 18.1:

Control Chart

Output for R Control Chart

Construct an R chart for the 20 samples of data in Demonstration Problem 18.1 on bearings.

Demonstration Problem 18.2: R Control Chart

Control Chart: Bearing Diameter

Sigma level: 3

20 19

18 17

16 15

14 13

12 11

10 9

8 7

6 5

4 3

2 1

Range

0.0

Bearing Diameter

UCL = .2725

Average = .1360

LCL = .0000

Demonstration Problem 18.2: R Control Chart

Monitor proportion in noncompliance: 1. Decide on the quality to be measured. 2. Determine a sample size. 3. Gather 20 to 30 samples. 4. Compute the sample proportion for each

sample. 5. Determine the average sample proportion

for all samples. 6. Compute the UCL and the LCL

P Charts

P Chart Formulas

A company produces bond paper and, at regular

intervals, samples of 50 sheets of paper are

inspected. Suppose 20 random samples of 50 sheets

of paper each are taken during a certain period of

time, with the following numbers of sheets in

noncompliance per sample.

Construct a p chart from these data.

Demonstration Problem 18.3: Twenty Samples of Bond Paper

Sample n

Number Out of

Compliance Sample n

Number Out of

Compliance 1 50 4 11 50 2 2 50 3 12 50 6 3 50 1 13 50 0 4 50 0 14 50 2 5 50 5 15 50 1 6 50 2 16 50 6 7 50 3 17 50 2 8 50 1 18 50 3 9 50 4 19 50 1

10 50 2 20 50 5

Demonstration Problem 18.3: Twenty Samples of Bond Paper

Sample n n non

1 50 4 0.08 11 50 2 0.04 2 50 3 0.06 12 50 6 0.12 3 50 1 0.02 13 50 0 0.00 4 50 0 0.00 14 50 2 0.04 5 50 5 0.10 15 50 1 0.02 6 50 2 0.04 16 50 6 0.12 7 50 3 0.06 17 50 2 0.04 8 50 1 0.02 18 50 3 0.06 9 50 4 0.08 19 50 1 0.02

10 50 2 0.04 20 50 5 0.10

Demonstration Problem 18.3: Preliminary Calculations

Demonstration Problem 18.3: Centerline, UCL, and LCL Computations

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

0 5 10 15 20

Sample Number

P = .053

UCL = .148

LCL = 0

Demonstration Problem 18.3: P Control Chart

Demonstration Problem 18.3: MINITAB P Control Chart

Monitor number of nonconformances per item: 1. Decide on nonconformances to be evaluated. 2. Determine the number of items to be studied

(at least 25). 3. Gather items. 4. Determine the value of c for each item by summing

the number of nonconformances in the item. 5. Determine the average number of

nonconformances per item. 6. Determine the UCL and the LCL.

c Charts

c Chart Formulas

A manufacturer produces gauges to measure oil pressure. As part of the company’s statistical process control, 25 gauges are randomly selected and tested for non-conformances. The results are shown here. Use these data to construct a c chart that displays the non-conformances per item.

Demonstration Problem 18.4: Number of Nonconformities in Oil Gauges

Item Number

Number of Nonconformities

Item Number

Number of Nonconformities

1 2 14 2 2 0 15 1 3 3 16 4 4 1 17 0 5 2 18 2 6 5 19 3 7 3 20 2 8 2 21 1 9 0 22 3

10 0 23 2 11 4 24 0 12 3 25 3 13 2

Demonstration Problem 18.4: Number of Nonconformities in Oil Gauges

Demonstration Problem 18.4: c Chart Calculations

0 1 2 3 4 5 6 7

0 5 10 15 20 25 Item Number

UCL = 6.2

LCL = 0

c = 2.0

Demonstration Problem 18.4: c Chart

Demonstration Problem 18.4: MINITAB c Chart

Interpreting Control Charts

• Points are above UCL and/or below LCL • Eight or more consecutive points fall above or below the

centerline. Ten out of 11 points fall above or below the centerline. Twelve out of 14 points fall above or below the centerline.

• A trend of 6 or more consecutive points (increasing or decreasing) is present

• Two out of 3 consecutive values are in the outer one-third.

• Four out 5 consecutive values are in the outer two-thirds.

• The centerline shifts from chart to chart.

Sheet1

SIC Code	No. Emp.	No. Prod. Wkrs.	Value Added by Mfg.	Cost of Materials	Value of Indus. Shipmnts	New Cap. Exp.	End Yr. Inven.	Indus. Grp.
201	433	370	23518	78713	4	1833	3630	1
202	131	83	15724	42774	4	1056	3157	1
203	204	169	24506	27222	4	1405	8732	1
204	100 Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline. Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax. Do you need an answer to this or any other questions? About Wridemy We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers. How It Works To make an Order you only need to click on “Order Now” and we will direct you to our Order Page. Fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline. Are there Discounts? All new clients are eligible for 20% off in their first Order. Our payment method is safe and secure. Hire a tutor today CLICK HERE to make your first order Related Tags Academic APA Writing College Course Discussion Management English Finance General Graduate History Information Justify Literature MLA About us Wridemy is an online group of proffesional writers that are willing to share their knownledge with other students by offering academic help to them. We have over two million past papers and 5 million documents for specific courses. Quick help Post A Question View Common Questions Register A Student Account Log into Your Account Get Academic Help About Writedemy Services offered Subjects covered Mathematics Physics Organic Chemistry Computer Science Advanced Statistics Economics Algebra Accounting Writing Biology Finance Psychology Psychology Engineering Python Programming Discrete Math General Chemistry Linear Algebra

12 Sep Submitted in PDF format only. Do not submit Excel spreadsheets or datasets. Please copy and paste ALL prompts in

intro

p chart

c chart

r chart

Sheet1

About Wridemy

We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers.

How It Works

Are there Discounts?

Hire a tutor today CLICK HERE to make your first order

Related Tags

About us

Quick help

Subjects covered