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
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 |
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
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) |
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.
,
Copyright 2011 John Wiley & Sons, Inc. 1
Statistical Quality Control
Copyright 2011 John Wiley & Sons, Inc. 2
• 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
Copyright 2011 John Wiley & Sons, Inc. 3
• 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
Copyright 2011 John Wiley & Sons, Inc. 4
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.
Copyright 2011 John Wiley & Sons, Inc. 5
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 =
Copyright 2011 John Wiley & Sons, Inc. 6
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.
Copyright 2011 John Wiley & Sons, Inc. 7
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.
Copyright 2011 John Wiley & Sons, Inc. 8
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.
Copyright 2011 John Wiley & Sons, Inc. 9
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.
Copyright 2011 John Wiley & Sons, Inc. 10
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
Copyright 2011 John Wiley & Sons, Inc. 11
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.
Copyright 2011 John Wiley & Sons, Inc. 12
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
Copyright 2011 John Wiley & Sons, Inc. 13
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.
Copyright 2011 John Wiley & Sons, Inc. 14
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
Copyright 2011 John Wiley & Sons, Inc. 15
Flowcharts A flowchart is a schematic representation of all the activities and interactions that occur in a process.
Copyright 2011 John Wiley & Sons, Inc. 16
Flow Charts – schematic representation of all the activities and interactions that occur in a process.
Copyright 2011 John Wiley & Sons, Inc. 17
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.
Copyright 2011 John Wiley & Sons, Inc. 18
Fishbone
Fishbone Diagram – display of potential cause-and-effect relationships.
Copyright 2011 John Wiley & Sons, Inc. 19
Check Sheets
Check Sheets or Checklists – Display the frequency of outcomes for some quality-related event or activity under study.
Copyright 2011 John Wiley & Sons, Inc. 20
Other Process Analysis
• Histograms – Depicts a frequency distribution of quantitative data.
• Scatter Chart or Scatter Diagram – for examining the relationship between two variables.
Copyright 2011 John Wiley & Sons, Inc. 21
• 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
Copyright 2011 John Wiley & Sons, Inc. 22
• 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
Copyright 2011 John Wiley & Sons, Inc. 23
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
Copyright 2011 John Wiley & Sons, Inc. 24
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
Copyright 2011 John Wiley & Sons, Inc. 25
R Chart Formulas
Copyright 2011 John Wiley & Sons, Inc. 26
Control Chart: Formulas
Copyright 2011 John Wiley & Sons, Inc. 27
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
Copyright 2011 John Wiley & Sons, Inc. 28
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
Copyright 2011 John Wiley & Sons, Inc. 29
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
Copyright 2011 John Wiley & Sons, Inc. 30
Demonstration Problem 18.1: Control Chart Computations
Copyright 2011 John Wiley & Sons, Inc. 31
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
Copyright 2011 John Wiley & Sons, Inc. 32
Output for R Control Chart
Copyright 2011 John Wiley & Sons, Inc. 33
Construct an R chart for the 20 samples of data in Demonstration Problem 18.1 on bearings.
Demonstration Problem 18.2: R Control Chart
Copyright 2011 John Wiley & Sons, Inc. 34
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
.4
.3
.2
.1
0.0
Bearing Diameter
UCL = .2725
Average = .1360
LCL = .0000
Demonstration Problem 18.2: R Control Chart
Copyright 2011 John Wiley & Sons, Inc. 35
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
Copyright 2011 John Wiley & Sons, Inc. 36
P Chart Formulas
Copyright 2011 John Wiley & Sons, Inc. 37
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
Copyright 2011 John Wiley & Sons, Inc. 38
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
Copyright 2011 John Wiley & Sons, Inc. 39
Sample n n non
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
pp
Demonstration Problem 18.3: Preliminary Calculations
Copyright 2011 John Wiley & Sons, Inc. 40
Demonstration Problem 18.3: Centerline, UCL, and LCL Computations
Copyright 2011 John Wiley & Sons, Inc. 41
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
p
Demonstration Problem 18.3: P Control Chart
Copyright 2011 John Wiley & Sons, Inc. 42
Demonstration Problem 18.3: MINITAB P Control Chart
Copyright 2011 John Wiley & Sons, Inc. 43
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
Copyright 2011 John Wiley & Sons, Inc. 44
c Chart Formulas
Copyright 2011 John Wiley & Sons, Inc. 45
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
Copyright 2011 John Wiley & Sons, Inc. 46
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
Copyright 2011 John Wiley & Sons, Inc. 47
Demonstration Problem 18.4: c Chart Calculations
Copyright 2011 John Wiley & Sons, Inc. 48
0 1 2 3 4 5 6 7
0 5 10 15 20 25 Item Number
c
UCL = 6.2
LCL = 0
c = 2.0
Demonstration Problem 18.4: c Chart
Copyright 2011 John Wiley & Sons, Inc. 49
Demonstration Problem 18.4: MINITAB c Chart
Copyright 2011 John Wiley & Sons, Inc. 50
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.
,
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
Who We AreWe are a professional custom 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. Do you handle any type of coursework?Yes. We have posted over our previous orders to display our experience. Since we have done this question before, we can also do it for you. To make sure we do it perfectly, please fill our Order Form. Filling the order form correctly will assist our team in referencing, specifications and future communication. Is it hard to Place an Order?1. Click on the “Place order tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled. 2. Fill in your paper’s requirements in the "PAPER INFORMATION" section and click “PRICE CALCULATION” at the bottom to calculate your order price. 3. Fill in your paper’s academic level, deadline and the required number of pages from the drop-down menus. 4. Click “FINAL STEP” to enter your registration details and get an account with us for record keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page. 5. From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it. |