Control ChartsProject Quality Management

Control Charts

Definition:- A statistical tool to determine if a process is in control.

History of Control Charts

Developed in 1920sBy Dr. Walter A. ShewhartShewhart worked for Bell Telephone Labs

Two Types of Control Charts

Variable Control ChartsAttribute Control Charts

Variable Control ChartsDeal with items that can be measured .Examples 1) Weight 2) Height 3) Speed 4) Volume

Types of Variable Control Charts

X-Bar chartR chartMA chart

Variable Control ChartsX chart: deals with a average value in a processR chart: takes into count the range of the valuesMA chart: take into count the moving average of a process

Attribute Control ChartsControl charts that factor in the quality attributes of a process to determine if the process is performing in or out of control.

Types of Attribute Control ChartsP chartC ChartU Chart

Attribute Control ChartsP Chart: a chart of the percent defective in each sample set.C chart: a chart of the number of defects per unit in each sample set.U chart: a chart of the average number of defects in each sample set.

Reasons for using Control ChartsImprove productivityMake defects visibleDetermine what process adjustments need to be madeDetermine if process is in or out of control

Real World Use of Control ChartsExample from Managing Quality by Foster.The Sampson company develops special equipment for the United States Armed Forces. They need to use control charts to insure that they are producing a product that conforms to the proper specifications. Sampson needs to produce high tech and top of the line products, daily so they must have a process that is capable to reduce the risks of defects.

How Will Using Control Charts help your Project?Possible Goals when using Control Charts in your project:Line reengineeringIncreased motivationContinually improve of your processIncreased profitsZero defects

Control Chart Key TermsOut of Control: the process may not performing correctlyIn Control: the process may be performing correctlyUCL: upper control limitLCL: lower control limitAverage value: average

Process is OUT of control if:One or multiple points outside the control limitsEight points in a row above the average valueMultiple points in a row near the control limits

Process is IN control if:The sample points fall between the control limitsThere are no major trends forming, i.e.. The points vary, both above and below the average value.

Calculating Major Lines in a Control ChartAverage Value: take the average of the sample dataUCL: Multiply the Standard deviation by three. Then add that value to the Average Value.LCL: Multiply the Standard deviation by three. Then subtract that value from the Average Value.

Examples of Control Charts

Examples of Control Charts

Control Charts

The following control chart shows the improvement of a process. The standard deviation decreases as the process becomes more capable.

Example of Control Charts

Wiley 2010*-Developing Control ChartsControl Charts (aka process or QC charts) show sample data plotted on a graph with CL, UCL, and LCLControl chart for variables are used to monitor characteristics that can be measured, e.g. length, weight, diameter, timeControl charts for attributes are used to monitor characteristics that have discrete values and can be counted, e.g. % defective, # of flaws in a shirt, etc.

Wiley 2010*Setting Control LimitsPercentage of values under normal curve Control limits balance risks like Type I error

Wiley 2010*Control Charts for VariablesUse x-bar and R-bar charts togetherUsed to monitor different variablesX-bar & R-bar Charts reveal different problemsIs statistical control on one chart, out of control on the other chart? OK?

Wiley 2010*Control Charts for VariablesUse x-bar charts to monitor the changes in the mean of a process (central tendencies)Use R-bar charts to monitor the dispersion or variability of the process System can show acceptable central tendencies but unacceptable variability orSystem can show acceptable variability but unacceptable central tendencies

Wiley 2010*Constructing an X-bar Chart: A quality control inspector at the Cocoa Fizz soft drink company has taken three samples with four observations each of the volume of bottles filled. If the standard deviation of the bottling operation is .2 ounces, use the below data to develop control charts with limits of 3 standard deviations for the 16 oz. bottling operation.Center line and control limit formulas

Time 1Time 2Time 3Observation 115.816.116.0Observation 216.016.015.9Observation 315.815.815.9Observation 415.915.915.8Sample means (X-bar)15.87515.97515.9Sample ranges (R)0.20.30.2

Wiley 2010*Solution and Control Chart (x-bar)Center line (x-double bar):

Control limits for3 limits:

Wiley 2010*X-Bar Control Chart

Wiley 2010*Control Chart for Range (R)Center Line and Control Limit formulas:Factors for three sigma control limits

Wiley 2010*R-Bar Control Chart

Wiley 2010*Second Method for the X-bar Chart Using R-bar and the A2 FactorUse this method when sigma for the process distribution is not knowControl limits solution:

ACTIVITY

Chart1

Chart2

10.731810.856245333310.6005813333

10.754610.856245333310.6005813333

10.758610.856245333310.6005813333

10.72710.856245333310.6005813333

10.72410.856245333310.6005813333

10.705210.856245333310.6005813333

10.734610.856245333310.6005813333

10.62410.856245333310.6005813333

10.710410.856245333310.6005813333

10.731810.856245333310.6005813333

10.747610.856245333310.6005813333

10.768210.856245333310.6005813333

10.733210.856245333310.6005813333

10.783210.856245333310.6005813333

10.69210.856245333310.6005813333

Sample

Means

Chart3

0.1160.4650440

0.2590.4650440

0.1710.4650440

0.2210.4650440

0.1190.4650440

0.1430.4650440

0.2740.4650440

0.6690.4650440

0.1320.4650440

0.1790.4650440

0.1630.4650440

0.250.4650440

0.3490.4650440

0.1580.4650440

0.1030.4650440

Sample

Ranges

Sheet1

x-barRange

SampleObs 1Obs 2Obs 3Obs 4Obs 5AvgRangeUCLLCLUCLLCLnA2D3D4

110.68210.68910.77610.79810.71410.7320.11610.856245333310.60058133330.465044021.8803.27

210.78710.8610.60110.74610.77910.7550.25910.856245333310.60058133330.465044031.0202.57

310.7810.66710.83810.78510.72310.7590.17110.856245333310.60058133330.465044040.7302.28

410.59110.72710.81210.77510.7310.7270.22110.856245333310.60058133330.465044050.5802.11

510.69310.70810.7910.75810.67110.7240.11910.856245333310.60058133330.465044060.4802

610.74910.71410.73810.71910.60610.7050.14310.856245333310.60058133330.465044070.420.081.92

710.79110.71310.68910.87710.60310.7350.27410.856245333310.60058133330.465044080.370.141.86

810.74410.77910.1110.73710.7510.6240.66910.856245333310.60058133330.465044090.340.181.82

910.76910.77310.64110.64410.72510.7100.13210.856245333310.60058133330.4650440100.310.221.78

1010.71810.67110.70810.8510.71210.7320.17910.856245333310.60058133330.4650440110.290.261.74

1110.78710.82110.76410.65810.70810.7480.16310.856245333310.60058133330.4650440

1210.62210.80210.81810.87210.72710.7680.25010.856245333310.60058133330.4650440

1310.65710.82210.89310.54410.7510.7330.34910.856245333310.60058133330.4650440

1410.80610.74910.85910.80110.70110.7830.15810.856245333310.60058133330.4650440

1510.6610.68110.64410.74710.72810.6920.10310.856245333310.60058133330.4650440

Averages10.7280.220400

A20.58X-BarUCLLCL

D3010.856245333310.6005813333

D42.11

Mean10.728R-Bar0.4650440

Range0.220

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Wiley 2010*Control Charts for Attributes P-Charts & C-ChartsAttributes are discrete events: yes/no or pass/failUse P-Charts for quality characteristics that are discrete and involve yes/no or good/bad decisionsNumber of leaking caulking tubes in a box of 48Number of broken eggs in a carton

Use C-Charts for discrete defects when there can be more than one defect per unitNumber of flaws or stains in a carpet sample cut from a production runNumber of complaints per customer at a hotel

Wiley 2010*P-Chart Example: A production manager for a tire company has inspected the number of defective tires in five random samples with 20 tires in each sample. The table below shows the number of defective tires in each sample of 20 tires. Calculate the control limits.Solution:

SampleNumber of Defective TiresNumber of Tires in each SampleProportion Defective1320.152220.103120.054220.105220.05Total9100.09

Wiley 2010*P- Control Chart

Wiley 2010*C-Chart Example: The number of weekly customer complaints are monitored in a large hotel using a c-chart. Develop three sigma control limits using the data table below.Solution:

WeekNumber of Complaints132233415363728193101Total22

Wiley 2010*C- Control Chart

Wiley 2010*Process CapabilityProduct SpecificationsPreset product or service dimensions, tolerances: bottle fill might be 16 oz. .2 oz. (15.8oz.-16.2oz.)Based on how product is to be used or what the customer expectsProcess Capability Cp and CpkAssessing capability involves evaluating process variability relative to preset product or service specificationsCp assumes that the process is centered in the specification range

Cpk helps to address a possible lack of centering of the process

*A simple basic definition that can be built on to service your companys needs.*http://deming.eng.clemson.edu/pub/tutorials/qctools/ccmain1.htm#History

Dr. Shewhart developed the control charts as an statistical approach to the study of manufacturing process variation for the purpose of improving the economic effectiveness of the process. These methods are based on continuous monitoring of processvariation. *These are the main to types of control charts. Each type has several specific charts that deal with a specific sample set of data.*Use variable charts should be used whenever the data is something that is measured. The data should be for example the weight of a piece of candy. *The main types of variable control charts are listed above. *These are the definitions of the specific types of variable control charts. This will help in determining what type of chart to use when you are collecting sample data.*Definition of attribute control charts. Tests the quality of the specific attributes of a product.*The main types of attribute control charts are listed above.*The definitions of the attribute control charts, help in determining the correct chart to use given a sample set of data.*Control charts can be a huge asset to a company if used correctly. The reason for using control charts are clear, they will help your company improve.*Real world example of a company that uses control charts to sell products to the United States. The products must be defect free to save lives.*Brainstorming Activity:This is to help your employees realize the need to improve. The goal with control charts is basically three fold:Reduce DefectsImprove processesImprove productivity*This is just a list of key terms that one should know and understand to create a control chart and understand its results.*There are other extreme examples of when a control charts is out of control but these are the main three that you should focus one.*If your process is currently in control continue to monitor it to insure that productivity remains at a high level to produce good quality products.*The control chart basically consists of three main lines. The center of mean line, and then the two control limits. This lines are called the Upper Control Limit, and the Lower Control Limit. They both can be shortened (UCL,and LCL).*http://www.robertluttman.com/vms/Week5/page6.htmStatistical Thinking Tools-Control Charts for the AverageDate:February 12, 2001 Bob Luttman, Robert Luttman & Associates

Example of a control chart that has points outside the UCL. This process may need to be reworked. The problem is becoming worse, you can see that the data is consistently above the mean towards the end of the data.*Processes and Process Variability, Date accessed: Feb 12, 2001http://www.sytsma.com/tqmtools/ctlchtprinciples.htmlExample of a process that is in-control.

*Process improvement.*Processes and Process Variability, Date accessed: Feb 12, 2001http://www.sytsma.com/tqmtools/ctlchtprinciples.htmlThe control chart above shows the improvements that a firm made in their process to improve quality.