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Six Sigma - Variation

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SPC - Module 1 Understanding variation and basic principles

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AIM OF SPC COURSE To enable delegates to better understand variation and be able to create and analyse control charts OBJECTIVES Delegates will be able to:- – Appreciate what variation is – Understand why it is the enemy of manufacturing – Know how we measure and calculate variation – Understand the basics of the normal distribution – Identify the two types of process variation – Understand the need for objective use of data – Produce I mR charts for variable data – Understand the basic theory behind control charts – Know how to analyse control charts

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The History Of SPC n 1924 - Walter Shewhart Of Bell Telephones Develops The Control Chart Still Being Used Today n 1950 - Dr W Edwards Deming Sells SPC To Japan After World War II n 1965 - Ford Failed To Implement SPC Due To No Management Commitment n 1985 - Ford Finally Implement SPC n 1989 - Boeing roll out SPC n 1992 - BAe Decide To Implement SPC n 2002 - Airbus UK start SPC in key business areas

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Variation No two products or processes are exactly alike. Variation exists because any process contains many sources of variation. The differences may be large or immeasurably small, but always present.

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They will vary due to common cause variation. If we introduce a special cause of variation into the process, then the process will vary more than usual. Variation is a naturally occurring phenomenon inherent within any process. Sign your name on a piece of paper three times, even if you sign it in the same pen, straight after one another, each one will vary slightly from the last one. Variation ------------- Signature 1 ------------- Signature 2 ------------- Signature 3 ----------------- Signature 4

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Rank in order of desirability Customer specification limits are the outside edge of yellow zone

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Why do we need to improve our processes…. To reduce the cost of manufacturing Our competitors may already be leading the way Our processes are not predictable To improve quality By improving processes we can…. Reduce costs Increase revenue (sales) Have happier customers Make our jobs more secure Increase job satisfaction

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So what to do….? Commit to improving quality - make process capability measurable and reportable. So we will know we are getting better. Solve problems as a team rather than individuals. Teams get better and more permanent improvements than individual efforts. Gain better understanding of our process by studying measurement data in an informed way (control charts) Consider all possible pitfalls when implementing improvements. When improvements are made - make them permanent ones.

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Quality of data: We may have lots of data, but …. Does it represent the process outputs we are interested in ? Is it representative of our current process ? Can we split it into subsets to aid problem solving ? Can it be paired with process inputs ? Is the operational definition for how measurements are taken and data recorded ? Has the measurement system been assessed for stability and reliability (gauge R&R) Garbage in, garbage out !

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Attribute (discrete) data is that which can be counted Examples: On or Off? Variable (continuous) data is that which can be physically be measured on a continuous scale Examples: Temperature Weight Broken or unbroken? Attribute Vs. Variable data

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Which type of data ? Length in millimeters SMC (standard manufacturing cost) Number of breakdowns per day Average daily temperature Proportion of defective items Number of spars with concession Lead time (days) Mean time between failure VariableAttribute

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Which is best ? Variable data should be the preferred type as it tells us more about what is happening to a process. Attribute - tells us little about the process Variable - gives plenty of insight into the process

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Histogram A GRAPHICAL REPRESENTATION OF DATA SHOWING HOW THE VALUES ARE DISTRIBUTED BY: Displaying The Distribution Of Data Displaying Process Variability (Spread) Identifying Data Concentration

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Histogram Graphic Representation of The Data Bar Chart Vertical (y) axis shows the frequency of occurrence Horizontal (x) axis shows increasing values 9.1 9.2 9.3 9.4 9.5 9.6 Note : To produce histograms quickly use Excels Data Analysis Tool pack.

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The sample Average or Mean. Example A set of numbers: 3,6,9,7,5,9,10,0,4,3 Total = 56 Average = 56 = 5.6 10

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The Sample Range t Use The Following Dataset t 5,2,9,12,3,19,7,5 The Sample Range is the largest value minus the smallest value t 19-2=17 t The Range = 17

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The Normal Distribution Curve Typical process range The normal curve illustrates how most measurement data is distributed around an average value. Probability of individual values are not uniform Examples Weight of componentWing skin thickness

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– Single peaked – Bell shaped – Average is centred – 50% above & below the average – Extends to infinity (in theory) Characteristics Of The Normal Curve

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How do we measure variation ? Variation in a process can be measured by calculating the standard deviation The Formula =² n-1

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The Standard Deviation o Use The Following Dataset o 5,2,9,12,3,19,7,5 o The Formula = x -x ) ² n-1 o (5-7.75)²+(2-7.75)²+(9-7.75)².....(5-7.75)² 7 i Note : In excel you can use the STDEV function. Its quicker than pen & paper !

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Normal Distribution Proportion 68.3% l +/- 1 Std Dev = 68.3% -4-3-2 0 1234 2

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Normal Distribution Proportion 95.5% l +/- 2 Std Dev = 95.5% -4-3-201234 4

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Normal Distribution Proportion 99.74% l +/- 3 Std Dev = 99.74% -4-3-201234 6

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Control charts A control chart is a run chart with control limits plotted on it. A control chart can be used to check whether a process is predictable within a range of values Control limits are an estimation of 3 standard deviations either side of the mean. 99.74% of data should be within 3 standard deviations of the mean if no special cause variation is present.

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Different types of variation Common cause - random variation Special cause variation The variation that naturally exists in your process assuming nothing changes. This type of variation is predictable in so far as you can predict the range that your process will operate within Difficult to reduce (advanced problem solving tools required) This is the type of variation is unpredictable and is exhibited in an unstable process. Variation may not look normal. No one knows what is going to happen next ! Easy to detect and reduce (but only if robust control systems are in place)

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Examples of different types of variation Common cause - random variation Special cause variation Temperature Humidity Standard operating methods Measurement systems Normal running speed Sudden breakdown of equipment Power failure Unskilled operator Tool breakage

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Objective use of data Reacting to a single item of data without first considering the normal variation expected from a process can :... waste time and effort correcting a problem that may be due to random variation....increase the process variation by tampering with it thus making the process worse Using data objectively can ensure you :...have the facts to back up your decisions....can quantify any improvements you make statistically

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Objective use of data… In God we trust…. ….for everything else show us the data !

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Upper spec limit = 8. Is this process in control ? 2 4 6 8 10 12 14

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Yes, the process is in control but not capable. 2 4 6 8 10 12 14 UCL LCL

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Attribute data is that which can be counted Examples: On or Off? Variable data is that which can be physically be measured Examples: Temperature Weight Broken or unbroken? Attribute Vs. Variable data

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Variable Control Chart – Establishes the values of a single component characteristic measured in physical units Product Weight (kg) Curing Time (hrs) Component Length (mm)

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Control Chart Individual - Moving Range Charts (Also known as X-mR or I-mR) Assumptions : Variable data. Normal distribution

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Decide on operation to be measured Decide on sample frequency Establish characteristic Record reading & date Record any changes to the process on chart Calculate range Plot Graphs Calculate control limits Identify and take appropriate action if process out of control

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Activity Exercise Groups of 2 or 3 people Objective: Represent a machine that cuts bar to length ~cut drinking straws to 30mm length (approx. 20 off) Operation: cut drinking straws Characteristic: Length Sample frequency: 100% Cut by eye, 1 straw at a time to an estimated 30mm Measure the straws in the order that they are cut Record the information on a chart (remember to input data and update chart as you go) One person records, one person cuts No communication between the operator and tester.

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UCL x = X bar + 2.66 x mR bar LCL x = X bar - 2.66 x mR bar UCL r = 3.267 x mR bar _ mRbar = CL =

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UCL x =X bar + 2.66 xmR bar LCL x =X bar - 2.66 xmR bar UCL r = 3.267 xmR bar 22 24 26 28 30 32 34 36 38 40 42 44 0 1 2 3 4 5 6 7 8 9 10 _ Date Time X383936 mR-----13 Process Control Chart (iX-mR) Dept. 019Sampling Frequency 100% Characteristic LengthChart No twoSpecification Limit 30mm +/- 6mm Xbar =UCL=LCL= mR bar =CL= X X X X X

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UCL x =X bar + 2.66 xmR bar LCL x =X bar - 2.66 xmR bar UCL r = 3.267 xmR bar 22 24 26 28 30 32 34 36 38 40 42 44 0 1 2 3 4 5 6 7 8 9 10 _ Date Time X383936 mR-----13 Process Control Chart (iX-mR) Dept. 019 Sampling Frequency 100% Characteristic LengthChart No twoSpecification Limit 30mm +/- 6mm Xbar =UCL=LCL= mR bar =CL=

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MOVING RANGE CHART AVERAGE CHART _ mR = ENTER mR FIGURES INTO CALCULATOR Upper Control Limit of mR = _ D 4 X mR = _ D 4 = _ X = ENTER X FIGURES INTO CALCULATOR = _ X ucl X+ (E 2 _ X ucl mR lcl X mR) _ X X + = = x - - X X X Lower Control Limit of X = _ X - (E 2 x mR) Upper Control Limit of X = _ X + (E 2 x mR) mR) (E 2 _ mR 8.36 3.2672.56 2.6639.4 25.8 32.6 2.56 2.66 32.6 _ _ _ _ X AND mR CONTROL CHART CALCULATING CONTROL LIMITS

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UCL x = X bar + 2.66 x mR bar LCL x = X bar - 2.66 x mR bar UCL r = 3.267 x mR bar _

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Analysing Control Charts Shake Down ïTo Convert a control chart into the form of a Histogram ïTurn the control chart on its side And imagine that the points would fall into a normal distribution curve

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Control Chart Analysis – Any Point Outside Control Limits – A Run of 8 Points Above or Below the mean – Any Non-Random Patterns 13 4 2 5 678 9 10 13 14 12 15 16 17 18 11 19 20 1 3 4 2 5 67 8 9 1013 14 12 15 1617 18 11 13 4 2 56 789 101211 19 20

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Control Chart Analysis Is there any signs of special cause present ?

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Control Chart Analysis Is there any signs of special cause present ?

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Control Chart Analysis Is there any signs of special cause present ?

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Control Chart Analysis Any special cause here ?

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Control Chart Analysis What has changed ?

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Control Chart Analysis What has changed ?

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Now make a change to the process Is the process in control ? Is there a better way of meeting your customers needs ? Modify the process to try to reduce variation and make production more on target. Plot the data on the chart. What should you do to the limits ?….

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NOTE : Not all data is normally distributed Variable control charts limits are based on normal theory. If the distribution is non-normal the theory falls down If your data is not normally distributed consult an expert in statistical analysis for advice

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Calculating Control limits When calculating limits remove any special causes that you know the reason for. Only recalculate limits when a change is made to the process. Ask whats changed?, and investigate root causes.

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When to change limits Changed supplier Re-calculate from here

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Limits changed to reflect shift in average… What would you do if you changed back to the original supplier ?

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Control Chart Analysis Where would you re-calculate limits ? New operator

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Control Chart Analysis What would you do here ? Would you change limits ?

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Why is 8 points on one side of the mean attributed to special cause ? First lets consider why we set the upper and lower control limits at +/- 3SD. 99.74% of the data falls within 3SD of the mean. How often will we be wrong when we judge data outside control limits to be special cause variation ? 0.26% (from normal theory)!

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Why is 8 points on one side of the mean attributed to special cause ? If we are satisfied with being wrong 0.26% of the time for one test, it makes sense have a similar level of risk for the other tests for special cause ! What is the probability of a point falling below the mean on a control chart? 50% What is the probability of another point falling below the mean? 50% x 50% = 25% And so on……. 50% x 50% x 50% x 50% x 50% x 50% x 50% x 50% = 0.39%

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Other types of chart Depending on the process you are measuring you may need to use the following charts : C chart : for count data where sample size remains constant. U chart : for count data where sample size changes nP chart : for proportion data where sample size remains constant P chart : for proportion data where sample size changes X bar R chart : when samples are taken in batches of production (sample size remains constant)

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So what to do next….? 1) Check that the data you are gathering is variable data where possible. 2) Ensure that it is recorded in a legible manner and in time order. Ensure everyone records it in the same way. 3) Ensure that other factors are recorded to aid the problem solving process. For example if you are measuring parts off several machines you may need to either use several different data collection sheets, or record the machine number against each reading taken. 4) Consider process inputs that could affect the outputs of the process. Some of these could be recorded against output data collection. (Or we could use SPC to control them also). 5) Maintain process logs to aid analysis. 6) Make sure everyone understands the part they play in process improvement

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Chapter 36 Quality Engineering (Part 2) EIN 3390 Manufacturing Processes Summer A, 2012.

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