Presentation on theme: "What is the point of these sports?"— Presentation transcript:
1What is the point of these sports? Have you ever…Shot a rifle?Played darts?Played basketball?Shot a round of golf?What is the point of these sports?What makes them hard?
2Have you ever… Who is the better shot? Shot a rifle? Played darts? EmmettJakeWho is the better shot?Shot a rifle?Played darts?Shot a round of golf?Played basketball?
3Discussion What do you measure in your process? Why do those measures matter?Are those measures consistently the same?Why not?
4Variability87109Deviation = distance between observations and the mean (or average)EmmettObservations10987averages8.4Deviations= 1.69 – 8.4 = 0.68 – 8.4 = -0.47 – 8.4 = -1.40.0Jake
5VariabilityDeviation = distance between observations and the mean (or average)EmmettObservations76averages6.6Deviations7 – 6.6 = 0.46 – 6.6 = -0.60.076Jake
6Variability87109Variance = average distance between observations and the mean squaredEmmettObservations10987averages8.4Deviations= 1.69 – 8.4 = 0.68 – 8.4 = -0.47 – 8.4 = -1.40.0Squared Deviations2.560.360.161.961.0JakeVariance
7VariabilityVariance = average distance between observations and the mean squaredEmmettObservations76averagesDeviationsSquared Deviations76Jake
8VariabilityVariance = average distance between observations and the mean squaredEmmettObservations76averages6.6Deviations= 0.46 – 6.6 = -0.60.0Squared Deviations0.160.360.2476JakeVariance
9But what good is a standard deviation VariabilityStandard deviation = square root of varianceEmmettVarianceStandard DeviationEmmett1.0Jake0.24JakeBut what good is a standard deviation?
10Variability The world tends to be bell-shaped Even very rare outcomes arepossible(probability > 0)Fewerin the“tails”(lower)(upper)Most outcomesoccur in themiddle
11Variability Here is why: Even outcomes that are equally likely (like dice), when you add them up, become bell shaped
12“Normal” bell shaped curve Add up about 30 of most thingsand you start to be “normal”Normal distributions are divide upinto 3 standard deviations oneach side of the meanOnce your that, youknow a lot aboutwhat is going on?And that is what a standard deviationis good for
13Usual or unusual? One observation falls outside 3 standard deviations? One observation falls in zone A?2 out of 3 observations fall in one zone A?2 out of 3 observations fall in one zone B or beyond?4 out of 5 observations fall in one zone B or beyond?8 consecutive points above the mean, rising, or falling?XXXXX XX X XX
14SPC uses samples to identify that special causes have occurred Causes of VariabilityCommon Causes:Random variation (usual)No patternInherent in processadjusting the process increases its variationSpecial CausesNon-random variation (unusual)May exhibit a patternAssignable, explainable, controllableadjusting the process decreases its variationSPC uses samples to identify that special causes have occurred
15Limits Process and Control limits: Specification limits: Statistical Process limits are used for individual itemsControl limits are used with averagesLimits = μ ± 3σDefine usual (common causes) & unusual (special causes)Specification limits:EngineeredLimits = target ± toleranceDefine acceptable & unacceptable
16Process vs. control limits Distribution of averagesControl limitsSpecification limitsVariance of averages < variance of individual itemsDistribution of individualsProcess limits
17Usual v. Unusual, Acceptable v. Defective μTarget
18Cpk measures “Process Capability” More about limitsGood quality: defects are rare (Cpk>1)μtargetPoor quality: defects are common (Cpk<1)μtargetCpk measures “Process Capability”If process limits and control limits are at the same location, Cpk = 1. Cpk ≥ 2 is exceptional.
19Process capability Good quality: defects are rare (Cpk>1) Poor quality: defects are common (Cpk<1)=USL – x3σ24 – 203(2)==.667Cpk = min=x - LSL3σ20 – 153(2)==.833==3σ = (UPL – x, or x – LPL)
20Going out of controlWhen an observation is unusual, what can we conclude?μ2The meanhas changedXμ1
21Going out of controlWhen an observation is unusual, what can we conclude?The standard deviationhas changedσ2σ1X
22Setting up control charts: Calculating the limits Sample n items (often 4 or 5)Find the mean of the sample (x-bar)Find the range of the sample RPlot on the chartPlot the R on an R chartRepeat steps 1-5 thirty timesAverage the ’s to create (x-bar-bar)Average the R’s to create (R-bar)
23Setting up control charts: Calculating the limits Find A2 on table (A2 times R estimates 3σ)Use formula to find limits for x-bar chart:Use formulas to find limits for R chart:
24Let’s try a small problem smpl 1smpl 2smpl 3smpl 4smpl 5smpl 6observation 1711610observation 285observation 312x-barRX-bar chartR chartUCLCenterlineLCL
25Let’s try a small problem smpl 1smpl 2smpl 3smpl 4smpl 5smpl 6Avg.observation 1711610observation 285observation 312X-bar7.33339.66679.33337.66678.0556R133.5X-bar chartR chartUCL9.0125Centerline8.05563.5LCL4.4751
28Interpreting chartsObservations outside control limits indicate the process is probably “out-of-control”Significant patterns in the observations indicate the process is probably “out-of-control”Random causes will on rare occasions indicate the process is probably “out-of-control” when it actually is not
29Show real time examples of charts here Interpreting chartsIn the excel spreadsheet, look for these shifts:ABCDShow real time examples of charts here
30Lots of other charts exist P chartC chartsU chartsCusum & EWMAFor yes-no questions like “is it defective?” (binomial data)For counting number defects where most items have ≥1 defects (eg. custom built houses)Average count per unit (similar to C chart)Advanced charts“V” shaped or Curved control limits (calculate them by hiring a statistician)
31Selecting rational samples Chosen so that variation within the sample is considered to be from common causesSpecial causes should only occur between samplesSpecial causes to avoid in samplingpassage of timeworkersshiftsmachinesLocations
32Chart advice Larger samples are more accurate Sample costs money, but so does being out-of-controlDon’t convert measurement data to “yes/no” binomial data (X’s to P’s)Not all out-of control points are badDon’t combine data (or mix product)Have out-of-control procedures (what do I do now?)Actual production volume matters (Average Run Length)