3Process Control ToolsProcess tools assess conditions in existing processes to detect problems that require intervention in order to regain lost control.Check sheets Pareto analysisScatter Plots HistogramsRun Charts Control chartsCause & effect diagrams
4Check Sheets 27 15 19 20 28 Check sheets explore what and where an event of interest is occurring.Attribute Check SheetOrder Types am-9am 9am-11am 11am-1pm pm-3pm 3pm-5-pmEmergencyNonemergencyReworkSafety StockPrototype OrderOther
5Run ChartsmeasurementtimeLook for patterns and trends…
6SCATTERPLOTS Variable A Variable B x x xx x x xxx x xx xx x x xx x xx xxx x x xx xx x x xx x xx x xx xx xxx x x xx xx xx x xx x xx x xx xxx xx x xx x xxx x x xxx x xx xx x xx x x xx xx xxx xx xx xxx xx xx xxx x x xx x x xx x x xx x x xxx x xx x xxx x x xVariable ALarger values of variable A appear to be associated with larger values of variable B.Variable B
7Frequency of Occurrences HISTOGRAMSA statistical tool used to show the extentand type of variance within the system.Frequency of OccurrencesOutcome
8A B C D E F G PARETO ANALYSIS H Percentage of Occurrences A method for identifying and separatingthe vital few from the trivial many.ABPercentage of OccurrencesCDEFGHIJFactor
12Deming’s Theory of Variance Variation causes many problems for most processesCauses of variation are either “common” or “special”Variation can be either “controlled” or “uncontrolled”Management is responsible for most variationCategories of VariationManagementEmployeeControlled VariationUncontrolled VariationCommon CauseSpecial Cause
13Causes of Variation What prevents perfection? Process variation... Natural CausesAssignable CausesInherent to processRandomCannot be controlledCannot be preventedExamplesweatheraccuracy of measurementscapability of machineExogenous to processNot randomControllablePreventableExamplestool wear“Monday” effectpoor maintenanceCommon causes: * Inherit to the process* Random* Not controllable by operators* Management is responsible(e.g., a filling cereal machine may be replaced by a better one)Assignable causes: * Not part of the process* Not random* Operators have control* Management is responsible for training operators.(e.g., a machine is not properly set)
14Specification vs. Variation Product specificationdesired range of product attributepart of product designlength, weight, thickness, color, ...nominal specificationupper and lower specification limitsProcess variabilityinherent variation in processeslimits what can actually be achieveddefines and limits process capabilityProcess may not be capable of meeting specification!
16Process Capability Capable process (Very) capable process Process variationLSLSpecUSLCapable process(Very) capable processOut of control - The process is out of control because the distribution is not centered around the target value. The assignable cause may be a wrong setting for the particularned.Not capable - The process is in control but is not capable. This is determined by the large probability of producing parts that do not meet the engineering index (called Cp) is less than 1. Cp has a value of one when the range of the distribution (measure by standard deviations from the mean) equals the range of the tolerances. Capable process have a Cp value of at least 1.3.Capable - The process is now capable because the entire distribution falls within the tolerance limits. Improvements occur when the range of the distribution is reduce, increasing the probability for producing on target.Capability - It is the ability to meet customer’s specifications.In control - A process that does not show signs of assignable causes of variation.Process not capable
17Process Capability 6 99.7% 3 LSL Spec USL Measure of capability of process to meet (fall within) specification limitsTake “width” of process variation as 6If 6 < (USL - LSL), then at least 99.7% of output of process will fall within specification limitsLSLSpecUSL699.7%3
19Process Capability Ratio Define Process Capability Ratio Cp asIf Cp > 1.0, process is... capableIf Cp < 1.0, process is... not capable
20Process Capability -- Example A manufacturer of granola bars has a weight specification2 ounces plus or minus 0.05 ounces. If the standard deviationof the bar-making machine is 0.02 ounces, is the process capable?USL = = 2.05 ouncesLSL = = 1.95 ouncesCp = (USL - LSL) / 6= ( ) / 6(0.02)= / 0.12=Therefore, the process is not capable!
21Process Centering Capable and centered Capable, but not centered LSLSpecUSLCapable and centeredCapable, but not centeredOut of control - The process is out of control because the distribution is not centered around the target value. The assignable cause may be a wrong setting for the particularned.Not capable - The process is in control but is not capable. This is determined by the large probability of producing parts that do not meet the engineering index (called Cp) is less than 1. Cp has a value of one when the range of the distribution (measure by standard deviations from the mean) equals the range of the tolerances. Capable process have a Cp value of at least 1.3.Capable - The process is now capable because the entire distribution falls within the tolerance limits. Improvements occur when the range of the distribution is reduce, increasing the probability for producing on target.Capability - It is the ability to meet customer’s specifications.In control - A process that does not show signs of assignable causes of variation.Not capable, andnot centered
22Process Centering -- Example For the granola bar manufacturer, if the process isincorrectly centered at 2.05 instead of 2.00 ounces, whatfraction of bars will be out of specification?2.0LSL=1.95USL=2.05Out of spec!50% of production will be out of specification!
23Process Capability Index Cpk Std dev Mean mIf Cpk > 1.0, process is... Centered & capableIf Cpk < 1.0, process is... Not centered &/or not capable
24Cpk Example 1A manufacturer of granola bars has a weight specification2 ounces plus or minus 0.05 ounces. If the standard deviationof the bar-making machine is s = 0.02 ounces and the process mean is m = 2.01, what is the process capability index?USL = 2.05 oz LSL = 1.95 ouncesCpk = min[(m -LSL) / 3 , (USL- m) / 3 ]= min[(2.01–1.95) / 0.06 , (2.05 – 2.01) / 0.06 ]= min[1.0 , 0.67 ]= 0.67Therefore, the process is not capable and/or not centered !
25Cpk Example 2Venture Electronics manufactures a line of MP3 audio players. One of the components manufactured by Venture and used in its players has a nominal output voltage of 8.0 volts. Specifications allow for a variation of plus or minus 0.6 volts. An analysis of current production shows that mean output voltage for the component is volts with a standard deviation of volts. Is the process "capable: of producing components that meet specification? What fraction of components will fall outside of specification? What can management do to improve this fraction?
27Process Control Charts Statistical technique for tracking a process anddetermining if it is going “out to control”Establish capability of process under normal conditionsUse normal process as benchmark to statistically identify abnormal process behaviorCorrect process when signs of abnormal performance first begin to appearControl the process rather than inspect the product!
28Process Control Charts Upper Spec LimitUpper Control Limit6Target Spec3Lower Control LimitLower Spec Limit
29Process Control Charts Look forspecialcause !In controlOut of control !Back in control!UCLTargetLCLTimeSamplesNatural variation
30When to Take ActionA single point goes beyond control limits (above or below)Two consecutive points are near the same limit (above or below)A run of 5 points above or below the process meanFive or more points trending toward either limitA sharp change in levelOther erratic behavior
31Samples vs. Population Sample Distribution Population Distribution Mean
32Types of Control Charts Attribute control chartsMonitors frequency (proportion) of defectivesp - chartsDefects control chartsMonitors number (count) of defects per unitc – chartsVariable control chartsMonitors continuous variablesx-bar and R charts
331. Attribute Control Charts p - chartsEstimate and control the frequency of defects in a populationExamplesInvoices with error s (accounting)Incorrect account numbers (banking)Mal-shaped pretzels (food processing)Defective components (electronics)Any product with “good/not good” distinctions
34Using p-chartsFind long-run proportion defective (p-bar) when the process is in control.Select a standard sample size nDetermine control limits
35p-chart ExampleChic Clothing is an upscale mail order clothing company selling merchandise to successful business women. The company sends out thousands of orders five days a week. In order to monitor the accuracy of its order fulfillment process, 200 orders are carefully checked every day for errors. Initial data were collected for 24 days when the order fulfillment process was thought to be "in control." The average percent defective was found to be 5.94%.
362. Defect Control Charts c-charts Estimate & control the number of defects per unitExamplesDefects per square yard of fabricCrimes in a neighborhoodPotholes per mile of roadBad bytes per packetMost often used with continuous process (vs. batch)
37Using c-chartsFind long-run proportion defective (c-bar) when the process is in control.Determine control limits
382. c-chart ExampleDave's is a restaurant chain that employs independent evaluators to visit its restaurants as secret shoppers to the asses the quality of service. The company evaluates restaurants in two categories, food quality, and service (promptness, order accuracy, courtesy, friendliness, etc.) The evaluator considers not only his/her order experiences, but also evaluations throughout the restaurant. Initial surveys find that the total number of service defects per survey is 7.3 when a restaurant is operating normally.
393. Control Charts for Variables x-bar and R chartsMonitor the condition or state of continuously variable processesUse to control continuous variablesLength, weight, hardness, acidity, electrical resistanceExamplesWeight of a box of corn flakes (food processing)Departmental budget variances (accountingLength of wait for service (retailing)Thickness of paper leaving a paper-making machine
40x-bar and R charts Two things can go wrong Two control solutions process mean goes out of controlprocess variability goes out of controlTwo control solutionsX-bar charts for meanR charts for variability
41Problems with Continuous Variables “Natural”ProcessDistributionMean notCenteredIncreasedVariabilityTarget
42Range (R) Chart Choose sample size n Determine average in-control sample ranges R-bar where R=max-minConstruct R-chart with limits:
43Mean (x-bar) Chart Choose sample size n (same as for R-charts) Determine average of in-control sample means (x-double-bar)x-bar = sample meank = number of observations of n samplesConstruct x-bar-chart with limits:
45R and x-bar Chart Example Resistors for electronic circuits are being manufactured on a high-speed automated machine. The machine is set up to produce resistors of 1,000 ohms each. Fifteen samples of 4 resistors each were taken over a period of time when the machine was operating normally. The average range of the samples was found to be R-bar=21.7 and the average mean of the samples was x-double-bar=999.1.
46When to Take ActionA single point goes beyond control limits (above or below)Two consecutive points are near the same limit (above or below)A run of 5 points above or below the process meanFive or more points trending toward either limitA sharp change in levelOther statistically erratic behavior
47Control Chart Error Trade-offs Setting control limits too tight (e.g., m ± 2) means that normal variation will often be mistaken as an out-of-control condition (Type I error).Setting control limits too loose (e.g., m ± 4) means that an out-of-control condition will be mistaken as normal variation (Type II error).Using control limits works well to balance Type I and Type II errors in many circumstances.3s is not sacred -- use judgement.