Chapter 03 Control Charts

08/02/1439University of HailCollege of EngineeringQEM 511 - Total Quality ManagementChapter 03Control ChartsProf. Mohamed AichouniLectures notes adapted from: PowerPoint presentation to accompanyBesterfield, Quality Improvement, 9th editionProcess Variations and Quality Quality is inversely proportional to variability(Variability & Quality are enemies). The more variation in product characteristics, in deliverytimes, in work practices: the more waste, highercosts and poor quality, is delivered to our customers.(Out of the Crisis, 1982)1

08/02/1439Causes of Product VariationsProduct characteristicsvariations are mainlycaused by thevariations in thecomponents of theprocess (5 M and E): Man entsMethodsProductProcessProcess Variations Causes1. Common causes are ever-present in the process; Natural Variations2. Special causes are intermittent effects that mustbe investigated immediately. Assignable Causes Variations Management and quality professionals (YOU)should help manufacturing people to identifyand remove special causes and reduce theoccurrence of common causes in the process.2

08/02/1439Process VariationProcess VariabilityVariations due to:Natural Causes:Temperature variation Material variation Customer differences Operator performance Must be monitoredSpecial Causes:Machine is breaking Untrained operative Machine movement Process has changed Early and visiblewarning requiredControl ChartsOf all the quality tools for analyzing data, thecontrol chart is the most useful.No other tool captures the voice of yourprocess better.Control charts are used to determine whetheryour process is operating in statisticalcontrol.63

08/02/1439Control ChartsThe control chart is ameans of visualizingthe variations thatoccur in the processdata and itscomponents.It shows whether theprocess is in a stablestate (in statisticalcontrol) or out ofstatistical control.Special causes variationNatural (common causes )variationFigure 1 Example of a control chart7Use of Variable Control Charts inManufacturingThe objectives of the variable control charts are: For process improvement To determine the process capability. For decisions regarding product specifications For current decisions on the production process For current decisions on recently produced items84

08/02/1439Control Charts9Control Charts TypesContinuousNumerical DataCategorical or DiscreteNumerical utesChartssChartPChartCChartOther Charts:ImR, EWMA, CUSUM.105

08/02/1439Variable Control Charts Interpretationcontrol charts help to determine if the process is :(a) in statistical control ; or (b) out of statistical control.11Quality Characteristic Variable - a single qualitycharacteristic that can bemeasured on a numericalscale. 6When working withvariables, we should monitorboth the mean value of thecharacteristic and thevariability associated with thecharacteristic.The Quality characteristicmust be measurable.It can expressed in terms ofthe seven basic units:1. Length2. Mass3. Time4. Electrical current5. Temperature6. Substance7. Luminosity

08/02/1439Part 1 – Variable Control ChartsExample of amethod of reportinginspection results13Control Chart TechniquesProcedure for establishing a pair of control charts forthe average Xbar and the range R:1.Select the quality characteristic2.Choose the rational subgroup3.Collect the data4.Determine the trial center line and control limits5.Establish the revised central line and control limits6.Achieve the objective147

08/02/1439Control Charts forand RNotation for variables control charts n - size of the sample (sometimes called asubgroup) chosen at a point in time m - number of samples selected average of the observations in the ithsample(where i 1, 2, ., m) grand average or “average of theaverages(this value is used as thecenter line of the control chart)Control Charts forand RNotation and values Ri range of the values in the ithsampleRi xmax - xmin average range for all m samples is the true process mean is the true process standard deviation8

08/02/1439Control Charts forand RStatistical Basis of the Charts Assume the quality characteristic of interest isnormally distributed with mean , and standarddeviation, . If x1, x2, , xn is a sample of size n, then he averageof this sample is is normally distributed with mean, , and standarddeviation,Control Charts forControl Limits for theand Rchart A2 is found in constants for various values ofn.9

08/02/1439Control Charts forand RControl Limits for the R chart D3 and D4 are constants for various values ofn.Control Charts Constants10

08/02/1439Control Charts forand s The sample standards deviation can be amore accurate estimation of the processvariability process, especially if the samplesize n 10. In this case control charts for Xbar and S canbe used to monitor the process.Control Charts forand s Construction of the control charts for Xbarand S follows the same procedure as for theXbar-R charts. Control Limits for s chart are: Control Limits for Xbar chart: A3, B3, B4 are constants11

08/02/1439Example of-R control chartsA component part for a jetaircraft engine ismanufactured by aninvestment castingprocess.The vane opening on thiscasting is an importantfunctional parameter of thepart.We will illustrate the use ofXbar and R control chartsto assess the statisticalstability of this process.Example ofDetermine themean and therange foreach sample.Determine thegrandaverage of themeans andthe average ofthe ranges.12-R control charts

08/02/1439Example of-R control chartsCalculate the control limits for the R chart:Calculate the control limits for the Xbar chart:Example ofThe process is Out ofstatistical control;It is not stable.Special causes shouldbe investigated usingcause and effectdiagram and otherquality tools.13-R control charts

08/02/1439Other Control Charts forvariables1. Individual Moving Range Charts2. Exponentially Weighted Mean Average(EWMA) charts3. Cumulative Sum (CUSUM) chart.Student should search on the net for the use of thesechartsPART 2CONTROL CHARTS FOR ATTRIBUTES14

08/02/1439Introduction Many quality characteristicscannot be convenientlyrepresented numerically. In such cases, each iteminspected is classified as eitherconforming or nonconformingto the specifications on thatquality characteristic. Quality characteristics of this typeare called attributes.Types of Control ChartsControl Charts for Variables DataX and R charts: for sample averages and ranges.X and s charts: for sample means and standard deviations.Md and R charts: for sample medians and ranges.X charts: for individual measures; uses moving ranges.Control Charts for Attributes Datac charts: count of nonconformities.p charts: proportion of units nonconforming.np charts: number of units nonconforming.u charts: count of nonconformities per unit.15

08/02/1439Control Chart SelectionQuality CharacteristicVariableAttributeDefectiven 1?nox and MRyesnon 10?Defectx and Rconstantsamplesize?yesnoyesx and sconstantsamplingunit?p ornpp-chart withvariable samplesizeyesnocuType of Attribute Chartsc charts This shows the number of defects or nonconformities produced by amanufacturing process.p charts This chart shows the fraction of nonconforming or defective productproduced by a manufacturing process. It is also called the control chart for fraction nonconforming.np charts This chart shows the number of nonconforming. Almost the same asthe p chart.u charts This chart shows the nonconformities per unit produced by amanufacturing process.16

08/02/1439c Chart In statistical quality control, the c-chart is a typeof control chart used to monitor "count“ or totalnumber of nonconformities per unit. It is also occasionally used to monitor the totalnumber of events occurring in a given unit oftime. c: counts of nonconformities. Control limits must be calculated (UCL, LCL): average count of nonconformitiesExample from ManufacturingSurface defects havebeen counted on 25rectangular steelplates, and the dataare shown below.The control chart fornonconformities (cchart) is used to studythe process stability.Is the Process underStatistical Control?.17

08/02/1439The c chart for nonconformities shows thatthe process is :Out of Statistical Control; it is unstable.Special causes must be inverstigated.Example 2Number .005Number of DefectsSample12345678910Total432101234567Sample NumberThe Process is in Statistical Control and Stable.188910

08/02/1439p chartsp charts In this chart, we plot the percent ofdefectives (per batch, per day, per machine,etc.). However, the control limits in this chart arenot based on the distribution of rate eventsbut rather on the binomial distribution (ofproportions).19

08/02/1439Formula Fraction nonconforming:p (np)/n where p proportion or fraction nc in thesample or subgroup, n number in the sample or subgroup, np number nc in the sample orsubgroup.Example During the first shift, 450 inspection are made of bookof the month shipments and 5 nc units are found.Production during the shift was 15,000 units. What isthe fraction nc?p (np)/n 5/450 0.011 The p, is usually small, say 0.10 or less. If p 0.10, indicate that the organization is in seriousdifficulty.20

08/02/1439p-Chart contruction for constantsubgroup size Select the quality characteristics.Determine the subgroup size and methodCollect the data.Calculate the trial central line and controllimits. Establish the revised central line and controllimits. Achieve the objective.Select the quality characteristicsThe quality characteristic?– A single quality characteristic– A group of quality characteristics– A part– An entire product, or– A number of products.21

08/02/1439Determine the subgroup size andmethod The size of subgroup is a function of the proportionnonconforming. If p 0.001, and n 1000, then the average numbernc, np 1. Not good, since a large number of valueswould be zero. If p 0.15, and n 50, then np 7.5, would make agood chart. Therefore, the selection subgroup size requires somepreliminary observations to obtain a rough idea of theproportion nonconforming.Calculate the trial central line andcontrol limits The formula: average of p for many subgroups n number inspected in a subgroup22

25TotalNegative value of LCL is possible in a theoritical result, butnot in practical (proportion of nc never negative).p Chart0.05323

08/02/1439Control Charts for FractionNonconforming (p chart) Example 2Example A process that produces bearing housings isinvestigated. Ten samples of size 100 areselected. Is this process operating in statistical control?Example24n 100, m 10

08/02/1439C chart – Example 2P Chart for C1Proportion0.103.0SL 0.095360.05P 0.03800- 3.0SL 0.0000.00012345678910Sampl e Numberu Chart The u chart is mathematically equivalent to the cchart.25

08/02/1439Example For January 30:26

08/02/1439Control Charts for Variables in Minitab27

08/02/1439Control Charts for Attributes in MinitabHome Work Study theprocess stabilityusing the datashown on thetable on nonconformingunits in themanufacturingprocess.28

08/02/1439Conclusion"Quality control trulybegins and endswith education",K. Ishikawa (1990).Lecture FinishedAnyQuestion?NoYesAsk questionsTeachers answersTrain your self (Google, YouTube,course webpageEnd(See you next lecture)29

variability process, especially if the sample size n 10. In this case control charts for Xbar and S can be used to monitor the process. Control Charts for and s Construction of the control charts for Xbar and S follows the same procedure as for the Xbar-R charts. Control Limits for s chart are: Control Limits for Xbar chart: