Learning Objectives

P Control ChartThe most versatile and widely used attributes control chart -- used when the subgroup size is not constantUsed to evaluate fraction defectiveControl limits are based on Binomial Distribution

P Control ChartUCL PERCENT90

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0 2 4 6 8 10 12 14 16 18 20 22 24 26P CONTROL CHART ALCAS PEFLOW SOLDER MACHINEPERCENT DEFECTIVESUBGROUP NUMBER

P ChartCompute the control limits

The UCL and LCL are not straight lines, they rise and fall with respect to the subgroup size

The P ChartWhen to use:Only when variable data cannot be obtained.When charting fraction rejected as nonconforming from a varying sample size.When screening multiple characteristics for potential monitoring on variable control charts.When tracking the quality level of a process before any rework is performed.

The P ChartHowBy counting the number of defective items from a sample and then plotting the percent that are defective.ConditionsIn order to be of help, there should be some rejects in each observed sample.The higher the quality level, the larger the sample size must be to contain rejects. For example, if 20% of a product is rejectable, a sample size of 5 will be needed. However, a sample of 1,000 will give an average of only one reject per sample if 0.1% of the product is rejectable.

The P ChartTable 1 Formulas for the P Chart

The P ChartTo calculate Plot PointsThe p plot point is the fraction defective in a sample. The centerline is the average fraction defective in series of samples. Figure 1 is a cross section showing countersunk holes for rivet installation.

The P ChartTo calculate Plot PointsIn a sheet metal assembly shop a common process is bucking rivets. Because of the combined variation in the rivets, the drilled holes, and the bucking process, there are quality problems. After the rivets in an assembly have been bucked into place they are checked for nonconformity. A P chart is used to track the first-time-through fraction defective.

Figure 1Cross section of sheet metal plates with countersunk holes for rivet installation

P Chart

P ChartTOTALS

X Relay

Fluorocarbon Leak Test

NP Control ChartNumber of defectivesUsed when subgroup size is constant (n)The actual number of defects is represented by pn (or np)

NP Control ChartNP Control Chart plating defects of assembled parts 2 4 6 8 10 12 14 16 18 20 22 24 26 28 3015

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LOT NUMBERUCL

NP Control ChartsComputationsControl limits are based on the Binomial Distribution1) Central line:

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NP Charts

4 Steps in control chat for Fraction RejectedI Preparatory DecisionsII Starting the control chartIII Continuing the control chartIV Reports and Action based on control chart

I. Preparatory DecisionsPurposeSelect Quality CharacteristicSelection of subgroup P or NP chartControl limit calculated

II. Starting the control chartRecording data , CalculationTrial limitsPlotting points

III Continuing the control chartSelection of P0Calculation of control limits Plotting the points/limitsInterpretation of lack of controlPeriodic Review/Revision of Pi

IV Reports and Action based on control chartAction to bring process into control-Pareto, high spot/low spot.Review of Design and specificationInformation to Management(Quality level)Sensitivity of p chart : 0.1% requires 1000s

Example of Attribute control chart

LOTNumber inspectingNumber of defectivesP1500270.054250120.2403800120.0154100140.1405150150.100Total160080

Example of Attribute Control Chart

SubgroupSubgroup Size n# of DefectivesPercent Defective P (%)UCL(%)LCL11151513.017.71.2220188.215.43.32102310.915.63.42202210.015.43.5255187.015.04.6365154.14.72554415.04.8300134.34.92803311.714.8103304212.714..3Total2550243

Purpose of maintaining attribute charts is to continuously improve the processes for defect free production by highlighting the key problems.How to work on getting desirable pattern

Recommend working on 3 top problems for the day or week of month as the time permits and solve by a systematic problem solving method namelyDefine problemsFind key causesSolution to cure the key causes demonstrated by statistics

Design of the Fraction Nonconforming ChartThree parameters must be specifiedThe sample sizeThe frequency of samplingThe width of the control limitsCommon to base chart on 100% inspection of all process output over timeRational subgroups may also play role in determining sampling frequency

Average sample size approach

Charts for NonconformitiesOften times there is interest in knowing how many defects an item has -- C charts: total number of nonconformities in subgroups of fixed size (defects per square yard of cloth) -- U charts: average number of nonconformities per unit (defects per TV set)C cart and U chart

Charts for NonconformitiesUsed during inspection of complex assemblies

Control limits based on Poisson Distribution

C Control ChartUCL and LCL are straight lines because of fixed sample sizes CL= UCL= LCL= Where is the central line and equal to

The data in table 2 represent the types of defects found on the first two boxes. Box 1 has nine defects and box 2 has twelve.

Notice that the types and quantity of defects are different for the two boxes; nevertheless, the total number of defects is plotted on the C chart.

Note: A C chart (as well as any other attribute chart) should only be used when there is absolutely no way to obtain variable data from the characteristic in which measurable data is available.

To get started, this data can be analyzed on an attribute chart to get ideas (using the Pareto analysis) on the characteristics.

U Control ChartAs the subgroup size varies, UCL and LCL varies

CL=

UCL=

LCL=

where is the central line and equal to

The U ChartWhen to use:Only when variable data cannot be obtained.When plotting the average number of defects found per unit.When screening multiple characteristics for potential monitoring on variable control charts.How:Each unit is examined and the average number of defects found are plotted.

The U ChartConditions:Constant unit size, but any convenient number of units per plot point. Unit size is different from samples size. For example, one unit could be defined as 1 square-foot of material. On a particular day, 12.3 square-feet of material is inspected. The plot point would represent the average number of defects per unit, but the sample size would be 12.3.

The U ChartThere are potentially several different types of defects per unit, but none of which would necessarily render the part a defective. For example: paint blemishes on a skin panel, or various electrical faults on a circuit board. A unit can be single part, an assembly of several parts, an area of material, or any rational grouping in which the likelihood of defect(s) is constant from unit to unit.

In order for this type of analysis to be of help, there should be some defects in each observed unit.

The U ChartTo Calculate Plot Points:The u plot point is the average number of defects per unit in a sample of n units. The centerline is the average of all the plot points on the chart. Figure 6-17 shows a roll of composite material/dyed cloth with potential multiple defects.

The U ChartComposite materials are generally made up of several layers of materials that are bonded to form the desired characteristics. Prior to lay up, are used each day, the number of rolls inspected for defects. Since different amounts of the material are used each day, the number of rolls inspected also changes daily.

Attribute Control Charts

Chart typeNames/remarksCentral lineControl LimitsFraction defectiveNumber defectivesNumber of defects per subgroupNumber of defects per inspection unit

AttributedataN>50N not constantFractiondefectiveN>50N is constantFractiondefectiven1n not constantDefectsper unitn1Is constantDefects per unitc chartVariable dataP chartnp chartu chartn6n>25n=1IndividualchartX-bar chartR chartX-bar chartS chartX-bar chartS2 chart

Low Defect Levels

Actions taken to improve a process

Learning Objectives