Chapter 7: Control Charts For Attributes

By Drew KellyIET 603 Introduction to Statistical Quality Control.Douglass C. MontgomeryChapter 7: Control Charts For Attributes7-1 IntroductionIn this Chapter we deal with what is called Attributes Data.Attributes Data deals with classifications of a product that is either defective or non-defective.

Taken from Google

7-1 IntroductionThe terms nonconformity and nonconforming are used more in todays time.However many feel that saying defect and defective gives a more clear distinction between the two.Attribute Charts are not as statistically informing as Variable charts. Simple due to the amount of numerical information Variable charts have to offer

Attribute charts are not as informative as variable charts due to the lack of numerical information. 37-2 The Control Chart for Fraction NonconformingThe fraction nonconforming is the ratio of the number of nonconforming units in a population to the total number of units in the population. Again nonconforming item simply means that the entire product is defective. And should not be put out for use.

7-2-1 Development and Operation of the Control ChartThe control chart is also called the P- Chart.Again this is for the fraction of nonconformingEquations for the control chart are:

Taken from GoogleThe control limits given here are called trial control limits.

7-2-1 Continued There are three parameters that must be need to be specified: the sample size, the frequency of sampling, and the widths of the control limits. When interpreting points on the control charts, one must use caution.Often it is found that points below the lower control limit do not represent a real improvement in process quality.

Bullet 3: Frequently caused by errors in the inspection process6NP Control ChartThe np chart is used when you want to display the number of nonconforming instead of the fraction nonconforming. The equations for the np chart are :

Look at example 7.2 on page 310Taken from Google

So instead of there being a fration of non conforming items in a population to the population as a whole.7NP Control ChartTaken From Google.

Questions?7-2-2 Variable Sample SizeIn some occasions the sample is a inspection of process output over a period of time. This will cause the control chart to have a variable sample size. There are three methods to construct control charts with variable sample sizes. Variable-Width Control LimitsDetermine the control limits for each individual sample that are based on the specific sample size. The equations the same as if you were using it for the p chartIf you will look at page 311 in your book to see an example

Control limits based on an average sample sizeBased on average sample size Which will give an approximation of the control charts.This approach assumes that future sample sizes will not differ from the ones previously used.To find the average sample size you take the total of the sample size, denoted by ni, and divide by the total number of observations. Then solve like you would for the p chartLook at page 312 if you feel the need to.The Standardized control ChartWhere the points are plotted in standard deviation units. Center line must be at 0And control limits are at +3 and -3

7-2-4 Operating-Characteristic FunctionThe OC function is of the fraction of nonconforming control chart; is a graphic display of the probability of incorrectly accepting the hypothesis of SC against the process fraction nonconforming. This mean it is a type II error (failure to reject the incorrect hypothesis)

Questions?7-3 Control charts for NonconformitiesReview: A nonconforming item is an unit of product that does not meet one or more of the specifications for that particular product. ( Defective unit ) A nonconformity is the specific point where the specification is not met. ( Defect within a unit )Not all products with nonconformities will be nonconforming.Depending on the degree of severity it may still pass operationsConstant Sample sizeControl charts can be created for either the total number of nonconformities in a unit or the average. The control chart is called a c-chart. And is for the number of nonconformities, or defects.

Taken from Google

Further Analysis of NonconformitiesOther useful techniques of further analyzing nonconformities are cause and effect diagrams. Defect or nonconformity data is more useful that defective data because there are always going to be more nonconformity data.Out-of-control-action plans can be and should be done when your process is out of control.

Nonconformities give better detail to help create a OCAP because there will be several different types of nonconformities.18Choice of sample sizeThe sample size should be chosen according to statistical considerations, such as picking a size large enough to make positive lower control limits.Economic factors should be considered when determining the sample size. U chartThe best approach for setting up an u chart is to use the following equations:

Taken From GoogleThe u chart is used when the sample size is considered a variable sample sizeAnd is the control chart for average number of nonconformities per unit.

7-3-3 Demerit SystemsDemerit systems are ways to classify the seriousness of defect within the unit. This method is best used when you have a very complex product such as a car, computer, electrical appliances.Demerit System ClassificationClass A-Very serious. Unit is completely unfit for service.Class B- Serious. The unit will most likely suffer a class A operating failure.Class C- Moderately Serious. The unit will possibly fail service or cause a good deal of troubleClass D- Minor. The unit will not fail but has minor defects.Demerit Class WeightsClass A-100Class B-50Class C-10Class D-1From this you can get the equation:D=100ciA+50ciB+10ciC+1ciDDealing with low Defect levelsWhen the defect level drops, c and u charts become ineffective.Time between occurrence control charts are a good way to deal with thisThey chart the time between the successive occurrences of the defect.

Taken from pqsystems.com

Questions?7-4 Choice Between Attributes and Variable Control ChartsAttribute Control ChartsEasy to understandEasy to makeAvoids the hassle of having to make several Xbar or Rbar charts, like you would have to with Variable Control Charts.7-4 Choice Between Attributes and Variable Control ChartsVariable Control ChartsProvide much more useful information about process performance.Produce identification of impending trouble and allow management to take action to prevent defects from even happening.7-5 Guidelines for Implementing Control ChartsEvery process can benefit from SPC There are general guide lines that are used in order to implement the correct control chart. In total there are 5Guidelines for selecting the appropriate control chartDetermining which process characteristic to controlDetermining where the charts should be implementedChoosing the proper type of control chartTaking action to improve processes as the result of control chart analysisSelecting data collection systems and computer software.ReviewAttribute charts are mostly used where there is not much information to be givenNonconforming and nonconformities are not the same thing.Nonconforming means defective.Nonconformity mean defect.Variable charts are more complex to make but provide useful informationAny final Questions?Referenceshttp://www.transtutors.com/homework-help/operations-management/quality-control/p-charts.aspxhttp://www.qimacros.com/control-chart-formulas/u-chart-formula/http://www.qimacros.com/control-chart-formulas/np-chart-formula/http://www.six-sigma-material.com/SPC-Charts.htmlhttp://www.pqsystems.com/qualityadvisor/DataAnalysisTools/t_chart.phpDouglass C. Montgomery, Intro to Statistical Quality Control.