Statistical Process Control Using Control Charts for Attributes

Statistical Process Control Using Control Charts for Attributes

2002 Auburn UniversityAll Rights Reserved 2002 Auburn UniversityAll Rights Reserved1Control Charts for AttributesAn attribute is a quality characteristic for which a numerical value is not specified. It is measured on a nominal scale; that is, it does not meet certain guidelines, or it is categorized according to a scheme of labels. For instance, microchips may be classified as acceptable or unacceptable. 2002 Auburn UniversityAll Rights ReservedControl Charts for AttributesA quality characteristic that does not meet certain prescribed standards (or specifications) is said to be a nonconformity (or defect). For example, if the thickness of a washer is expected to be 3 0.05 mm, a thickness of 3.08 mm is not acceptable. A product with one or more nonconformities, such that it is unable to meet the intended standards and is unable to function as required, is a nonconforming item (or defective). It is possible for a product to have several nonconformities without being classified as a nonconforming item. 2002 Auburn UniversityAll Rights ReservedAdvantages of Attribute ChartsCertain quality characteristics are best measured as attributes.In most manufacturing and service operations there are numerous quality characteristics that can be analyzed. If a variable chart (such as an X- or R-chart) is selected then one variable chart is needed for each characteristic. The total number of control charts being constructed and maintained can be overwhelming. A control chart for attributes can provide overall quality information at a fraction of the cost. 2002 Auburn UniversityAll Rights ReservedAdvantages of Attribute ChartsAttributes are encountered at all levels of an organization the company, plant, department, work center, and machine (or operator) level. Variable charts are typically used at the lowest level namely, the machine level. Attribute charts assist in going from the general to a more focused level. 2002 Auburn UniversityAll Rights ReservedQuality Characteristics for a Simple Component HLW 2002 Auburn UniversityAll Rights ReservedLevels at Which Attribute Charts are UsedPlantDepartment ADepartment BDepartment CWork center 1Work center 2Work center 1Work center 2Work center 1Work center 2Work center 3Work center 4 2002 Auburn UniversityAll Rights ReservedDisadvantages of Attribute ChartsAttribute information indicates whether a certain quality characteristic is within specification limits. It does not state the degree to which specifications are met or not met.Variable information, on the other hand, indicates the level of the data values. Variable control charts thus provide more information on the performance of a process. Specific information about the process mean and variability can be obtained. Furthermore, for out-of-control situations, variable plots generally provide more information as to the potential causes and hence make identification of remedial actions easier. 2002 Auburn UniversityAll Rights ReservedDisadvantages of Attribute ChartsIf we can assume that the process is very capable that is, its inherent variability is much less than the spread between the specification limits then variable charts can forewarn us when the process is about to go out of control. This of course, allows us to take corrective action before any nonconforming items are produced. A variable chart can indicate an upcoming out-of-control condition even though items are not yet nonconforming. 2002 Auburn UniversityAll Rights ReservedDisadvantages of Attribute ChartsAttribute charts require larger sample sizes than variable charts to ensure adequate protection against a certain level of process changes. Larger sample sizes can be problematic if the measurements are expensive to obtain or the testing is destructive. 2002 Auburn UniversityAll Rights ReservedForewarning of a Lack of Process Control as Indicated by a Variable Chart

Lower specification limitUpper specification limitMean A: Target value. Mean B: Variables chart reacts to change in process mean. Mean C: Attribute chart reacts.ACBProportion nonconforming

2002 Auburn UniversityAll Rights Reserved 2002 Auburn UniversityAll Rights ReservedPreliminary ConsiderationsIf no historical information is available, attribute control charts are generally used first. As problem areas are identified, the attribute charts may be replaced by variable charts to collect more specific information. The choice of sample size for attribute charts is important. It should be large enough to allow nonconformities or nonconforming items to be observed in the sample. 2002 Auburn UniversityAll Rights ReservedPreliminary ConsiderationsFor situations in which summary measures are required, attribute charts are preferred. Information about the output at the plant level is often best described by proportion-nonconforming charts or charts on the number of nonconformities. On the other hand, variable charts are more meaningful at the operator or supervisor level, because they provide specific clues for remedial actions. What is going to constitute a nonconformity should be properly defined. This definition will depend on the product, its functional use, and customer needs. 2002 Auburn UniversityAll Rights ReservedSelection of Control ChartControl Chart X, s X, RX- chart, moving rangep or nppc or uuVariablen largen smalln = 1AttributeDefectiveDefectsn constantn variablen constantn variable 2002 Auburn UniversityAll Rights ReservedControl Chart for Proportion Non -conforming or Defective (p-chart) The proportion nonconforming for a given sample is given by

where x is the number of nonconforming items and n represents the sample size.

2002 Auburn UniversityAll Rights ReservedControl Chart for Proportion Non -conforming or Defective (p-chart)Center line

where n is the sample size and g represents the number of samples.Control limits

If the lower control limit is calculated to be less than zero, it is converted to zero.

2002 Auburn UniversityAll Rights ReservedExampleRandom samples of size 400 are chosen from a plastic injection molding machine producing small containers. The number of nonconforming containers for each sample is shown for 25 such samples. Construct a control chart for the proportion of nonconforming containers and comment on the process. 2002 Auburn UniversityAll Rights ReservedData on Nonconforming Containers

2002 Auburn UniversityAll Rights ReservedData on Nonconforming Containers

2002 Auburn UniversityAll Rights ReservedMinitab Commands for p ChartStat > Control Charts > P.In Variable, enter the column number or name of the variable containing the number of defectives.a. If subgroups are of equal size, check Subgroup size, and enter its value.b. If subgroup sizes are unequal, check Subgroups in, and enter the column that contains subgroup sizes. 2002 Auburn UniversityAll Rights ReservedMinitab Commands for p ChartIf desirable, use any of the options, such as tests for special causes, omit certain subgroups, and use historical values of the center line, among other options.

2002 Auburn UniversityAll Rights Reservedp ChartCenter Line:

Control Limits:

2002 Auburn UniversityAll Rights Reservedp Chart for Nonconforming Containers

2002 Auburn UniversityAll Rights ReservedControl Chart for Number of Non -conforming Items (np Chart)Operating personnel may find it easier to relate to.Same assumptions as the p-chart.If sample size changes, the center line and control limits changes as well, making inferences in such circumstances difficult.Desirable to use an np chart when the sample size remains constant. 2002 Auburn UniversityAll Rights Reservednp Chart Center line

where n = sample size p = average proportion nonconforming

2002 Auburn UniversityAll Rights Reservednp ChartControl limits

np 3 np (1 p)

If the lower control limit is calculated to be less than zero, it is converted to zero. 2002 Auburn UniversityAll Rights ReservedExampleData for the number of dissatisfied customers in a department store observed for 20 samples of size 300 is shown in the table. Construct an np- chart for the number of dissatisfied customers. 2002 Auburn UniversityAll Rights ReservedTableNo. of Dissatisfied CustomersSampleNumber of Dissatisfied Customers11021238495661171381098109SampleNumber of Dissatisfied Customers1161219131014715816417111810196207Total 184 2002 Auburn UniversityAll Rights ReservedExample np ChartCenter line = 184 / 20 = 9.2 .

Control limits :9.2 3 9.2 (1 9.2/300)= (0.241, 18.159).

2002 Auburn UniversityAll Rights ReservedMinitab Commands for np ChartStat > Control Charts > NP .In Variable, enter the column number or name of the variable containing the number of defectives.a. If subgroups are of equal size, enter the size in Subgroup size.b. If subgroups are unequal, choose Subgroups in and enter the column that contains the subgroup sizes.If desirable, use any of the options. 2002 Auburn UniversityAll Rights Reservednp Chart for Dissatisfied Customers

2002 Auburn UniversityAll Rights ReservedAnalysis of np ChartSample number 12 plots above the UCL.Assuming special cause has been identified and remedial action taken, we revise the control limits, omitting sample number 12 from the computations. 2002 Auburn UniversityAll Rights ReservedControl Chart for Number of Nonconformities or Defects (c-chart)Nonconformity or Defect: A quality characteristic that does not conform to specifications. The c-chart is based on the Poisson distribution which is suited to modeling the number of events that happen over a specified amount of time, space, volume, or units produced. 2002 Auburn UniversityAll Rights ReservedControl Chart for Number of Nonconformities or Defects (c-chart)AssumptionsThe opportunity for defects is large, while the average number of defects per unit is small.Ex. Rivets on an airplane. There are a large number of rivets but a small chance of any one rivet being a defect.Different subgroups (usually a unit of the item) should have equal opportunity for the occurrence of nonconformities (defects).Ex. In the production of molded castings, the same set of process conditions should have been in place. Occurrences of defects must be independent of each other. 2002 Auburn UniversityAll Rights Reservedc-Chart ConstructionCenter line

where g is the number of subgroups.Control limits

If the lower control limit is calculated to be less than zero, it is converted to zero.

2002 Auburn UniversityAll Rights ReservedExampleThe number of defects in printed circuit boards found by the inspector is shown on a daily basis. The number of boards inspected each day is 500. Construct a control chart for the number of defects and comment on the process. 2002 Auburn UniversityAll Rights ReservedData on Printed Circuit Board Defects

2002 Auburn UniversityAll Rights ReservedData on Printed Circuit Board Defects

2002 Auburn UniversityAll Rights ReservedMinitab Commands for c- ChartStat > Control Charts > C .In Variable, enter the column number or name containing the number of defects.If desired, select any of the options. 2002 Auburn UniversityAll Rights Reservedc-ChartCenter Line:

Control Limits:

2002 Auburn UniversityAll Rights Reservedc Chart for Printed Circuit Board Defects

2002 Auburn UniversityAll Rights ReservedControl Chart for Number of Nonconformities per Unit (u-chart)A u-chart is used when the sample size varies. For companies who inspect all items produced, the output per production run can vary because of fluctuating supplies of labor, machinery, and raw materials. Chart ConstructionWhen the sample size varies, the number of nonconformities per unit for the ith sample is given by

where ci is the number of nonconformities in the ith sample, and ni is the size of the ith sample.

2002 Auburn UniversityAll Rights ReservedControl Chart for Number of Nonconformities per Unit (u-chart)Center line

where g represents the number of samples.

2002 Auburn UniversityAll Rights ReservedControl Chart for Number of Nonconformities per Unit (u-chart)Control limits

If the lower control limit is calculated to be less than zero, it is converted to zero.

2002 Auburn UniversityAll Rights ReservedExampleThe number of flaws in rolled sheet metal and the number inspected (in units of 200 square meters) are shown on a daily basis. Construct a control chart for the number of flaws per 200 square meters and comment on the process. 2002 Auburn UniversityAll Rights ReservedData on Flaws in Rolled Sheet Metal

2002 Auburn UniversityAll Rights ReservedData on Flaws in Rolled Sheet Metal

2002 Auburn UniversityAll Rights ReservedMinitab Commands for u-ChartStat > Control Charts >U .In Variable, enter the column number or name containing the number of defects.a. If subgroup sizes are equal, enter the size in Subgroup size.b. If subgroup sizes are unequal, select Subgroups in and enter the column containing the subgroup sizes.If desired, select any of the options. 2002 Auburn UniversityAll Rights Reservedu-ChartCenter Line: Control Limits:Sample Number 1 -

Sample Number 2 -

2002 Auburn UniversityAll Rights Reservedu Chart for Flaws in Rolled Sheet Metal

2002 Auburn UniversityAll Rights Reserved