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Chapter 7
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Chapter 7
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Learning Objectives Chapter 7
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P Control Chart The most versatile and widely used attributes control chart -- used when the subgroup size is not constant Used to evaluate fraction defective Control limits are based on Binomial Distribution Chapter 7
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P Control Chart P CONTROL CHART ALCAS PEFLOW SOLDER MACHINE 90 80 70
60 50 40 30 20 10 PERCENT DEFECTIVE UCL PERCENT SUBGROUP NUMBER Chapter 7
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P Chart Compute the control limits
The UCL and LCL are not straight lines, they rise and fall with respect to the subgroup size Chapter 7
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The P Chart When 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. Chapter 7
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The P Chart How Conditions
By counting the number of defective items from a sample and then plotting the percent that are defective. Conditions In 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. Chapter 7
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The P Chart Table 1 Formulas for the P Chart p Chart Control limits
Centerline Plot point Sample size p Varying Chapter 7
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The P Chart To calculate Plot Points
The 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. Chapter 7
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The P Chart To calculate Plot Points
In 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. Chapter 7
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Figure 1 Cross section of sheet metal plates with countersunk holes for rivet installation Chapter 7
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P Chart Chapter 7
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P Chart TOTALS Chapter 7
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X Relay Chapter 7
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Fluorocarbon Leak Test
7 6 5 4 3 2 1 UCL FLUOROCARB. LEAK TEST P Chart (%) Chapter 7
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NP Control Chart Number of defectives
Used when subgroup size is constant (n) The actual number of defects is represented by pn (or np) Chapter 7
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NP Control Chart NP Control Chart plating defects of assembled parts
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 UCL Chapter 7 LOT NUMBER
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NP Control Charts Computations
Control limits are based on the Binomial Distribution 1) Central line: 2) 3) Chapter 7
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NP Charts Chapter 7
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4 Steps in control chat for Fraction Rejected
I Preparatory Decisions II Starting the control chart III Continuing the control chart IV Reports and Action based on control chart Chapter 7
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I. Preparatory Decisions
Purpose Select Quality Characteristic Selection of subgroup P or NP chart Control limit calculated Chapter 7
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II. Starting the control chart
Recording data , Calculation Trial limits Plotting points Chapter 7
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III Continuing the control chart
If chart in control Selection of P0 Calculation of control limits Plotting the points/limits Interpretation of lack of control Periodic Review/Revision of Pi Chapter 7
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IV Reports and Action based on control chart
Action to bring process into control-Pareto, high spot/low spot. Review of Design and specification Information to Management(Quality level) Sensitivity of p chart : 0.1% requires 1000s Chapter 7
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Example of Attribute control chart
LOT Number inspecting Number of defectives P 1 500 27 0.054 2 50 12 0.240 3 800 0.015 4 100 14 0.140 5 150 15 0.100 Total 1600 80 Chapter 7
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Example of Attribute Control Chart
Subgroup Subgroup Size n # of Defectives Percent Defective P (%) UCL(%) LCL 1 115 15 13.0 17.7 1. 2 220 18 8.2 15.4 3. 3 210 23 10.9 15.6 4 22 10.0 5 255 7.0 15.0 4. 6 365 4.1 7 44 8 300 13 4.3 9 280 33 11.7 14.8 10 330 42 12.7 14..3 Total 2550 243 Chapter 7
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How to work on getting desirable pattern
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 namely Define problems Find key causes Solution to cure the key causes demonstrated by statistics Chapter 7
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Design of the Fraction Nonconforming Chart
Three parameters must be specified The sample size The frequency of sampling The width of the control limits Common to base chart on 100% inspection of all process output over time Rational subgroups may also play role in determining sampling frequency Chapter 7
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Average sample size approach
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Charts for Nonconformities
C cart and U chart Often 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) Chapter 7
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Charts for Nonconformities
Used during inspection of complex assemblies Control limits based on Poisson Distribution Chapter 7
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C Control Chart UCL and LCL are straight lines because of fixed sample sizes CL= UCL= LCL= Where is the central line and equal to Chapter 7
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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. Chapter 7
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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. Chapter 7
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U Control Chart As the subgroup size varies, UCL and LCL varies CL=
where is the central line and equal to Chapter 7
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The U Chart When 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. Chapter 7
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The U Chart Conditions:
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. Chapter 7
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The U Chart There 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. Chapter 7
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In order for this type of analysis to be of help, there should be some defects in each observed unit. Chapter 7
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The U Chart To 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. Chapter 7
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The U Chart Composite 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. Chapter 7
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Attribute Control Charts
Chart type Names/remarks Central line Control Limits Fraction defective Number defectives Number of defects per subgroup Number of defects per inspection unit Chapter 7
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Attribute data Variable data N>50 N not constant Fraction defective
X-bar chart R chart P chart n<6 N>50 N is constant Fraction defective X-bar chart S chart n>6 np chart n>25 n1 n not constant Defects per unit X-bar chart S2 chart u chart n=1 n1 Is constant Defects per unit Individual chart c chart Chapter 7
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Low Defect Levels Chapter 7
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Actions taken to improve a process
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Learning Objectives Chapter 7
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