15- statistical quality control

*15Statistical Quality ControlCHAPTER OUTLINE

John Wiley & Sons, Inc. Applied Statistics and Probability for Engineers, by Montgomery and Runger.

Learning Objectives for Chapter 15After careful study of this chapter, you should be able to do the following:Understand the role of statistical tools in quality improvement.Understand the different types of variability, rational subgroups, and how a control chart is used to detect assignable causes.Understand the general form of a Shewhart control chart and how to apply zone rules (such as the Western Electric rules) and pattern analysis to detect assignable causes.Construct and interpret control charts for variables such as X-bar, R, S, and individuals charts.Construct and interpret control charts for attributes such as P and U charts.Calculate and interpret process capability ratios.Calculate the ARL performance for a Shewhart control chart.Construct and interpret a cumulative sum and exponentially-weighted moving average control chart.Use other statistical process control problem-solving tools.*

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15-1: Quality Improvement and Statistics

Definitions of Quality Quality means fitness for use - quality of design - quality of conformance Quality is inversely proportional to variability.*

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15-1: Quality Improvement and Statistics

Quality Improvement Quality improvement is the reduction of variability in processes and products. Alternatively, quality improvement is also seen as waste reduction.

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15-1.2: Statistical Process Control

Statistical process control is a collection of tools that when used together can result in process stability and variance reduction

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15-1.2: Statistical Process Control

The seven major tools are

1) Histogram2) Pareto Chart4) Cause and Effect Diagram5) Defect Concentration Diagram6) Control Chart 7) Scatter Diagram 8) Check Sheet*

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15-2: Introduction to Control Charts

A process that is operating with only chance causes of variation present is said to be in statistical control.A process that is operating in the presence of assignable causes is said to be out of control.The eventual goal of SPC is the elimination of variability in the process.15-2.1 Basic Principles*

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15-2.1 Basic PrinciplesA typical control chart has control limits set at values such that if the process is in control, nearly all points will lie within the upper control limit (UCL) and the lower control limit (LCL).Figure 15-1 A typical control chart. 15-2: Introduction to Control Charts*

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15-2.1 Basic PrinciplesFigure 15-2 Process improvement using the control chart. 15-2: Introduction to Control Charts*

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15-2.1 Basic Principleswhere k = distance of the control limit from the center line w = mean of some sample statistic, W. w = standard deviation of some statistic, W.15-2: Introduction to Control Charts*

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15-2.1 Basic PrinciplesImportant uses of the control chartMost processes do not operate in a state of statistical controlConsequently, the routine and attentive use of control charts will identify assignable causes. If these causes can be eliminated from the process, variability will be reduced and the process will be improvedThe control chart only detects assignable causes. Management, operator, and engineering action will be necessary to eliminate the assignable causes.15-2: Introduction to Control Charts*

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15-2.1 Basic PrinciplesTypes of control chartsVariables Control ChartsThese charts are applied to data that follow a continuous distribution.Attributes Control ChartsThese charts are applied to data that follow a discrete distribution.15-2: Introduction to Control Charts*

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15-2.1 Basic PrinciplesPopularity of control charts

1) Control charts are a proven technique for improving productivity.2) Control charts are effective in defect prevention.3) Control charts prevent unnecessary process adjustment.4) Control charts provide diagnostic information.5) Control charts provide information about process capability.15-2: Introduction to Control Charts*

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15-2.2 Design of a Control Chart Suppose we have a process that we assume the true process mean is = 74 and the process standard deviation is = 0.01. Samples of size 5 are taken giving a standard deviation of the sample average, is

15-2: Introduction to Control Charts*

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15-2.2 Design of a Control ChartControl limits can be set at 3 standard deviations from the mean in both directions.3-Sigma Control Limits UCL = 74 + 3(0.0045) = 74.0135 CL= 74 LCL = 74 - 3(0.0045) = 73.9865

15-2: Introduction to Control Charts*

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15-2.2 Design of a Control Chart15-2: Introduction to Control ChartsFigure 15-3 X-bar control chart for piston ring diameter. *

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15-2.2 Design of a Control ChartChoosing the control limits is equivalent to setting up the critical region for hypothesis testing H0: = 74 H1: 7415-2: Introduction to Control Charts*

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15-2.3 Rational Subgrouping15-2: Introduction to Control ChartsSubgroups or samples should be selected so that if assignable causes are present, the chance for differences between subgroups will be maximized, while the chance for differences due to these assignable causes within a subgroup will be minimized.*

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15-2.3 Rational Subgrouping15-2: Introduction to Control ChartsConstructing Rational SubgroupsSelect consecutive units of production.Provides a snapshot of the process.Good at detecting process shifts. Select a random sample over the entire sampling interval.Good at detecting if a mean has shifted out-of-control and then back in-control.*

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15-2.4 Analysis of Patterns on Control Charts15-2: Introduction to Control ChartsLook for runs - this is a sequence of observations of the same type (all above the center line, or all below the center line)Runs of say 8 observations or more could indicate an out-of-control situation.Run up: a series of observations are increasingRun down: a series of observations are decreasing*

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15-2.4 Analysis of Patterns on Control Charts15-2: Introduction to Control ChartsFigure 15-4 X-bar control chart. *

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15-2.4 Analysis of Patterns on Control Charts15-2: Introduction to Control ChartsFigure 15-5 An X-bar chart with a cyclic pattern. *

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15-2.4 Analysis of Patterns on Control Charts15-2: Introduction to Control ChartsFigure 15-6 (a) Variability with the cyclic pattern. (b) Variability with the cyclic pattern eliminated. *

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15-2.4 Analysis of Patterns on Control Charts15-2: Introduction to Control ChartsWestern Electric Handbook RulesA process is considered out of control if any of the following occur:1) One point plots outside the 3-sigma control limits.2) Two out of three consecutive points plot beyond the 2-sigma warning limits.3) Four out of five consecutive points plot at a distance of 1-sigma or beyond from the center line.4) Eight consecutive points plot on one side of the center line.*

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15-2.4 Analysis of Patterns on Control Charts15-2: Introduction to Control ChartsFigure 15-7 The Western Electric zone rules. *

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15-3: X-bar and R or S Control Charts 3-sigma control limits:The grand mean:*

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15-3: X-bar and R or S Control Charts The average range:An unbiased estimator of :*

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15-3: X-bar and R or S Control Charts Control Chart (from ):R Chart:*

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15-3: X-bar and R or S Control Charts 3-sigma control limits for S:An unbiased estimator of :*

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15-3: X-bar and R or S Control Charts S Chart:Control Chart (from ):*

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15-3: X-bar and R or S Control Charts Example 15-1*

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15-3: X-bar and R or S Control Charts Example 15-1Figure 15-8 and R control charts for vane opening. *

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15-3: X-bar and R or S Control Charts Example 15-1Figure 15-9 The S control chart for vane opening. *

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15-3: X-bar and R or S Control Charts Example 15-1Figure 15-10 The X-bar and R control charts for vane opening. *

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15-4: Control Charts for Individual MeasurementsWhat if you could not get a sample size greater than 1 (n =1)? Examples includeAutomated inspection and measurement technology is used, and every unit manufactured is analyzed.The production rate is very slow, and it is inconvenient to allow samples sizes of N > 1 to accumulate before analysisRepeat measurements on the process differ only because of laboratory or analysis error, as in many chemical processes.The individual control charts are useful for samples of sizes n = 1.*

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15-4: Control Charts for Individual MeasurementsThe moving range (MR) is defined as the absolute difference between two successive observations:MRi = |xi - xi-1| which will indicate possible shifts or changes in the process from one observation to the next.*

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15-4: Control Charts for Individual MeasurementsIndividuals Control Chart*

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15-4: Control Charts for Individual MeasurementsInterpretation of the ChartsX Charts can be interpreted similar to X-bar charts. MR charts cannot be interpreted the same as X-bar or R charts.Since the MR chart plots data that are correlated with one another, then looking for patterns on the chart does not make sense. MR chart cannot really supply useful information about process variability.More emphasis should be placed on interpretation of the X chart.*

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15-5: Process CapabilityProcess capability refers to the performance of the process when it is operating in control.Two graphical tools are helpful in assessing process capability:Tolerance chart (or tier chart)Histogram

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15-5: Process CapabilityTolerance ChartFigure 16-12 Tolerance diagram of vane openings. *

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15-5: Process CapabilityHistogramFigure 15-13 Histogram for vane openings. *

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15-5: Process CapabilityProcess Capability RatioPCRk*

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15-5: Process CapabilityFigure 15-14 Process Fallout and the process capability ratio (PCR). *

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15-5: Process CapabilityExample 15-3*

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15-5: Process CapabilityFigure 15-15 Mean of a six-sigma process shifts by 1.5 standard deviations. *

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15-6: Attribute Control Charts 15-6.1 P Chart (Control Chart for Proportions)*

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15-6: Attribute Control Charts Example 15-4*

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15-6: Attribute Control Charts Example 15-4Figure 15-16 P chart for a ceramic substrate. *

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15-6: Attribute Control Charts 15-6.2 U Chart (Control Chart for Defects per Unit)*

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15-6: Attribute Control Charts Example 15-5Figure 15-17 U chart of defects per unit on printed circuit boards. *

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15-7: Control Chart Performance Average Run LengthThe average run length (ARL) is a very important way of determining the appropriate sample size and sampling frequency.Let p = probability that any point exceeds the control limits. Then,*

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15-7: Control Chart Performance *

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15-7: Control Chart Performance Figure 15-18 Process mean shift of 2. *

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15-8: Time-Weighted Charts The cusum chart incorporates all information in the sequence of sample values by plotting the cumulative sums of the deviations of the sample values from a target value.If 0 is the target for the process mean, is the average of the jth sample, then the cumulative sum control chart is formed by plotting the quantity

15-8.1 Cumulative Sum Control Chart*

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15-8: Time-Weighted Charts Figure 15-19 Plot of the cumulative sum for the concentration data, Table 15-7. *

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15-8: Time-Weighted ChartsFigure 15-20 The cumulative sum control chart. (a) The V-mask and scaling. (b) The cumulative sum control chart in operation. *

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15-8: Time-Weighted ChartsCUSUM Control Chart15-8.1 Cumulative Sum Control Chart*

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15-8: Time-Weighted Charts Example 15-6*

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15-8: Time-Weighted Charts Example 15-6Figure 15-21 The CUSUM status chart for Example 15-6. *

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15-8: Time-Weighted Charts *

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15-8: Time-Weighted Charts 15-8.2 Exponential Weighted Moving Average Control Chart*

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15-8: Time-Weighted Charts 15-8.2 Exponential Weighted Moving Average Control Chart*

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15-8: Time-Weighted Charts 15-8.2 Exponential Weighted Moving Average Control ChartFigure 15-22 EWMAs with =0.8 and =0.2 show a compromise between a smooth curve and a response to a shift*

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15-8: Time-Weighted Charts EWMA Control Chart15-8.2 Exponential Weighted Moving Average Control Chart*

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15-8: Time-Weighted Charts 15-8.2 Exponential Weighted Moving Average Control ChartFigure 15-23 EWMA control chart for the Chemical Process Concentration Data from Minitab.*

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15-9: Other SPC Problem-Solving Tools Pareto DiagramFigure 15-24 Pareto diagram for printed circuit board defects. *

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15-9: Other SPC Problem-Solving ToolsCause-and-effect DiagramFigure 15-25 Cause-and-effect diagram for the printed circuit board flow solder process. *

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15-9: Other SPC Problem-Solving ToolsDefect Concentration DiagramFigure 15-26 Defect concentration diagram for a printed circuit board. *

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15-10: Implementing SPC Strategic Management of Quality Demings 14 points*

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Important Terms & Concepts of Chapter 15*

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Dear Instructor: This file is an adaptation of the 4th edition slides for the 5th edition. It will be replaced as slides are developed following the style of the Chapters 1-7 slides.**********************************************************************************

15- statistical quality control

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