List of Figures

Introduction

Figure I.1: A typical chart used in SPC.

Figure I.2: Process control.

Figure I.3: Product control. Filtered outputs; process control in a feed-forward loop.

Chapter 1: The Need for Improvement

Figure 1.1: A typical SPC model.

Figure 1.2: The goalpost mentality .

Figure 1.3: The loss function.

Chapter 2: Problem Solving

Figure 2.1: Fishbone diagramBlaine surface area of good clinker.

Figure 2.2: Cause and effect diagramseal failure example.

Figure 2.3: Affinity diagram and Pareto chart.

Figure 2.4: Pareto chart for delays.

Figure 2.5: Work flow analysis overview.

Figure 2.6: Process flow diagram for a quality improvement project (with specific tools associated with specific tasks ).

Figure 2.7: Input-output analysis overview.

Figure 2.8: Flowchart of five-why sequence.

Figure 2.9: A strategy for operational excellence and financial performance.

Chapter 3: Summarizing Data

Figure 3.1: A typical histogram.

Figure 3.2: A histogram representing a machine that is worn out.

Figure 3.3: An example of a histogram showing the data of the starter motor.

Figure 3.4: A frequency polygon.

Figure 3.5: The Ogive curve.

Figure 3.6: A typical dot plot.

Figure 3.7: A typical stem and leaf display.

Figure 3.8: Typical box plots.

Figure 3.9: Scatter diagrams.

Chapter 4: Descriptive Statistics

Figure 4.1: Distribution of the five samples.

Figure 4.2: The median of odd numbers .

Figure 4.3: The median of even numbers.

Figure 4.4: The mode of the shaft length.

Figure 4.5: A comparison of the average and the range.

Figure 4.6: A comparison of population and sample.

Figure 4.7: The relationship of the inflection point and the standard deviation.

Figure 4.8: Steps in calculating the standard deviation using a handheld calculator.

Figure 4.9: Calculating standard deviation using a statistical calculator (Sharp series).

Chapter 5: Normal Distribution

Figure 5.1: A typical output of a normal distribution pattern.

Figure 5.2: Characteristics of the normal curve.

Figure 5.3: Normal distribution divided into zones of percentage.

Figure 5.4: A histogram of 184 items.

Figure 5.5: Distribution of the height items.

Figure 5.6: The relationship of the z value to the distribution.

Figure 5.7: Negative exponential distribution.

Figure 5.8: Histogram of deviations.

Figure 5.9: The range and the histogram data from the lead placement analysis for attachment to soldering pads on a ceramic substrate.

Chapter 6: Process Variation and Control Charts

Figure 6.1: A typical natural variation of a process.

Figure 6.2: A system with common variation over time.

Figure 6.3: A process that is in control but not capable.

Figure 6.4: A typical out-of-control system.

Figure 6.5: A typical process in control.

Figure 6.6: A typical in-control and capable process.

Figure 6.7: A typical improvement to the process.

Figure 6.8: Histogram of distances for Rule 1.

Figure 6.9: Histogram of distances for Rule 2.

Figure 6.10: Histogram of distances for Rule 3.

Figure 6.11: Histogram of distances for Rule 4.

Figure 6.12: A p chart for the red bead experiment.

Figure 6.13: The relationship of the normal curve and the control chart.

Figure 6.14: A control chart with Type I (a) and Type II (b) error.

Chapter 7: Preparing for Control Charts

Figure 7.1: A stable and in-control process.

Figure 7.2: A pictorial view of a distribution with specifications and the z-values.

Figure 7.3: A typical Xbar and R chart form. Note that the form is coded with numbers 1 through 28. Each number is explained in the key.

Chapter 8: Variable Charts

Figure 8.1: A stable and predictable process.

Figure 8.2: A process with a point out of UCL on the range chart.

Figure 8.3: A process with a point out of LCL on the range chart.

Figure 8.4: A process with a run above the Rbar.

Figure 8.5: A process with a run below the Rbar.

Figure 8.6: A process with a degrading trend.

Figure 8.7: A process with an improvement in variation.

Figure 8.8: A process with cycles.

Figure 8.9: A process with unusual variation.

Figure 8.10: A stable and predictable process.

Figure 8.11: A process with points outside the UCL and LCL on the Xbar chart.

Figure 8.12: A process with a run below the Xdouble bar.

Figure 8.13: A process with a downward trend.

Figure 8.14: A process with cycles.

Figure 8.15: A process with unusual variation.

Figure 8.16: A sample X and moving R control chart.

Figure 8.17: A sample Xbar and s chart.

Figure 8.18: A process with sudden and persistent change.

Figure 8.19: The cumulative sum of the difference, shown chronologically.

Figure 8.20: V Masks for cusum control charts.

Chapter 9: Control Charts for Attributes

Figure 9.1: The steps for calculating the standard deviation for proportions .

Figure 9.2: A stable and predictable process.

Figure 9.3: A process with out-of-control points.

Figure 9.4: A process with a run below the average.

Figure 9.5: A process with a downward trend.

Figure 9.6: A process with cycles.

Figure 9.7: A process with unusual variation.

Figure 9.8: The sequence of operations needed to calculate the standard deviation for proportions.

Figure 9.9: The sequence of operations needed to calculate the standard deviation for defects.

Figure 9.10: A typical stable and predictable process.

Figure 9.11: A process with points out of control limits.

Figure 9.12: A process with a run below the cbar.

Figure 9.13: A process with a downward trend and a run below the cbar.

Figure 9.14: A process with cycles.

Figure 9.15: A process with unusual variation.

Figure 9.16: The sequence of operations needed to calculate the standard deviation for proportions.

Figure 9.17: A typical D chart.

Chapter 10: Other Charts

Figure 10.1: A stable and predictable process.

Figure 10.2: A process with a point outside of UCL.

Figure 10.3: A process with a point out of LCL.

Figure 10.4: A process with a run above Rbar.

Figure 10.5: A process with a run below the Rbar.

Figure 10.6: A process with degrading variation.

Figure 10.7: A process with an improvement in variation.

Figure 10.8: A process with cycles.

Figure 10.9: A process with unusual variation.

Figure 10.10: A stable and predictable process.

Figure 10.11: A process with points outside of the control limits.

Figure 10.12: A process with a run below the median.

Figure 10.13: A process with a downward trend.

Figure 10.14: A process with cycles.

Figure 10.15: A process with unusual variation.

Figure 10.16: A tool wear control chart.

Figure 10.17: A tool wear process control chart.

Figure 10.18: Exponentially weighted moving average chartworking time.

Figure 10.19: Location of PRE-control limit.

Chapter 11: Control Chart Signals

Figure 11.1: A process in control.

Figure 11.2: An undesirable situation with defectives.

Figure 11.3: Points beyond control limits.

Figure 11.4: A "run" in a process.

Figure 11.5: A trend in a process.

Figure 11.6: Process with "cycles."

Figure 11.7: A process with a "hugging" situation.

Figure 11.8: A process with extreme variation close to the control limits.

Figure 11.9: A typical control chart divided into zones.

Figure 11.10: A p chart in an aircraft factory.

Chapter 12: Process Control and Capability

Figure 12.1: The four possible combinations of "control" and "capability."

Figure 12.2: A process that is in control and capable.

Figure 12.3: A process in control and not capable.

Figure 12.4: A process out of control and not capable.

Figure 12.5: A process out of control and unknown capability.

Figure 12.6: An Xbar and R chart with some hypothetical data.

Figure 12.7: Frequency distribution based on the hypothetical data.

Figure 12.8: A graphical representation of capability analysis.

Figure 12.9: Specifications to the population curve.

Figure 12.10: Collection of data for a machine capability study.

Figure 12.11: The tallied frequency distribution of the shaft example.

Figure 12.12: Data transferred onto the capability analysis sheet.

Figure 12.13: The generation of the EAF.

Figure 12.14: Plotting the points on the graph paper.

Figure 12.15: A machine capable within a 4 sigma.

Figure 12.16: A machine that is not capable.

Figure 12.17: Process capability and specifications.

Figure 12.18: Histogram and probability combination form.

Figure 12.19: Nonnormal data plotted on normal probability paper.

Figure 12.20: Nonnormal data plotted on log log graph.

Figure 12.21: C _pk example.

Figure 12.22: C _p and C _pk comparison example.

Figure 12.23: Information for drawing the distribution shape from capability indices and specifications.

Figure 12.24: A process with a 1.5-sigma shift to the right.

Figure 12.25: A process with potential capability of 12 sigma equaling the tolerance.

Chapter 13: Short-Run SPC

Figure 13.1: Data collection sheet for short-run control charting.

Figure 13.2: A typical control chart with coded values.

Figure 13.3: A short-run c chart (trend).

Figure 13.4: A short-run c chart (run).

Figure 13.5: A short-run R chart.

Figure 13.6: Short-run Xbar.

Figure 13.7: Short-run attribute chart.

Figure 13.8: Recalculating control limits.

Figure 13.9: Recalculating target values.

Chapter 14: Distribution Shape and Stability

Figure 14.1: Data from a process that is not stable.

Figure 14.2: The three major types of distributions.

Figure 14.3: A skewed distribution showing the difference in spread.

Figure 14.4: The lack of fit between the skewed distribution and the normal curve.

Figure 14.5: Histogram and a skew curve superimposed.

Figure 14.6: Build of the symmetrical distribution (left side).

Figure 14.7: Build of the symmetrical distribution (right side).

Figure 14.8: Skewed distribution showing the s of both sides.

Figure 14.9: Exponential distribution with the associated data.

Figure 14.10: Original measurement scale and transformed scale.

Figure 14.11: The area under the exponential distribution and above a standardized ratio.

Figure 14.12: Procedure to calculate the natural antilogarithm with the use of the Sharp Series scientific calculators .

Figure 14.13: A process with modified control limits and in control.

Figure 14.14: Curves illustrating the derivation of safety limits.

Figure 14.15: A trending process with MinSPA and MaxSPA.

Chapter 15: The Measurement Process

Figure 15.1: Process capability, the result of larger processes.

Figure 15.2: The measurement process.

Figure 15.3: Repeatability.

Figure 15.4: Reproducibility.

Figure 15.5: Stability.

Figure 15.6: The distinction between precision and accuracy.

Figure 15.7: Bias.

Figure 15.8: Linearity.

Figure 15.9: The relationship of error and acceptance.

Figure 15.10: R&R data collection sheet.

Figure 15.11: A complete R&R data sheet.

Figure 15.12: R&R report.

Figure 15.13: R&R calculation sheet.

Figure 15.14: Form used for short R&R.

Figure 15.15: Attribute gauge study.

Figure 15.16: Control chart measuring stability.

Figure 15.17: Sample coded data recorded on a control chart.

Figure 15.18: Scatter diagram for S _RPT and part average Xbar _PART .

Chapter 16: Machine Acceptance Overview

Figure 16.1: Machine acceptance overview.

Figure 16.2: The relationship of frequency polygons, standardized values, and normal probability paper on a 3 ƒ arrangement.

Figure 16.3: The relationship of frequency polygons, standardized values, and normal probability paper on a 4 ƒ arrangement.

Figure 16.4: The relationship of frequency polygons, standardized values, and normal probability paper showing rejects on the high side of specification.

Figure 16.5: The relationship of frequency polygons, standardized values, and normal probability paper showing rejects on both sides of the specifications.

Figure 16.6: The relationship of frequency polygons, standardized values, and normal probability paper of a skew distribution.

Figure 16.7: A bimodal curve presented in a polygon form and on probability graphical representation.

Figure 16.8: Phase I flow chart.

Figure 16.9: Phase II flow chart.

Figure 16.10: Phase III flow chart.

Chapter 17: SPC in Nonmanufacturing

Figure 17.1: Inventory variation, constant demand.

Appendix D: Common SPC Forms

Figure I: Flow process chart.

Figure II: Variable control chart form.

Figure III: Attribute control chart form.

Figure IV: Control chart process log sheet.

Figure V: Data collection sheet for capability analysis.

Figure VI: Capability analysis sheet.

Figure VII: Capability sheet for normal distribution.

Figure VIII: Capability sheet for skew distribution.