QUALITY CONTROL CHAPTER 8

8.10. Tools of Statistical Quality Control Quality: meeting design specifications 8 tools to understand process & improve quality Flow chart Cause-and-effect diagram Data collection form (check sheet) Pareto analysis Histogram Scatter plots Designed experimentation Control charts

8.10.1. Flowchart Picture of activities (steps) of a process Shows sequence & relationships among steps Avoid: Dead ends, Endless loops Symbols: Start/end Operation Decision Flow (sequence)

Flow chart example

8.10.2. Cause-and-Effect Diagram Also called: Fishbone diagram, Ishikawa diagram Organizes quality problems into logical categories Problems statement in box to the right (fish head) Major bones brainstormed by a team Standard major bones: Men Machines Methods Materials Measurement Environment

Cause-and Effect diagram example

8.10.3. Data Collection forms Used to collect, organize, and analyze new data Specify which data to collect, and units of measurement Decide when, where, how, in what order data is collected 2 types: Traditional Check sheet

8.10.4. Pareto Analysis Pareto = prioritization or classification Order data by type, category, or other classification Help to focus attention on important things 80/20 Rule: 80% of quality problems are caused by 20% of the factors ABC analysis: Class A: most important Class B: fairly important Class C: less important

Pareto chart example

8.10.5. Histograms Useful for seeing shape, centering, and spread of data Usually used for determining probability distribution of data Horizontal axis: broken into 5-20 equal-width cells (usually 10) Vertical axis: frequency of % of occurrence Number of data points should be  30, usually  100

Histogram example

8.10.6. Scatter Plots x-y plot: shows relationship between 2 variables (x, y) One variable increases as the other increases: positive correlation One variable decreases as the other increases: negative correlation No relationship: zero correlation

Scatter Plot example

8.10.7. Designed Experiments One of the most important & needed scientific areas in industry today Determines which factor (of many) has max effect on quality 1FAT (1 Factor At a Time): varies one factor only. Inefficient, misleading Common designs in industry: Factorial design fractional factorial design Taguchi design central composite design, …

8.11. Background on Control Charts Useful for studying process variation, developed by Shewhart Stable process: consistent variation, in-control process, common-cause process Unstable process: inconsistent variation, out-of-control process, common –cause plus special-cause process Common (natural, random) causes: inherent in the process, present all the time, affect everyone & all outputs Special (assignable) causes: not inherent in the process, not present all the time, arise due to specific (exceptional) reasons

8.11. Background on Control Charts Main types of control charts Control charts for variables: apply on numbers, measurements charts: used together to analyze centering & spread of data Control charts for attributes: apply on categories, characteristics (Ex: conforming, not conforming) P chart: measures fraction of non-conforming items C chart: measures number of non-conforming items

8.11. Background on Control Charts Three control lines Central Line (CL): center (mean ) of data Lower Control Limit (LCL): CL - 3 Upper Control Limit (UCL): CL + 3 For normal distribution, the control-limit range [ - 3,  + 3] contains 99.7% of the data (almost all “usual” data) Therefore, any observation outside the control limits indicates something “unusual” (out of control).

8.12. Control Charts for Variables , charts Take m samples (sub-groups), each of size n m = 20 – 30 n = 4 – 5 Assumption: Variation within each single sub-group = common cause Variation between different sub-groups = special cause For each sub-group i, calculate

8.12. Control Charts for Variables: charts Calculations for the R chart (done first) D3, D4 , A2 are given in Tables for each value of n Calculations for the chart (done only if R chart is in control)

8.12. Example for Charts Given the following measurements Sample 1.02 1.04 1.00 2 0.99 0.98 3 0.97 1.01 4 1.06 0.96 5

8.12. Example for Charts m = 5, n = 4 Sample Measurements R 1 1.02 1.04 1.00 0.04 2 0.99 0.98 1.0075 0.06 3 0.97 1.01 0.9925 4 1.06 0.96 1.005 0.10 5 Ave 1.006

8.12. Example for charts R-chart limits -chart limits

8.12. Example for charts R-chart

8.12. Example for charts -chart

8.13. Sensitivity Checks for Control Charts The process is judged out of control if one of the following is observed: At least 1 point outside the control limits (LCL-UCL) At least 7 consecutive points all above or all below the center line (CL) At least 2 consecutive points very close to the center line At least 5 consecutive points continuously increasing or continuously decreasing

8.13. Sensitivity Checks for Control Charts When the process is found out of control: the system is inspected, the special cause(s) are identified and removed, out of control points are removed, control limits are re-calculated.

End of Chapter 8 Questions?