Chapter 10: Statistical Quality Control

Introduction
1. Statistical Quality Control
  1. use stat tech & sampling to monitor & test Q of goods & services
    1. Acceptance Sampling: accept or reject a product
    2. Stat process control: if process is operating within acceptable limits
  2. Best company: design Q into process, reduce need for inspections
2. Inspection
  1. appraisal of goods/services against standards
3. Phases of Q Control
  1. least progressive: Acceptance sampling (inspection before & after production)
  2. medium progressive: Statistical process control (corrective action during production)
  3. most progressive: Continuous improvement & Six Sigma (Q built into process)
4. Stat Process Control Planning process
  1. 1. DEFINE important Q characteristics & how to measure
  2. 2. For each charact
    1. a. determine Q control point
    2. b. PLAN
      1. i. HOW to inspect
      2. ii. HOW MUCH to inspect
      3. iii. WHERE centralized or on-site
    3. c. plan the corrective action process
5. Inspection
  1. How much/How often; Where/When; Centralized vs. On-site
  2. Inputs (acceptance sampling) ==> Transformation (stat process control) ==> Outputs (acceptance sampling)
  3. WHERE to inspect
    1. raw materials & purchased parts
    2. before costly operation; before irreversible process; before covering process
    3. finished products
  4. Inspection costs
    1. GRAPH
  5. Centralized vs. On-site
    1. On-Site
      1. immovable product; simple/handled measuring equip; automated inspection
    2. In-Lab
      1. specialized equip, skilled Q control inspectors; more favourable test env
Statistical Process Control
1. def: stat evaluation of output of a process during production
  1. 1. QC steps
  2. 2. type of Variations
  3. 3. control charts
  4. 4. design control charts
  5. 5. individual unit & moving range charts
  6. 6. control charts for attributes
  7. 7. using control charts
2. SPC steps
  1. compare to predetermined limits
    1. if OUTSIDE limits, stop process & take corrective action
    2. if INSIDE limits, continue process
3. Control Chart
  1. purpose: monitor process output to distinguish between random & assignable variation
  2. def: time ordered plot of stat obtained from ongoing process
    1. UCL & LCL define range of acceptable variation
  3. Normal Distribution
    1. Standard deviation
  4. Control limits: dividing lines between random & nonrandom deviations from the process mean (+/- 2SD, 3SD)
    1. out of control
    2. abnormal V most likely due to assignable causes
    3. normal V due to chance
    4. Errors
      1. Type I error: process has changed when it has not
        e.g. assignable V is present when only random V is present ==> LOWER than LCL, producers risk
      2. Type II error: process has not changed when it has
        e.g. only random V is present when assignable V is present ==> HIGHER than UCL, consumers risk
      3. CHART
4. types of variations
  1. random V
    1. natural V in output, created by countless minor factors
  2. assignable V
    1. V whose source can be identified
5. Design control chart
  1. 1. determine a sample size
  2. 2. obtain 20 to 25 samples
  3. 3. establish & graph preliminary control limits
  4. 4. plot sample stat values on control chart
  5. 5. any points outside CL?
    1. NO: assume no assignable cause
    2. YES: investigate & correct
6. Control charts for attributes
  1. variables: measured
    1. sample mean
      1. monitor mean of process & x-bar charts
    2. sample range
      1. monitor process dispersion & R charts
  2. sample mean chart
    1. FORMULAS & EXAMPLES
    2. Alternative method
      1. FORMULAS & EXAMPLES
  3. sample range control chart
    1. FORMULAS & EXAMPLES
  4. variables: counted
    1. p-chart: monitor proportion of defectives in process:
      1. use: observations into 2 categories (e.g. good or bad); multiple samples of several observations each
        FORMULAS
    2. c-chart: monitor # of defects/unit
      1. use: # of occurrences per unit of measure can be counted; non-occurrences can't be counted (e.g. breaks per unit of area)
        FORMULAS
7. Choose right control chart
  1. continuous measurement
    1. n=1
      1. individual unit & moving range charts
    2. n>or=2
      1. sample mean & range charts
  2. discrete measurement
    1. 2 types of results can be counted
      1. p-chart
    2. only occurrences can be counted
      1. c-chart
  3. QUESTIONS
Process Capability
1. PC indices
  1. process is centered ==> Cp
    1. FORMULA
  2. process is NOT centered ==> Cpk
    1. FORMULA
2. EXAMPLES
3. PC analysis
  1. < 1 = not capable
    1. 1. redesign process; 2. use alternate; 3. more inspection; 4. relax specfication
  2. > 1 = better than needed
    1. charge more for better quality?
    2. Cpk = 0.4253: produce a relatively high # of defects
    3. many companies look for > 1.3; six-sigma looks for 2
4. terminology
  1. design specifications / aka tolerances: range of acceptable values established by engineering design or customer requirements
  2. process variability: natural variability in a process
  3. process capability: process variability relative to specification
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Chapter 10: Statistical Quality Control

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