Chapter 10: Statistical Quality Control

Chapter 10: Statistical Quality Control

1. Introduction

   • Statistical Quality Control
     • use stat tech & sampling to monitor & test Q of goods & services
       • Acceptance Sampling: accept or reject a product
       • Stat process control: if process is operating within acceptable limits
     • Best company: design Q into process, reduce need for inspections
   • Inspection
     • appraisal of goods/services against standards
   • Phases of Q Control
     • least progressive: Acceptance sampling (inspection before & after production)
     • medium progressive: Statistical process control (corrective action during production)
     • most progressive: Continuous improvement & Six Sigma (Q built into process)
   • Stat Process Control Planning process
     • 1. DEFINE important Q characteristics & how to measure
     • 2. For each charact
       • a. determine Q control point
       • b. PLAN
         • i. HOW to inspect
         • ii. HOW MUCH to inspect
         • iii. WHERE centralized or on-site
       • c. plan the corrective action process
   • Inspection
     • How much/How often; Where/When; Centralized vs. On-site
     • Inputs (acceptance sampling) ==> Transformation (stat process control) ==> Outputs (acceptance sampling)
     • WHERE to inspect
       • raw materials & purchased parts
       • before costly operation; before irreversible process; before covering process
       • finished products
     • Inspection costs
       • GRAPH
     • Centralized vs. On-site
       • On-Site
         • immovable product; simple/handled measuring equip; automated inspection
       • In-Lab
         • specialized equip, skilled Q control inspectors; more favourable test env

2. Statistical Process Control

   • def: stat evaluation of output of a process during production
     • 1. QC steps
     • 2. type of Variations
     • 3. control charts
     • 4. design control charts
     • 5. individual unit & moving range charts
     • 6. control charts for attributes
     • 7. using control charts
   • SPC steps
     • compare to predetermined limits
       • if OUTSIDE limits, stop process & take corrective action
       • if INSIDE limits, continue process
   • Control Chart
     • purpose: monitor process output to distinguish between random & assignable variation
     • def: time ordered plot of stat obtained from ongoing process
       • UCL & LCL define range of acceptable variation
     • Normal Distribution
       • Standard deviation
     • Control limits: dividing lines between random & nonrandom deviations from the process mean (+/- 2SD, 3SD)
       • out of control
       • abnormal V most likely due to assignable causes
       • normal V due to chance
       • Errors
         • 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
         • 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
         • CHART
   • types of variations
     • random V
       • natural V in output, created by countless minor factors
     • assignable V
       • V whose source can be identified
   • Design control chart
     • 1. determine a sample size
     • 2. obtain 20 to 25 samples
     • 3. establish & graph preliminary control limits
     • 4. plot sample stat values on control chart
     • 5. any points outside CL?
       • NO: assume no assignable cause
       • YES: investigate & correct
   • Control charts for attributes
     • variables: measured
       • sample mean
         • monitor mean of process & x-bar charts
       • sample range
         • monitor process dispersion & R charts
     • sample mean chart
       • FORMULAS & EXAMPLES
       • Alternative method
         • FORMULAS & EXAMPLES
     • sample range control chart
       • FORMULAS & EXAMPLES
     • variables: counted
       • p-chart: monitor proportion of defectives in process:
         • use: observations into 2 categories (e.g. good or bad); multiple samples of several observations each
           • FORMULAS
       • c-chart: monitor # of defects/unit
         • use: # of occurrences per unit of measure can be counted; non-occurrences can't be counted (e.g. breaks per unit of area)
           • FORMULAS
   • Choose right control chart
     • continuous measurement
       • n=1
         • individual unit & moving range charts
       • n>or=2
         • sample mean & range charts
     • discrete measurement
       • 2 types of results can be counted
         • p-chart
       • only occurrences can be counted
         • c-chart
     • QUESTIONS

3. Process Capability

   • PC indices
     • process is centered ==> Cp
       • FORMULA
     • process is NOT centered ==> Cpk
       • FORMULA
   • EXAMPLES
   • PC analysis
     • < 1 = not capable
       • 1. redesign process; 2. use alternate; 3. more inspection; 4. relax specfication
     • > 1 = better than needed
       • charge more for better quality?
       • Cpk = 0.4253: produce a relatively high # of defects
       • many companies look for > 1.3; six-sigma looks for 2
   • terminology
     • design specifications / aka tolerances: range of acceptable values established by engineering design or customer requirements
     • process variability: natural variability in a process
     • process capability: process variability relative to specification

4. Six Sigma Quality