Statistical Process Control

Statistical Process Control

• 1.
  © Production &Industrial Engineering Mechanical Engineering Department Statistical Process Control Operations Management by R. Dan Reid & Nada R. Sanders 2nd Edition © Wiley 2005 PowerPoint Presentation by Naveen Banshiwal
• 2.
  Sources of Variationin Production and Service Processes  Common causes of variation  Random causes that we cannot identify  Unavoidable  Cause slight differences in process variables like diameter, weight, service time, temperature, etc.  Assignable causes of variation  Causes can be identified and eliminated  Typical causes are poor employee training, worn tool, machine needing repair, etc.
• 3.
  Measuring Variation: The StandardDeviation Small vs. Large Variation
• 4.
  Process Capability  Ameasure of the ability of a process to meet preset design specifications:  Determines whether the process can do what we are asking it to do  Design specifications (tolerances):  Determined by design engineers to define the acceptable range of individual product characteristics (e.g.: physical dimensions, elapsed time, etc.)  Based upon customer expectations & how the product works (not statistics!)
• 5.
  Relationship between Process Variabilityand Specification Width
• 6.
  Three Sigma Capability Mean output +/- 3 standard deviations falls within the design specification  It means that 0.26% of output falls outside the design specification and is unacceptable.  The result: a 3-sigma capable process produces 2600 defects for every million units produced
• 7.
  Six Sigma Capability Six sigma capability assumes the process is capable of producing output where the mean +/- 6 standard deviations fall within the design specifications  The result: only 3.4 defects for every million produced  Six sigma capability means smaller variation and therefore higher quality
• 8.
  Process Control Charts ControlCharts show sample data plotted on a graph with Center Line (CL), Upper Control Limit (UCL), and Lower Control Limit (LCL).
• 9.
  Setting Control Limits
• 10.
  Types of ControlCharts  Control chart for variables are used to monitor characteristics that can be measured, e.g. length, weight, diameter, time, etc.  Control charts for attributes are used to monitor characteristics that have discrete values and can be counted, e.g. % defective, number of flaws in a shirt, number of broken eggs in a box, etc.
• 11.
  Control Charts forVariables  Mean (x-bar) charts  Tracks the central tendency (the average value observed) over time  Range (R) charts:  Tracks the spread of the distribution over time (estimates the observed variation)
• 12.
  x-bar and Rcharts monitor different parameters!
• 13.
  Constructing a X-barChart: A quality control inspector at the Cocoa Fizz soft drink company has taken three samples with four observations each of the volume of bottles filled. If the standard deviation of the bottling operation is .2 ounces, use the data below to develop control charts with limits of 3 standard deviations for the 16 oz. bottling operation. Time 1 Time 2 Time 3 Observation 1 15.8 16.1 16.0 Observation 2 16.0 16.0 15.9 Observation 3 15.8 15.8 15.9 Observation 4 15.9 15.9 15.8
• 14.
  Step 1: Calculate theMean of Each Sample Time 1 Time 2 Time 3 Observation 1 15.8 16.1 16.0 Observation 2 16.0 16.0 15.9 Observation 3 15.8 15.8 15.9 Observation 4 15.9 15.9 15.8 Sample means (X-bar) 15.875 15.975 15.9
• 15.
  Step 2: Calculatethe Standard Deviation of the Sample Mean x σ .2 σ .1 n 4        
• 16.
  Step 3: CalculateCL, UCL, LCL  Center line (x-double bar):  Control limits for ±3σ limits (z = 3): 15.875 15.975 15.9 x 15.92 3         x x x x UCL x zσ 15.92 3 .1 16.22 LCL x zσ 15.92 3 .1 15.62          
• 17.
  Step 4: Drawthe Chart
• 18.
  An Alternative Methodfor the X-bar Chart Using R-bar and the A2 Factor Use this method when sigma for the process distribution is not known. Use factor A2 from Table 6.1 Factor for x-Chart A2 D3 D4 2 1.88 0.00 3.27 3 1.02 0.00 2.57 4 0.73 0.00 2.28 5 0.58 0.00 2.11 6 0.48 0.00 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.72 13 0.25 0.31 1.69 14 0.24 0.33 1.67 15 0.22 0.35 1.65 Factors for R-Chart Sample Size (n)
• 19.
  Step 1: Calculatethe Range of Each Sample and Average Range Time 1 Time 2 Time 3 Observation 1 15.8 16.1 16.0 Observation 2 16.0 16.0 15.9 Observation 3 15.8 15.8 15.9 Observation 4 15.9 15.9 15.8 Sample ranges (R) 0.2 0.3 0.2 0.2 0.3 0.2 R .233 3    
• 20.
  Step 2: CalculateCL, UCL, LCL  Center line:  Control limits for ±3σ limits:     2x 2x 15.875 15.975 15.9 CL x 15.92 3 UCL x A R 15.92 0.73 .233 16.09 LCL x A R 15.92 0.73 .233 15.75               
• 21.
  Control Chart forRange (R-Chart) Center Line and Control Limit calculations: 4 3 0.2 0.3 0.2 CL R .233 3 UCL D R 2.28(.233) .53 LCL D R 0.0(.233) 0.0            Factor for x-Chart A2 D3 D4 2 1.88 0.00 3.27 3 1.02 0.00 2.57 4 0.73 0.00 2.28 5 0.58 0.00 2.11 6 0.48 0.00 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.72 13 0.25 0.31 1.69 14 0.24 0.33 1.67 15 0.22 0.35 1.65 Factors for R-Chart Sample Size (n)
• 22.
  R-Bar Control Chart
• 23.
  Control Charts forAttributes – P-Charts & C-Charts  Use P-Charts for quality characteristics that are discrete and involve yes/no or good/bad decisions  Percent of leaking caulking tubes in a box of 48  Percent of broken eggs in a carton  Use C-Charts for discrete defects when there can be more than one defect per unit  Number of flaws or stains in a carpet sample cut from a production run  Number of complaints per customer at a hotel
• 24.
  Constructing a P-Chart: AProduction manager for a tire company has inspected the number of defective tires in five random samples with 20 tires in each sample. The table below shows the number of defective tires in each sample of 20 tires. Sample Sample Size (n) Number Defective 1 20 3 2 20 2 3 20 1 4 20 2 5 20 1
• 25.
  Step 1: Calculate thePercent defective of Each Sample and the Overall Percent Defective (P-Bar) Sample Number Defective Sample Size Percent Defective 1 3 20 .15 2 2 20 .10 3 1 20 .05 4 2 20 .10 5 1 20 .05 Total 9 100 .09
• 26.
  Step 2: Calculatethe Standard Deviation of P. p p(1-p) (.09)(.91) σ = = =0.064 n 20
• 27.
  Step 3: CalculateCL, UCL, LCL CL p .09   Center line (p bar):  Control limits for ±3σ limits:     p p UCL p z σ .09 3(.064) .282 LCL p z σ .09 3(.064) .102 0            
• 28.
  Step 4: Drawthe Chart
• 29.
  Constructing a C-Chart: Thenumber of weekly customer complaints are monitored in a large hotel. Develop a three sigma control limits For a C-Chart using the data table On the right. Week Number of Complaints 1 3 2 2 3 3 4 1 5 3 6 3 7 2 8 1 9 3 10 1 Total 22
• 30.
  Calculate CL, UCL,LCL  Center line (c bar):  Control limits for ±3σ limits: UCL c c 2.2 3 2.2 6.65 LCL c c 2.2 3 2.2 2.25 0 z z             #complaints 22 CL 2.2 # of samples 10   
• 31.
  SQC in Services Service Organizations have lagged behind manufacturers in the use of statistical quality control  Statistical measurements are required and it is more difficult to measure the quality of a service  Services produce more intangible products  Perceptions of quality are highly subjective  A way to deal with service quality is to devise quantifiable measurements of the service element  Check-in time at a hotel  Number of complaints received per month at a restaurant  Number of telephone rings before a call is answered  Acceptable control limits can be developed and charted
• 32.
  Conclusion  In thisslide we discuss about variable type control charts.  We study control chart and understood application in the industry and various department.
• 33.
  Thank You