Process Capability Process Capability Overview A process capability
Process Capability
Process Capability Overview § A process capability study assesses the stability and capability of process outputs § A separate capability study must be carried out for each process output § Control charts are used to assess the process stability § Histograms are drawn to depict the data and to determine if the data is normally distributed § Process capability indices are then calculated to determine the “capability” of the process
Process Capability Studies § Capability studies measure progress during process improvement activities § Steps for conducting studies include: • • • Collect Data Calculate Required Statistics Generate Control Charts Interpret Charts & Draw Conclusions Draw Histogram and Check for Normality Calculate Cp and Cpk and Draw Conclusions
Process Capability and Potential § Cp and Cpk are numerical indicators of a process performance based on its capability when compared to specifications § Cp = simple process capability (potential indication of process capability; does not evaluate how close the average is to the target) § Cpk = process capability index (assess actual process performance) Inadequate Process Capability Unstable Parts & Materials LSL Defects Inadequate Design Margin USL Acceptable Process Capability Defects
Definition of Cp Cp = USL – LSL 6 s § Think of Cp as the number of times the distribution can fit within the specification limits USL Cp = 0. 5 Cp = 1 Cp = 2 LSL
Definition of Cpk Cpl = X – LSL Cpu = USL – X Cpk = min Cpl or Cpu 3 s 3 s § Cpk is the Process Capability Index and contains an adjustment of Cp for the effect of a non-centered distribution with respect to the specification limits § Cpk is the smaller of Cpl (lower spec) or Cpu (upper spec) for two-sided specifications § Cpk will decrease to below 1 when a distribution is not centered in the specification and parts of the distribution fall outside the specification limits
Control Charts • A modified Run Chart where process measurements are plotted in chronological order. • Has an average line and upper and lower control limits. • Control Charts, Run Charts, and Histograms are related to each other.
Control Charts • Calculated from the data collected. This is in contrast to Specification Limits – which are imposed on the data. • Control limits are determined by first calculating the value of one unit of process variation – this is a Standard Deviation. • Each control limit can then be determined by either adding (UCL) or subtracting (LCL) three of these units from the average.
Example Car Mileage (MPG) Histogram Run Chart Control Chart Note: An accompanying “moving range” chart is not shown.
Uses of Control Charts • • • Provides on-going monitoring and tracking of key process variables. Requires at least 15 data points on it for valid interpretation. It is recommended to have more than 20 points. Can be used in the active monitoring and feedback loop to control a process in a preventative mode. Can be used to assess the stability of a process prior to conducting a process capability study (the likelihood of a process producing good products or levels of service). Indicates fundamental process changes of any kind by identifying special signals in the data. Distinguishes between Common and Special causes of variation…
Common Causes of Variation are: § Unassignable, unidentifiable, and characteristic of the process. Common Causes of Variation result in: • Random behavior of the data / process. • A process that is “in statistical control”, stable, and predictable. All processes have Common Cause Variation
Special Causes of Variation are: § Assignable, identifiable, uncharacteristic of the process. Special Causes of Variation result in: • Non-random behavior of the data / process. • A process that is “out of statistical control”, unstable, and unpredictable.
Problem Solving Pathways When your Out-of-Control In-Control process is. . . You have. . . Special causes of variation Common causes of variation In order to continuously improve you must. . . Address specific Change the process identifiable causes or system of variation
Rules for Determining if a Process is Out of Statistical Control I. Shifts – Consecutive points above or below the average - 7 minimum UCL Average LCL II. Trends – Runs up or down - 6 minimum UCL Average LCL III. Outliers – Any point above or below the control limits UCL Average LCL
Rules for Determining if a Process is Out of Statistical Control (continued) IV. Patterns – Less than 2/3 points in the middle 1/3 UCL Less than 2/3 points in the middle 1/3 Average LCL 0. 135% 2. 135% -3 ± 1 s = 68. 26% of data ± 2 s = 95. 46% of data ± 3 s = 99. 73% of data ± 3 s UCL and LCL = 13. 60% -2 34. 13% -1 Avg. 34. 13% - +1 13. 60% +2 2. 135% 0. 135% +3
Summary Control Charts • A powerful statistical tool. • Build upon the concepts learned with Histograms and Run Charts. • Distinguish Special Causes of Variation from Common Causes of Variation. • Basic interpretation rules determine if a process is in a state of statistical control • Are used during process capability studies to assess the stability of the process.
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