. Process Control Outline. Optimization. Statistical Process Control 3. In-Process Control What is quality? Variation: Common and Special Causes Pieces vary from each other: But they form a pattern that, if stable, is called a distribution: 3 Common and Special Causes (cont d) Distributions can differ in Common and Special Causes (cont d) If only common causes of variation are present, the output of a process forms a distribution that is stable over time and is predictable: Location Spread Shape Prediction or any combination of these
i 7 Common and Special Causes (cont d) If special causes of variation are present, the process output is not stable over time and is not predictable: Prediction Diameter of part.9.9.9.9.9.9. Variation: Run Chart Specified diameter =.9 +/-.. 3 Process change. - Spr ng Process Control Statistical Process Control In Control ( Special causes elimi nated). Detect disturbances (special causes) Out of Control ( Special causes present). Take corrective actions 9 Central Limit Theorem Shewhart Control Chart A large number of independent events have a continuous probability density function that is normal in shape. Averaging more samples increases the precision of the estimate of the average. Average (of samples ) Di ameter....99.99 Lower control limit 3 7 9
i Sampling and Histogram Creation Sampling and Histogram Creation (cont d) Wheel of Fortune: Equal probability of outcome -, P=. 9 Taking random samples, the resulting histogram would look like this 3 7 9 Outcome Frequency Wheel of Fortune: Equal probability of outcome -, P=. 9 Take random samples, calculate their average, and repeat times, the resulting histogram would resemble Frequency 3 3 3 7 9 Outcome 3 3 7 Taking random samples, the resulting histogram would look like this Frequency 7 Take random samples, calculate their average, and repeat times, the resulting histogram would approach the continuous distribution shown 3 7 9 3 7 9 Outcome. - Spr ng 3 Uniform Distributions Normal Distribution Probability distr i but ion.. Underlying Distribution Probab ili ty d i stribut i on Distribution resulting from averaging of random values.. Underlying distribution average of random values.....3....7..9....3....7..9. average of 3 random values average of random values average of 3 random values average of random values...3....7..9....3....7..9....3....7..9....3....7..9. Precision Shewhart Control Chart Not accurate Not precise Precise Upper Control Limit (UCL), Lower Control Limit (LCL) Accurate Subgroup size ( < n < ) 7 3
i 9 Shewhart Control Chart (cont d) Shewhart Control Chart (cont d). Control chart based on samples. Control chart based on average of samples, note the step change that occurs at run Average (of samples ) Di ameter...99 Lower control limit Average (of samples ) Di ameter...99 Lower control limit Step disturbance Step disturbance.99 3 7 9.99 3 7 9. - Spr ng Control Charts Setting the Limits Process average Lower control limit 3 7 9. Collection: Gather data and plot on chart.. Control: Calculate control limits from process data, using simple formulae. Identify special causes of variation; take local actions to correct. 3. Capability: Quantify common cause variation; take action on the system. Idea: Points outside the limits will signal that something is wrongan assignable cause. We want limits set so that assignable causes are highlighted, but few random causes are highlighted accidentally. Convention for Control Charts: (UCL) = x + 3σ sg Lower control limit (LCL) = x- 3σ sg (Where σ sg represents the standard deviation of a subgroup of samples) These three phases are repeated for continuing process improvement. Setting the Limits (cont d) Benefits of Control Charts Convention for Control Charts (cont d): σ sub group = σ sg σ process σsubgroup = σ process / n UCL = x + 3σ process/ n LCL = x - 3σ process / n As n increases, the UCL and LCL move closer to the center line, making the control chart more sensitive to shifts in the mean. Properly used, control charts can: Be used by operators for ongoing control of a process Help the process perform consistently, predictably, for quality and cost Allow the process to achieve: Higher quality Lower unit cost Higher effective capacity Provide a common language for discussing process performance Distinguish special from common causes of variation; as a guide to local or management action 3
Process Capability Process Capability Index Lower specification limit In Control and Capable (Variation from common cause reduced) Upper specification limit. Cp = Range/σ. Cpk In Contro l but not Capable ( Variation from common causes excessive) Process Capability Process Capability (cont d) Take an example with: Mean =.73 Standard deviation, σ =.7 UCL =.9 LCL =. Normalizing the specifications: UCL x.9.73 = = =.3 σ.7 Z Z LCL MIN LCL x..73 = = = 3. σ.7 =.3 (on an absolute basis) LCL x UCL..73.9 σ Z LCL -3..3 Using the tables of areas under the Normal Curve, the proportions out of specification would be: P UCL =.9 PLCL =. Ptotal =.3 The Capability Index would be: C PK = Z min /3 =.3 / 3 =.7 7 Process Capability (cont d) Process Capability (cont d) If this process could be adjusted toward the center of the specification, the proportion of parts falling beyond either or both specification limits might be reduced, even with no change in Standard deviation. For example, if we confirmed with control charts a new mean =.7, then: UCL x new.9.7 = = =.7 σ.7 LCL x new..7 Z LCL = = =. 7 σ.7 Z min =.7 LCL x UCL..7.9 σ Z LCL -.7.7 The proportions out of specification would be: P UCL =.9 PLCL =.9 Ptotal =. The Capability Index would be: CPK = Z min /3 =.7 / 3 =.9 9 3
Improving Process Capability To improve the chronic performance of the process, concentrate on the common causes that affect all periods. These will usually require management action on the system to correct. Chart and analyze the revised process: Confirm the effectiveness of the system by continued monitoring of the Control Chart 3