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Statistical Process Control Chapters 20 1 A B C D E F G H 2 3 4 5 6 7 8 Some Common Problems in Planning We plan in terms of actions (tasks) rather than objectives Responsibilities are not clear We plan in silos, out of context We underestimate the time and effort required to implement We don’t make reviews part of the plan. Six-Step Problem-Solving Process Step 1: Identify and Select the problem Step 2: Analyze the problem Step 3: Generate Potential Solutions Step 4: Select and Plan the Solution Step 5: Implement the Solution Step 6: Evaluate the Solution Types of Statistical Quality Control Statistical Quality Control Process Control Variables Charts Attributes Charts Acceptance Sampling Variables Attributes Statistical Quality Control (SPC) key tool for 6 Sigma Measures performance of a process Uses mathematics (i.e., statistics) Involves collecting, organizing, & interpreting data Objective: Regulate quality Used to Control the process as products are produced or service is performed Control Chart Types Continuous Numerical Data Control Charts Categorical or Discrete Numerical Data Variables Charts R Chart Attributes Charts `X Chart P Chart C Chart Quality Characteristics Variables ¨ Characteristics that you measure, e.g., weight, length ¨ May be in whole or in fractional numbers ¨ Continuous random variables Attributes Characteristics for which you focus on defects Classify products as either ‘good’ or ‘bad’, or count # defects e.g., radio works or not Categorical or discrete random variables Statistical Process Control Variations Common cause: due to process itself Special cause 2 ways of investigating variation Plot data using histogram, looking for a normal distribution. Standard Deviation 1 σ away from mean in either direction accounts for approx. 68% of readings in the group (red area) 2 σ away from mean in either direction accounts for approx. 95% of readings in the group (red and green area) 3 σ away from mean in either direction accounts for approx. 99% of readings in the group (red, green, and blue areas) Process Control Charts Sample Value Plot of Sample Data Over Time 70 60 50 40 30 20 10 0 Sample Value UCL Average LCL 1 5 9 13 Time 17 21 Control Chart Purposes Show changes in data pattern e.g., trends Make corrections before process is out of control Show causes of changes in data Assignable Data causes outside control limits or trend in data Natural causes Random variations around average `X Chart Type of variables control chart Interval or ratio scaled numerical data Shows sample means over time Monitors process average Example: Weigh samples of coffee & compute means of samples; Plot R Chart Type of variables control chart Interval or ratio scaled numerical data Shows sample ranges over time Difference between smallest & largest values in inspection sample Monitors variability in process Example: Weigh samples of coffee & compute ranges of samples; Plot Formulas p Chart Type of attributes control chart Nominally scaled categorical data e.g., good-bad Shows % of nonconforming items Example: Count # defective chairs & divide by total chairs inspected; Plot Chair is either defective or not defective p Chart Control Limits UCL LCL p = p + z p (1 - p ) n p = p -z p (1 - p ) n k n = i =1 k xi # Defective Items in Sample i ni Size of sample i k ni and p = z = 2 for 95.5% limits; z = 3 for 99.7% limits i =1 k i =1 Statistical Process Control Chart Using SPC to Address On-Time Medication Delivery c Chart Type of attributes control chart Discrete quantitative data Shows number of nonconformities (defects) in a unit Unit may be chair, steel sheet, car etc. Size of unit must be constant Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot c Chart Control Limits UCL LCL c c = c + c = c - c k c = ci i=1 k Use 3 for 99.7% limits # Defects in Unit i # Units Sampled Process Capability Cpk Upper Specification Limit - x x - Lower Specification Limit C pk = minimum of , where x = process mean = standard deviation of the process population Assumes that the process is: •under control •normally distributed What Is Acceptance Sampling? Form of quality testing used for incoming materials or finished goods e.g., purchased material & components Procedure Take one or more samples at random from a lot (shipment) of items Inspect each of the items in the sample Decide whether to reject the whole lot based on the inspection results What Is an Acceptance Plan? Set of procedures for inspecting incoming materials or finished goods Identifies Type of sample Sample size (n) Criteria (c) used to reject or accept a lot Producer (supplier) & consumer (buyer) must negotiate Producer’s & Consumer’s Risk Producer's risk (a) Probability of rejecting a good lot Type 1 error – results in over adjustment Consumer's risk (ß) Probability of accepting a bad lot Type II error – results in under adjustment ANY QUESTIONS?