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S6-1 Operations Management Statistical Process Control Supplement 6.

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Presentation on theme: "S6-1 Operations Management Statistical Process Control Supplement 6."— Presentation transcript:

1 S6-1 Operations Management Statistical Process Control Supplement 6

2 S6-2 Outline  Statistical Process Control (SPC).  Mean charts or X -Charts.  Range chart or R -Charts.  Control charts for attributes.  Managerial issues and control charts.  Acceptance Sampling.

3 S6-3  Statistical technique to identify when non- random variation is present in a process.  All processes are subject to variability.  Natural causes: Random variations.  Assignable causes: Correctable problems.  Machine wear, unskilled workers, poor materials.  Uses process control charts. Statistical Process Control (SPC)

4 S6-4 Produce Good Provide Service Stop Process No Yes Is process in control? Take Samples Find Out Why Create Control Chart Start Statistical Process Control Steps Take Sample Inspect Sample

5 S6-5 Process Control Charts Plot of Sample Data Over Time Time Sample Value Upper control limit Lower control limit

6 S6-6  Process is not in control if:  Sample is not between upper and lower control limits.  A non-random pattern is present, even when between upper and lower control limits.  Based on sample being normally distributed. Control Charts

7 S6-7 Distribution of Sample Means Standard deviation of the sample means (mean)

8 S6-8 As sample size gets large enough, distribution of mean values becomes approximately normal for any population distribution. Central Limit Theorem

9 S6-9 Control Charts R Chart Variables Charts Attributes Charts X Chart P C Continuous Numerical Data Categorical or Discrete Numerical Data Control Chart Types

10 S6-10  Characteristics for which you focus on defects.  Categorical or discrete values.  ‘Good’ or ‘Bad’.  # of defects. AttributesVariables Quality Characteristics  Characteristics that you measure, e.g., weight, length.  Continuous values.

11 S6-11  Shows sample means over time.  Monitors process average.  Example: Weigh samples of coffee.  Collect many samples, each of n bags.  Sample size = n.  Compute mean and range for each sample.  Compute upper and lower control limits (UCL, LCL).  Plot sample means and control limits.  X Chart

12 S6-12  X Chart Control Limits - Std. Dev. of Process Is Known sample mean at time i  = known process standard deviation

13 S6-13 Each sample is 4 measurements. Process mean is 5 lbs. Process standard deviation is 0.1 lbs. Determine 3  control limits.  X Chart - Example 1

14 S6-14  X Chart Control Limits - Std. Dev. of Process is Not Known sample range at time i A 2 is from Table S6.1 sample mean at time i

15 S6-15 Factors for Computing Control Chart Limits Sample Size, n Mean Factor, A 2 Upper Range, D 4 Lower Range, D

16 S6-16 Each sample is 4 measurements. Determine 3  control limits. sample mean range , 5.03, 5.01,  X Chart - Example 2

17 S6-17  X Chart - Example Time Sample Mean Upper control limit Lower control limit

18 S6-18 sample valuesmean range , 5.00, 4.80, , 5.10, 5.10, , 5.20, 5.10, Time Sample Mean Upper control limit Lower control limit Example 2 – New Samples

19 S6-19  Shows sample ranges over time.  Sample range = largest - smallest value in sample.  Monitors process variability.  Example: Weigh samples of coffee.  Collect many samples, each of n bags.  Sample size = n.  Compute range for each sample & average range.  Compute upper and lower control limits (UCL, LCL).  Plot sample ranges and control limits. R Chart

20 S6-20 sample range at time i From Table S6.1 R Chart Control Limits

21 S6-21 Each sample is 4 measurements. Determine 3  control limits. sample mean range R Chart - Example , 5.03, 5.01, 5.08

22 S6-22 R Chart - Example Time Sample Range Upper control limit Lower control limit 0.1

23 S6-23 sample valuesmean range , 5.00, 4.80, , 5.10, 5.10, , 5.20, 5.10, Example 2 – New Samples Time Sample Range Upper control limit Lower control limit 0.1

24 S6-24 Control Chart Steps  Collect 20 to 25 samples of n=4 or n=5 from a stable process & compute the mean and range.  Compute the overall mean and average range.  Calculate upper and lower control limits.  Collect new samples, and plot the means and ranges on their respective control charts.

25 S6-25 Control Chart Steps - Continued  Investigate points or patterns that indicate the process is out of control. Assign causes for the variations.  Collect additional samples and revalidate the control limits.

26 S6-26 Use of Control Charts

27 S6-27 sample valuesmean range 1 4.9, 5.0, , 5.3, , 5.6, , 5.9, Example 3

28 S6-28 Example 3 – Control Charts Time Sample Mean Upper control limit = Lower control limit = Time Sample Range Upper control limit = Lower control limit = 0

29 S6-29 sample valuesmean range 1 5.0, 5.0, , 5.0, , 5.0, , 5.0, Example 4

30 S6-30 Example 4 – Control Charts Time Sample Mean Upper control limit = Lower control limit = Time Sample Range Upper control limit = Lower control limit = 0

31 S6-31  Attributes control chart.  Shows % of nonconforming items.  Example: Count # defective chairs & divide by total chairs inspected.  Chair is either defective or not defective. p Chart

32 S6-32  Attributes control chart.  Shows number of 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. c Chart

33 S6-33  Quality testing for incoming materials or finished goods.  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. Acceptance Sampling

34 S6-34  Inspecting all items is too expensive.  The larger the sample inspected:  The greater the cost for inspection.  The less likely you are to accept a “bad” lot or to reject a “good” lot.  Key questions:  How many should be inspected in each lot?  How confident are you in the accept/reject decision? Acceptance Sampling


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