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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 0 20 40 60 80 159131721 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 3 21.8803.2680 31.0232.5740 40.7292.2820 50.5772.1150 60.4832.0040 70.4191.9240.076 80.3731.8640.136 90.3371.8160.184 100.3081.7770.223

16 S6-16 Each sample is 4 measurements. Determine 3  control limits. sample mean range. 1 5.02.124.96, 5.03, 5.01, 5.08 2 4.99.08. 3 4.97.13. 4 5.03.18. 5 4.99.14.  X Chart - Example 2

17 S6-17  X Chart - Example 2 4.9 5.0 5.1 Time Sample Mean Upper control limit Lower control limit

18 S6-18 sample valuesmean range 6 5.05, 5.00, 4.80, 4.95 4.95 0.25 7 5.00, 5.10, 5.10, 5.00 5.05 0.10 8 4.80, 5.20, 5.10, 5.00 5.025 0.40 4.9 5.0 5.1 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 1 5.02.12 2 4.99.08 3 4.97.13 4 5.03.18 5 4.99.14 R Chart - Example 2 4.96, 5.03, 5.01, 5.08

22 S6-22 R Chart - Example 2 0 0.2 0.3 Time Sample Range Upper control limit Lower control limit 0.1

23 S6-23 sample valuesmean range 6 5.05, 5.00, 4.80, 4.95 4.95 0.25 7 5.00, 5.10, 5.10, 5.00 5.05 0.10 8 4.80, 5.20, 5.10, 5.00 5.025 0.40 Example 2 – New Samples 0 0.2 0.3 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, 5.1 5.0 0.2 2 5.2, 5.3, 5.4 5.3 0.2 3 5.5, 5.6, 5.7 5.6 0.2 4 5.8, 5.9, 6.0 5.9 0.2 Example 3

28 S6-28 Example 3 – Control Charts 5.0 5.5 6.0 Time Sample Mean Upper control limit = 5.6546 Lower control limit = 5.2454 0.0 0.5 1.0 Time Sample Range Upper control limit = 0.5148 Lower control limit = 0

29 S6-29 sample valuesmean range 1 5.0, 5.0, 5.0 5.0 0.0 2 4.5, 5.0, 5.5 5.0 1.0 3 4.0, 5.0, 6.0 5.0 2.0 4 3.0, 5.0, 7.0 5.0 4.0 Example 4

30 S6-30 Example 4 – Control Charts 3.0 5.0 7.0 Time Sample Mean Upper control limit = 6.79025 Lower control limit = 3.20975 0.0 3.0 6.0 Time Sample Range Upper control limit = 4.5045 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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