Presentation on theme: "Operations Management Statistical Process Control Supplement 6"— Presentation transcript:
1 Operations Management Statistical Process Control Supplement 6
2 Outline Statistical Process Control (SPC). Acceptance Sampling. Mean charts or X-Charts.Range chart or R-Charts.Control charts for attributes.Managerial issues and control charts.Acceptance Sampling.
3 Statistical Process Control (SPC) 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.This slide introduces the difference between “natural” and “assignable” causes.The next several slides expand the discussion and introduce some of the statistical issues.
4 Statistical Process Control Steps StartTake SampleProduce GoodProvide ServiceInspect SampleTake SamplesNoIs processin control?This slide introduces the statistical control process.It may be helpful here to walk students through an example or two of the process. The first walk through should probably be for a manufacturing process.The next several slides present information about the various types of process control slides:CreateStop ProcessControl ChartYesFind Out Why
5 Process Control Charts Plot of Sample Data Over Time20406080159131721TimeSample ValueUpper control limitLower control limitAn example of a control chart..
6 Control Charts 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.
7 Distribution of Sample Means Standard deviation of the sample means(mean)
8 Central Limit Theorem Central Limit Theorem As sample size gets large enough,distribution of mean values becomes approximately normal for any population distribution.Central Limit TheoremThe next three slides can be used in a discussion of the theoretical basis for statistical process control.
9 Control Chart Types Control Categorical or Discrete Numerical Data Continuous Numerical DataChartsVariablesAttributesChartsChartsThis slide simply introduces the various types of control charts.RXPCChartChartChartChart
10 Quality Characteristics VariablesAttributesCharacteristics that you measure, e.g., weight, length.Continuous values.Characteristics for which you focus on defects.Categorical or discrete values.‘Good’ or ‘Bad’.# of defects.Once the categories are outlined, students may be asked to provide examples of items for which variable or attribute inspection might be appropriate. They might also be asked to provide examples of products for which both characteristics might be important at different stages of the production process.
11 X Chart 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.
12 X Chart Control Limits - Std. Dev. of Process Is Known The following slide provides much of the data from Table S4.1.sample mean at time i = known process standard deviation
13 X Chart - Example 1 Each sample is 4 measurements. Process mean is 5 lbs.Process standard deviation is 0.1 lbs.Determine 3 control limits.
14 X Chart Control Limits - Std. Dev. of Process is Not Known A2 is from Table S6.1The following slide provides much of the data from Table S4.1.sample range at time isample mean at time i
15 Factors for Computing Control Chart Limits SampleSize, nMeanFactor, A2UpperRange, D4Lower31.8803.2681.0232.5740.7292.28250.5772.11560.4832.00470.4191.9240.07680.3731.8640.13690.3371.8160.184100.3081.7770.223
16 X Chart - Example 2 sample mean range. Each sample is 4 measurements. Determine 3 control limits.sample mean range., 5.03, 5.01, 5.08
17 X Chart - Example 2 5.1 Sample Mean 5.0 4.9 Time Upper control limit Lower control limitAn example of a control chart..4.9Time
18 Example 2 – New Samples 5.1 Sample Mean 5.0 4.9 Time sample values mean range, 5.00, 4.80,, 5.10, 5.10,, 5.20, 5.10,5.1Upper control limitSample Mean5.0Lower control limit4.9Time
19 R Chart Shows sample ranges over time. Monitors process variability. 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.
20 R Chart Control LimitsFrom Table S6.1sample range at time i
21 R Chart - Example 2 sample mean range Each sample is 4 measurements. Determine 3 control limits.sample mean range4.96, 5.03, 5.01, 5.08
22 R Chart - Example 2 0.3 Sample Range 0.2 0.1 Time Upper control limit An example of a control chart..Lower control limitTime
23 Example 2 – New Samples 0.3 Sample Range 0.2 0.1 Time sample values mean range, 5.00, 4.80,, 5.10, 5.10,, 5.20, 5.10,0.3Upper control limitSample Range0.20.1Lower control limitTime
24 Control Chart StepsCollect 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 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.
27 Example 3 sample values mean range 1 4.9, 5.0, 5.1 5.0 0.2 , 5.0,, 5.3,, 5.6,, 5.9,
28 Example 3 – Control Charts 5.05.56.0TimeSample MeanUpper control limit =Lower control limit =0.00.51.0TimeSample RangeUpper control limit =Lower control limit = 0
29 Example 4 sample values mean range 1 5.0, 5.0, 5.0 5.0 0.0 , 5.0,, 5.0,, 5.0,, 5.0,
30 Example 4 – Control Charts 3.05.07.0TimeSample MeanUpper control limit =Lower control limit =0.03.06.0TimeSample RangeUpper control limit =Lower control limit = 0
31 p Chart Attributes control chart. Shows % of nonconforming items. Example: Count # defective chairs & divide by total chairs inspected.Chair is either defective or not defective.
32 c Chart 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.
33 Acceptance SamplingQuality 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.Here again it is useful to stress that acceptance sampling relates to the aggregate, not the individual unit. You might also discuss the decision as to whether one should take only a single sample, or whether multiple samples are required.
34 Acceptance Sampling 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?Here again it is useful to stress that acceptance sampling relates to the aggregate, not the individual unit. You might also discuss the decision as to whether one should take only a single sample, or whether multiple samples are required.