1 / 74

840 likes | 1.38k Views

Statistical Process Control. Overview. Variation Control charts R charts X-bar charts P charts. Statistical Quality Control (SPC). Measures performance of a process Primary tool - statistics Involves collecting, organizing, & interpreting data Used to:

Download Presentation
## Statistical Process Control

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Overview**• Variation • Control charts • R charts • X-bar charts • P charts**Statistical Quality Control (SPC)**• Measures performance of a process • Primary tool - statistics • Involves collecting, organizing, & interpreting data • Used to: • Control the process as products are produced • Inspect samples of finished products**Bottling Company**• Machine automatically fills a 20 oz bottle. • Problem with filling too much? Problems with filling to little? • So Monday the average is 20.2 ounces. • Tuesday the average is 19.6 ounces. • Is this normal? Do we need to be concerned? • Wed is 19.4 ounces.**Natural Variation**• Machine can not fill every bottle exactly the same amount – close but not exactly.**Assignable variation**• A cause for part of the variation**SPC**• Objective: provide statistical signal when assignable causes of variation are present**Control Chart Types**Continuous Numerical Data Categorical or Discrete Numerical Data Control Charts Variables Attributes Charts Charts R P C X Chart Chart Chart Chart**Measuring quality**• 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 Attributes Variables • Characteristics that you measure, e.g., weight, length • May be in whole or in fractional numbers • Continuous random variables**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 causes • Data outside control limits or trend in data • Natural causes • Random variations around average**Steps to Follow When Using Control Charts**TO SET CONTROL CHART LIMITS • Collect 20-25 samples of n=4 or n=5 a stable process • compute the mean of each sample. • Calculate control limits • Compute the overall means • Calculate the upper and lower control limits.**Steps to Follow When Using Control Charts - continued**TO MONITOR PROCESS USING THE CONTROL CHARTS: • Collect and graph data • Graph the sample means and ranges on their respective control charts • Determine whether they fall outside the acceptable limits. • 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.**Control Charts for Variables**Glacier Bottling • Management at Glacier Bottling is concerned about their filling process. In particular, they want to know whether or not the machines are really filling the bottles with 16 ounces. • Create an Xbar chart that will be used to monitor the process. • Collected data for 25 days. Each day, pulled 4 bottles from the filling line and measured the amount in the bottle.**Glacier Bottling**Remember: There are 25 samples of size 4 to calculate the control limits. We are doing the first 5 right now…**Setting Control Limits for**R chart**R Chart**• Monitors variability in process • Variables control chart • Interval or ratio scaled numerical data • Shows sample ranges over time • Difference between smallest & largest values in inspection sample**R Chart Control Limits**From Table S6.1 Sample Range at Time i # Samples**Glacier Bottling**16.02 – 15.83 = 0.19**Glacier Bottling**16.02 – 15.83 = 0.19 16.12 – 15.85 = 0.27**R = 0.29**UCLR = D4R LCLR = D3R Glacier Bottling R-Charts**Control Chart Factors**Factor for UCL Factor for Factor Size of and LCL for LCL for UCL for Sample x-Charts R-Charts R-Charts (n) (A2) (D3) (D4) 2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 This chart is in your text and will be provided for exams if needed.**R = 0.29**UCLR = D4R LCLR = D3R Glacier Bottling R-Charts D4 = 2.282 D3 = 0 UCLR = 2.282 (0.29) = 0.654 ounce LCLR = 0(0.29) = 0 ounce**R = 0.29**UCLR = D4R LCLR = D3R Glacier Bottling R-Charts D4 = 2.282 D3 = 0 UCLR = 2.282 (0.29) = 0.654 ounce LCLR = 0(0.29) = 0 ounce**Setting Control Limits for**Xbar chart**X Chart**• Monitors process average • Variables control chart • Interval or ratio scaled numerical data • Shows sample means over time**X Chart Control Limits**From Table S6.1 Sample Range at Time i Sample Mean at Time i # Samples**Glacier Bottling**(15.85+16.02+15.83+15.93)/4 = 15.908**Glacier Bottling**(16.12+16.00+15.85+16.01)/4 = 15.995**RBar = 0.29 ounce**XBarBar = 15.9469 ounces**Rbar = 0.29**xbarbar = 15.9469 Glacier Bottling:Setting Control Limits for XBar chart Xbar –Chart UCLx = x + A2R LCLx = x - A2R**Control Chart Factors**Factor for UCL Factor for Factor Size of and LCL for LCL for UCL for Sample x-Charts R-Charts R-Charts (n) (A2) (D3) (D4) 2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 This chart is in your text and will be provided for exams if needed.**R = 0.29**x = 15.9469 A2 = 0.729 UCLx = 15.9469 + 0.729 (0.29) = 16.156 oz. Glacier Bottling:Setting Control Limits for XBar chart X –Chart = UCLx = x + A2R LCLx = x - A2R = =**R = 0.29**x = 15.9469 A2 = 0.729 UCLx = 15.9469 + 0.729 (0.29) = 16.156 oz. LCLx = 15.9469 – 0.729 (0.29) = 15.738 oz. Glacier Bottling:Setting Control Limits for XBar chart X –Chart = UCLx = x + A2R LCLx = x - A2R = =

More Related