Data eval notes
Data eval notes BME 3721
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This 42 page Class Notes was uploaded by Kathleen Quijada on Friday February 13, 2015. The Class Notes belongs to BME 3721 at Florida International University taught by Wei-Chiang Lin in Spring2015. Since its upload, it has received 82 views. For similar materials see Data Evaluation Principals in Biomedical Sciences at Florida International University.
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Date Created: 02/13/15
E 811 m orhbll Chapter 5 Methods and Philosophy of Statistical Process Control Introduction to Statistical Quality Control 6th Fditinn iitl quot 39 of OU I pU i wSpca 39ca bfts manoFucl m process W39s 3 Characteristics of a process Equipment Material People Environment Method Tutor no 1an Input vow mammals 0 Output hI39S ch Vm uor Parameters poms M WWW Process Parameters Process Parameters are defined as characteristics or conditions that are required within boundaries in order for the process to produce the desired output given the proper input was introduced ie Temperature Humidity Speed Pressure Lighting Time etc 51 Introduction Statistical process control is a collection of tools that when used together can result in process stability and variability reduction dis lrubu on narrow 3004 pm uah39on normal olisiributv39on 1 Tbols 51 Introduction high u39tlo The seven major tools for process monitoring are 1 Histogram or Stern and Leaf plot 2 Check Sheet 3 Pareto Chart 4 Cause and Effect Diagram 5 Defect Concentration Diagram 6 Scatter Diagram 7 Control Chart 52 Chance and Assignable Causes of Quality Variation Ha A process that is operating with only chance causes Cgtlt of variation present is said to be in statistical control A process that is operating in the presence of 9 assignable causes is said to be out of control The eventual goal of SPC is reduction or elimination of variability in the process by identification of assignable causes 8W ALS JL K W Mimi charl Seang 5y 8m wtaw ailsMb Woo vaL liN quot39 Un t UM 0 W 7 Wu mm ll39m di a 10W 52 Chance and ASSIgnable Causes of Quality Variation jun Com 5 chm arc SQ 1quot w an W39rb was 5W WW 7 T Tvar39mbzliij 1 sm m w 53 Statistical Basis of the Control Chart Basic Principlg A typical control chart has control limits set at values such that if the process is in control nearly all points will lie between the upper control limit UCL and the lower control limit LCL 53 Statistical Basis of the Control Chart Basic Principl s Sampb i SW3 1quot f 0 unit I I I I I I I I I I I I I I I ll ASOPDOEJKKPNJFMFAN ALE 39h39rNL 53 Statistical Basis of the Control Chart OutofControl Situations If at least one point plots beyond the control limits the process is out of control If the points behave in a systematic or nonrandom manner then the process could be out of control 53 Statistical Basis of the Control Chart Relationship between hypothesis testing and control charts We have a process that we assume the true process mean is E 74 and the process standard deviation is 001 Samples of size 5 are taken giving a standard deviation of the sample average i as tf thmU RS 00045 oi 81 Aurel or r W n j 53 Statistical Basis of the Control Chart Relationship between hypothesis testing and control charts Control limits can be set at 3 standard deviations from the mean This results in CSSigma Control Limits UCL 74 300045 740135 CL 74 LCL 74300045 739865 53 Statistical Basis of the Control Chart Relationship between hypothesis testing and control charts Choosing the control limits is equivalent to setting up the critical region for testing hypothesis HO 75 H1 i 75 53 Statistical Basis of the Control Chart Relationship between the process and the control chart Distribution of 0 3 l individual measrsgerggrts x Distribtmon with mean 0N a 74 and Normal Wlth 39gzom meanp74 I and X 00045 UCL 740135 3 l1 A M Center Asg a 3 uJ V l W Line 740000 3 1 Sample n 5 LCL 739865 39 l Summe Tl l mm abstr Figure 44 How the control chart works 53 Statistical Basis of the Control Chart Mportant uses of the control chart Most processes do not operate in a state of statistical control Consequently the routine and attentive use of control charts will identify assignable causes If these causes can be eliminated from the process variability will be reduced and the process will be improved The control chart only detects assignable causes Management operator and engineering action will be necessary to eliminate the assignable causes Outofcontrol action plans OCAPs are an important aspect of successful control chart usage see page 160 Refer to the process improvement cycle Figure 55 page 160 manufacior moss 53 Statistical Basis of the Control Chart Iypes the control chart These charts are applied to data that follow a continuous distribution measurement data These charts are applied to data that follow a discrete distribution x5 LCD Hinds 3 Statistical Basis of the Control Chart pularity of control cha 1 Control charts are a proven technique for improving productivity 2 Control charts are effective in defect prevention 3 Control charts prevent unnecessary process adjustment 4 Control charts provide diagnostic information 5 Control charts provide information about process capability 532 Choice of Control Limits General model of a control chart basic rm UCL p 4 LOW w DOM Mt13 Center Lme uw LCL W L0W where L distance of the control limit from the center line it mean of the sample statistic w ow standard deviation of the statistic w Type Vs Type II Errors V vvvv 7m Refers to detecting a failure when the output is Within the desirable limits false detection Producer Error Financial burden Refers to failure to detect a defect that eXIsts missed detection Consumer Error QualitySafety Issue NOTE Manufacturers often have to yield to Type I error in order to minimize type II errors f 32 Choice of Control Limits 997 of the Data If approximately 997 of the data lies within 36 of the mean ie 997 of the data should lie within the control limits then 1 0997 0003 or 03 of the data can fall outside 36 or 03 of the data lies outside the control limits Actually we should use the more exact value 00027 00027 is the probability of a Iype I error or a false alarm in this situation 532 Choice of Control Limits ThreeSigma Limits The use of 3sigma limits generally gives good results in practice If the distribution of the quality characteristic is reasonably well approximated by the normal distribution then the use of 3sigma limits is applicable These limits are often referred to as action limits 5 a Warning Limits on Control Charts 32 Choice of Control Limits Warning limits if used are typically set at 2 standard deviations from the mean If one or more points fall between the warning limits and the control limits or close to the warning limits the process may not be operating properly warning limits often increase the sensitivity of the control chart warning limits could result in an increased risk of false alarms 044 mm Ramg tunua39 533 Sample Size and Sampling Frequency quot AA Am In designing a control chart both the sample size to be selected and the frequency of selection must be specified Larger samples make it easier to detect small shifts in the process Current practice tends to favor smaller more frequent samples 1 of bloswva bns a di uml39 hm Point 533 Sample Size and Sampling Frequency VAVA39AV39AA39 AVA AVAV Average Run Lengm Th is a very important way of determining the appropriate sample size and sampling frequency Let p probability that any point exceeds the control limits Then 533 Sample Size and Sampling Frequency w Consider a problem with control limits set at 3 standard deviations from the mean The probability that a point plots beyond the control limits is again 00027 ie p 00027 Then the average run length is F m ARL 1 370 00027 533 Sample Size and Sampling Frequency What does the ARL tell us The average run length gives us the length of time or number of samples that should plot in control before a point plots outside the control limits For our problem even if the process remains in control an outof control signal will be generated every 370 samples on average 533 Sample Size and Sampling Frequency Average Time to Signal Sometimes it is more appropriate to express the performance of the control chart in terms of the average time to signal ATS Say that samples are taken at fixed intervals h hours apart 9S miUSi M how n incurs 534 Rational Subgroups Subgroups or samples should be selected so that if assignable causes are present the chance for differences between subgroups will be maximized while the chance for differences due to these assignable causes within a subgroup will be minimized can dikef l m Jx39FCcrwce loml No groups 534 Rational Subgroups Selection of Rational Subgroups LXI POW owing2 Select consecutive units of production Provides a snapshot of the process Effective at detecting process shifts Select a random sample over the entire sampling interval Can be effective at detecting if the mean has wandered outof control and then back incontrol Space ouf quot a 535 Analysis of Patterns on Control Charts Nonrandom patterns can indicate outofcontrol conditions Patterns such as cycles trends are often of considerable diagnostic value more about this in Chapter 5 Look for runs this is a sequence of observations of the same type all above the center line or all below the center line Runs of say 8 observations or more could indicate an outofcontrol situation Run up a series of observations are increasing Run down a series of observations are decreasing Wk 0 39l39lmmb elvtmg ovzlw39i Shwlul lot romele 535 Analysis of Patterns on Control Charts Western Electric Handbook Rules Should be used carefully because of the increased risk of false alarms A process is considered out of control if any of the following occur 1 One point plots outside the 3sigma control limits 2 Two out of three consecutive points plot beyond the 2 sigma warning limits 3 Four out of five consecutive points plot at a distance of 1sigma or beyond from the center line 4 Eight consecutive points plot on one side of the center line 4 The Rest of the Magnificent Seven The control chart is most effective when integrated into a comprehensive SPC program The seven major SPC problemsolving tools should be used routinely to identify improvement opponunMes The seven major SPC problemsolving tools should be used to assist in reducing variability and eliminating waste W b Tools 4 The Rest of the Magnificent Seven Recall the magnificent seven 1 Histogram or Stern and Leaf plot 2 Check Sheet 3 Pareto Chart 4 Cause and Effect Diagram 5 Defect Concentration Diagram 6 Scatter Diagram 7 Control Chart 4 The Rest of the Magnificent Seven Check Sheets Useful for collecting historical or current operating data about the process under investigation Can provide a useful timeoriented summary of data rusted insuf cient weld out of order issued Un nished Adhesive failure alodinc Paint out of limits Paint Film on v Iu N OWNampN Primer cans Voids in Delaminated Incorrect dimensions test failure I4 20 TOTAL 0 7 29 7 4 The Rest of the Magnificent Seven Pareto Chart The Pareto chart is a frequency distribution or histogram of attribute data arranged by category Plot the frequency of occurrence of each defect type against the various defect types lncorr dimensions Parts damaged Machining lnsuff masking Parts rusted Adhesive failure Film on parts Salt spray failure J Out of order A Unfinished fairing w Wrong part issued w Weld misaligned Paint out of spec Delam composite Voids in casting Paint damaged Primer damaged o Improper procedure i Powdery alodine H 2222 4 The Rest of the Magnificent Seven Cause and Effect Diagram Once a defect error or problem has been identified and isolated for further study potential causes of this undesirable effect must be analyzed Cause and effect diagrams are sometimes called fishbone diagrams because of their appearance tool Too much play Surface finish Paint flow rate Defective from Wronq work P39We39 supplier sequence type Damaged in Planning P mer handling viscosity Paint Materials viscosity handling Incorrect specifications Inspectors don39t understand specification Ambient temperature too high InsuffiCient training Inadequate Dust supervrsnon Figure 419 Causeand effcct diagram for the tank defect problem 54 The Rest of the Magnificent Seven How to Construct a CauseandEffect Diagram pg 181 Define the problem or effect to be analyzed Form the team to perform the analysis Often the team will uncover potential causes through brainstorming Draw the effect box and the center line Specify the major potential cause categories and join them as boxes connected to the center line Identify the possible causes and classify them into the categories in step 4 Create new categories if necessary Rank order the causes to identify those that seem most likely to impact the problem Take corrective action 54 The Rest of the Magnificent Seven Defect Concentration Diagm A defect concentration diagram is a picture of the unit showing all relevant views Various types of defects that can occur are drawn on the picture The diagram is then analyzed to determine if the location of the defects on the unit provides any useful information about the potential causes of the defects 4 The Rest of the Magnificent Seven Scatter Diagram The scatter diagram is a plot of two variables that can be used to identify any potential relationship between the variables The shape of the scatter diagram often indicates what type of relationship may exist
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