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1 Chapter 9A. Process Capability & Statistical Quality Control Outline:  Basic Statistics  Process Variation  Process Capability  Process Control Procedures.

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Presentation on theme: "1 Chapter 9A. Process Capability & Statistical Quality Control Outline:  Basic Statistics  Process Variation  Process Capability  Process Control Procedures."— Presentation transcript:

1 1 Chapter 9A. Process Capability & Statistical Quality Control Outline:  Basic Statistics  Process Variation  Process Capability  Process Control Procedures  Variable data  X-bar chart and R-chart  Attribute data  p-chart  Acceptance Sampling  Operating Characteristic Curve

2 2 Focus  This technical note on statistical quality control (SQC) covers the quantitative aspects of quality management  SQC is a number of different techniques designed to evaluate quality from a conformance view  How are we doing in meeting specifications?  SQC can be applied to both manufacturing and service processes  SQC techniques usually involve periodic sampling of the process and analysis of data  Sample size  Number of samples  SQC techniques are looking for variance variance  Most processes produce variance in output  we need to monitor the variance (and the mean also) and correct processes when they get out of range

3 3 Mean Basic Statistics Normal Distributions have a mean ( μ ) and a standard deviation (σ) For a sample of N observations: where: x i = Observed value N = Total number of observed values Standard Deviation  99.7% μ

4 4 Statistics and Probability  SQC relies on central limit theorem and normal dist.  We establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations. Based on this we can expect 99.7% of our sample observations to fall within these limits.  Acceptance sampling relies on Binomial and Hyper geometric probability concepts  99.7% LCLUCL  /2  Prob. of Type I error

5 5  Using SQC,  samples of a process output are taken, and  sample statistics are calculated  The purpose of sampling is to find when the process has changed in some nonrandom way  The reason for the change can then be quickly determined and corrected detect changes  This allows us to detect changes in the actual distribution process Basic Stats

6 6 Variation  Random ( common ) variation is inherent in the production process.  Assignable variation is caused by factors that can be clearly identified and possibly managed  Using a saw to cut 2.1 meter long boards as a sample process  Discuss random vs. assignable variation  Generally, when variation is reduced, quality improves.  It is impossible to have zero variability. T or F ?

7 7 Incremental Cost of Variability High Zero Lower Spec Target Spec Upper Spec Traditional View Incremental Cost of Variability High Zero Lower Spec Target Spec Upper Spec Taguchi’s View Exhibits TN8.1 & TN8.2 Taguchi’s View of Variation Traditional view is that quality within the LS and US is good and that the cost of quality outside this range is constant, where Taguchi view s costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs.

8 8 Process Capability  Tolerance (specification, design) Limits  Bearing diameter inches  LTL = inches UTL = inches  Process Limits  The actual distribution from the process  Run the process to make 100 bearings, compute the mean and std. dev. (and plot/graph the complete results)  Suppose, mean = 1.250, std. dev =  How do they relate to one another?

9 9 Tolerance Limits vs. Process Capability Actual Process Width Specification Width Actual Process Width

10 10 Process Capability Example  Design Specs: Bearing diameter inches  LTL = inches UTL = inches  The actual distribution from the process  mean = 1.250, s =  +- 3s limits  (0.002)  [1.244, 1.256]  Anew process,  std. dev. =

11 11 Process Capability Index, C pk  Capability Index shows how well parts being produced fit into design limit specifications  Compute the C pk for the bearing example.  Old process, mean = 1.250, s =  What is the probability of producing defective bearings?  New process, mean = 1.250, s= , re-compute the C pk  When the computed (sample) mean = design (target) mean, what does that imply?

12 12 The Cereal Box Example  Recall the cereal example. Consumer Reports has just published an article that shows that we frequently have less than 15 ounces of cereal in a box.  Let’s assume that the government says that we must be within ± 5 percent of the weight advertised on the box.  Upper Tolerance Limit = (16) = 16.8 ounces  Lower Tolerance Limit = 16 – 0.05(16) = 15.2 ounces  We go out and buy 1,000 boxes of cereal and find that they weight an average of ounces with a standard deviation of ounces.

13 13 Cereal Box Process Capability  Specification or Tolerance Limits  Upper Spec = 16.8 oz,  Lower Spec = 15.2 oz  Observed Weight  Mean = oz, Std Dev = oz  What does a C pk of mean?  Many companies look for a C pk of 1.3 or better… 6-Sigma company wants 2.0!

14 14 Types of Statistical Sampling 1.Sampling to accept or reject the immediate lot of product at hand (Acceptance Sampling).  Attribute (Binary; Yes/No; Go/No-go information)  Defectives refers to the acceptability of product across a range of characteristics.  Defects refers to the number of defects per unit which may be higher than the number of defectives.  p -chart application 2.Sampling to determine if the process is within acceptable limits (Statistical Process Control)  Variable (Continuous)  Usually measured by the mean and the standard deviation.  X-bar and R chart applications

15 15 Evidence for Investigation…

16 16 Control Limits  If we establish control limits at +/- 3 standard deviations, then we would expect 99.7% of our observations to fall within these limits x LCL UCL

17 17 Attribute Measurements ( p -Chart)  Item is “good” or “bad”  Collect data, compute average fraction bad (defective) and std. dev. using:  The, UCL, LCL using:  Excel time!

18 18 Variable Measurements (x-Bar and R Charts)  A variable of the item is measured (e.g., weight, length, salt content in a bag of chips)  Note that the item (sample) is not declared good or bad  Since the actual the standard deviation of the process is not known (and it may indeed fluctuate also) we use the sample data to compute the UCL & LCL  For 3-sigma limits, factors A 2, D 3, and D 4 and are given in Exhibit 9A.6, p. 341  Excel time!

19 19 3 Acceptance Sampling vs. SPC  Sampling to accept or reject the immediate lot of product at hand (Acceptance Sampling).  Determine quality level  Ensure quality is within predetermined (agreed) level  Sampling to determine if the process is within acceptable limits - Statistical Process Control (SPC)

20 20 Acceptance Sampling  Advantages  Economy  Less handling damage  Fewer inspectors  Upgrading of the inspection job  Applicability to destructive testing  Entire lot rejection (motivation for improvement)  Disadvantages  Risks of accepting “bad” lots and rejecting “good” lots  Added planning and documentation  Sample provides less information than 100-percent inspection

21 21 A Single Sampling Plan Single Sampling Plan  A Single Sampling Plan simply requires two parameters to be determined: 1. n the sample size (how many units to sample from a lot) 2. c the maximum number of defective items that can be found in the sample before the lot is rejected.

22 22 RISK  RISKS for the producer and consumer in sampling plans:  Acceptable Quality Level (AQL)  Max. acceptable percentage of defectives defined by producer.   (Producer’s risk)  The probability of rejecting a good lot.  Lot Tolerance Percent Defective (LTPD)  Percentage of defectives that defines consumer’s rejection point.   (Consumer’s risk)  The probability of accepting a bad lot.

23 23 9 Operating Characteristic Curve n = 99 c = 4 AQLLTPD Percent defective Probability of acceptance  =.10 (consumer’s risk)  =.05 (producer’s risk) The OCC brings the concepts of producer’s risk, consumer’s risk, sample size, and maximum defects allowed together The shape or slope of the curve is dependent on a particular combination of the four parameters

24 24 10 Example: Acceptance Sampling Zypercom, a manufacturer of video interfaces, purchases printed wiring boards from an outside vender, Procard. Procard has set an acceptable quality level of 1% and accepts a 5% risk of rejecting lots at or below this level. Zypercom considers lots with 3% defectives to be unacceptable and will assume a 10% risk of accepting a defective lot. Develop a sampling plan for Zypercom and determine a rule to be followed by the receiving inspection personnel.

25 25 Developing A Single Sampling Plan  Determine:  AQL?  ?  LTPD?  ?  Divide LTPD by AQL  0.03/0.01 = 3  Then find the value for “c” by selecting the value in the TN8.10 “n(AQL)”column that is equal to or just greater than the ratio above (3).  Thus, c = 6  From the row with c=6, get  nAQL = and divide it by AQL  3.286/0.01 = 328.6, round up to 329,  n = 329 c LTPD/AQL n AQL c LTPD/AQL n AQL Sampling Plan: Take a random sample of 329 units from a lot. Reject the lot if more than 6 units are defective. Sampling Plan: Take a random sample of 329 units from a lot. Reject the lot if more than 6 units are defective.


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