Process Capability and SPC Chapter 9A Process Capability and SPC

OBJECTIVES Process Variation Process Capability Process Control Procedures Variable data Attribute data 2

Basic Forms of Variation Assignable variation is caused by factors that can be clearly identified and possibly managed Example: A poorly trained employee that creates variation in finished product output. Common variation is inherent in the production process Example: A molding process that always leaves “burrs” or flaws on a molded item. 3

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 views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs. Incremental Cost of Variability High Zero Lower Spec Target Upper Traditional View Incremental Cost of Variability High Zero Lower Spec Target Upper Taguchi’s View 30

How do the limits relate to one another? Process Capability Process limits Specification limits How do the limits relate to one another? 28

Process Capability Index, Cpk Capability Index shows how well parts being produced fit into design limit specifications. As a production process produces items small shifts in equipment or systems can cause differences in production performance from differing samples. Shifts in Process Mean 29

Process Capability – A Standard Measure of How Good a Process Is. A simple ratio: Specification Width _________________________________________________________ Actual “Process Width” Generally, the bigger the better.

This is a “one-sided” Capability Index Process Capability This is a “one-sided” Capability Index Concentration on the side which is closest to the specification - closest to being “bad”

Upper Tolerance Limit = 16 + .05(16) = 16.8 ounces The Cereal Box Example We are the maker of this cereal. Consumer reports has just published an article that shows that we frequently have less than 16 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 + .05(16) = 16.8 ounces Lower Tolerance Limit = 16 – .05(16) = 15.2 ounces We go out and buy 1,000 boxes of cereal and find that they weight an average of 15.875 ounces with a standard deviation of .529 ounces.

Cereal Box Process Capability Specification or Tolerance Limits Upper Spec = 16.8 oz Lower Spec = 15.2 oz Observed Weight Mean = 15.875 oz Std Dev = .529 oz

9A-11 What does a Cpk of .4253 mean? An index that shows how well the units being produced fit within the specification limits. This is a process that will produce a relatively high number of defects. Many companies look for a Cpk of 1.3 or better… 6-Sigma company wants 2.0!

Types of Statistical Sampling Attribute (Go or 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 Variable (Continuous) Usually measured by the mean and the standard deviation. X-bar and R chart applications 6

Statistical Process Control (SPC) Charts Normal Behavior UCL Normal Behavior LCL 1 2 3 4 5 6 Samples over time UCL Possible problem, investigate LCL 1 2 3 4 5 6 Samples over time UCL Possible problem, investigate LCL 1 2 3 4 5 6 Samples over time 16

Control Limits are based on the Normal Curve x m z -3 -2 -1 1 2 3 Standard deviation units or “z” units. 14

9A-15 Control Limits We establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations from some x-bar or mean value. Based on this we can expect 99.7% of our sample observations to fall within these limits. x 99.7% LCL UCL 15

Example of Constructing a p-Chart: Required Data Number of defects found in each sample Sample No. No. of Samples 17

Statistical Process Control Formulas: Attribute Measurements (p-Chart) Given: Compute control limits: 18

Example of Constructing a p-chart: Step 1 1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample 19

Example of Constructing a p-chart: Steps 2&3 2. Calculate the average of the sample proportions 3. Calculate the standard deviation of the sample proportion 20

Example of Constructing a p-chart: Step 4 4. Calculate the control limits UCL = 0.0924 LCL = -0.0204 (or 0) 21

Example of Constructing a p-Chart: Step 5 5. Plot the individual sample proportions, the average of the proportions, and the control limits UCL LCL

Example of x-bar and R Charts: Required Data 23

9A-23 Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges. 24

9A-24 Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values From Exhibit 9A.6 25

9A-26 Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values UCL LCL 26

9A-27 Example of x-bar and R charts: Steps 5&6. Calculate R-chart and Plot Values UCL LCL 27

Answer: a. Capability index Question Bowl A methodology that is used to show how well parts being produced fit into a range specified by design limits is which of the following? Capability index Producer’s risk Consumer’s risk AQL None of the above Answer: a. Capability index 7

Can not be computed on data above Question Bowl You want to prepare a p chart and you observe 200 samples with 10 in each, and find 5 defective units. What is the resulting “fraction defective”? 25 2.5 0.0025 0.00025 Can not be computed on data above Answer: c. 0.0025 (5/(2000x10)=0.0025) 7

9A-31 Question Bowl You want to prepare an x-bar chart. If the number of observations in a “subgroup” is 10, what is the appropriate “factor” used in the computation of the UCL and LCL? 1.88 0.31 0.22 1.78 None of the above Answer: b. 0.31 7

9A-32 Question Bowl You want to prepare an R chart. If the number of observations in a “subgroup” is 5, what is the appropriate “factor” used in the computation of the LCL? 0.88 1.88 2.11 None of the above Answer: a. 0 7

9A-33 Question Bowl You want to prepare an R chart. If the number of observations in a “subgroup” is 3, what is the appropriate “factor” used in the computation of the UCL? 0.87 1.00 1.88 2.11 None of the above Answer: e. None of the above 7

9A-34 End of Chapter 9A