spc Statistical process control Key Quality characteristic :Forecast Error for demand
BENEFITS of SPC Monitors and provides feedback for keeping processes in control. Triggers when a problem occurs Differentiates between problems that are correctable and those that are due to chance. Gives you better control of your process. Reduces need for inspection Provides valuable knowledge in the working of the process
Have you ever Shot a rifle? Played darts? Played basketball? Shot a round of golf? What is the point of these sports? What makes them hard?
Have you ever Shot a rifle? Played darts? Shot a round of golf? Played basketball? Player A Player B Who is the better shot?
Discussion What do you measure in your process? Why do those measures matter? Are those measures consistently the same? Why not?
Variability 8 7 10 8 9 Deviation = distance between observations and the mean (or average) Player A Observations 10 9 8 8 7 averages 8.4 Deviations 10-8.4 = 1.6 9 8.4 = 0.6 8 8.4 = -0.4 8 8.4 = -0.4 7 8.4 = -1.4 0.0 Player B
Variability Deviation = distance between observations and the mean (or average) Emmett Observations 7 7 7 6 Deviations 7 6.6 = 0.4 7 6.6 = 0.4 7 6.6 = 0.4 6 6.6 = -0.6 7 6 7 7 6 Jake 6 6 6.6 = -0.6 averages 6.6 0.0
Variability Variance = average distance between observations and the mean squared 8 7 10 8 9 Emmett Observations 10 9 8 8 7 averages 8.4 Deviations 10-8.4 = 1.6 9 8.4 = 0.6 8 8.4 = -0.4 8 8.4 = -0.4 7 8.4 = -1.4 0.0 Squared Deviations 2.56 0.36 0.16 0.16 1.96 Jake 1.0 Variance
Variability Variance = average distance between observations and the mean squared Emmett Observations 7 7 7 6 Deviations Squared Deviations 7 6 7 7 6 Jake 6 averages
Variability Variance = average distance between observations and the mean squared Emmett Observations 7 7 7 6 Deviations 7-6.6 = 0.4 7-6.6 = 0.4 7-6.6 = 0.4 6 6.6 = -0.6 Squared Deviations 0.16 0.16 0.16 0.36 7 6 7 7 6 Jake 6 averages 6.6 6 6.6 = -0.6 0.0 0.36 0.24 Variance
Variability Standard deviation = square root of variance Emmett Variance Standard Deviation Emmett 1.0 1.0 Jake 0.24 0.4898979 Jake But what good is a standard deviation
Variability The world tends to be bellshaped Even very rare outcomes are possible (probability > 0) Fewer in the tails (lower) Most outcomes occur in the middle Fewer in the tails (upper) Even very rare outcomes are possible (probability > 0)
Probability Variability Even outcomes that are equally likely (like dice), when you add them up, become bell shaped Here is why: Add up the dots on the dice 0.2 0.15 0.1 0.05 1 die 2 dice 3 dice 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Sum of dots
Normal bell shaped curve Add up about 30 of most things and you start to be normal Normal distributions are divide up into 3 standard deviations on each side of the mean Once your that, you know a lot about what is going on And that is what a standard deviation is good for
Usual or unusual? 1. One observation falls outside 3 standard deviations? 2. One observation falls in zone A? 3. 2 out of 3 observations fall in one zone A? 4. 2 out of 3 observations fall in one zone B or beyond? 5. 4 out of 5 observations fall in one zone B or beyond? 6. 8 consecutive points above the mean, rising, or falling? X XX X X XX X 1 2 3 4 5 6 7 8
Causes of Variability Common Causes: Random variation (usual) No pattern Inherent in process adjusting the process increases its variation Special Causes Non-random variation (unusual) May exhibit a pattern Assignable, explainable, controllable adjusting the process decreases its variation SPC uses samples to identify that special causes have occurred
Limits Process and Control limits: Statistical Process limits are used for individual items Control limits are used with averages Limits = μ ± 3σ Define usual (common causes) & unusual (special causes) Specification limits: Engineered Limits = target ± tolerance Define acceptable & unacceptable
Process vs. control limits Distribution of averages Control limits Specification limits Variance of averages < variance of individual items Distribution of individuals Process limits
Usual v. Unusual, Acceptable v. Defective A B C D E μ Target
More about limits Good quality: defects are rare (C pk >1) μ target Poor quality: defects are common (C pk <1) μ target C pk measures Process Capability If process limits and control limits are at the same location, C pk = 1. C pk 2 is exceptional.
Process capability Good quality: defects are rare (Cpk>1) Poor quality: defects are common (Cpk<1) Cpk = min = USL x 3σ = x - LSL 3σ 24 20 = =.667 3(2) 20 15 = =.833 3(2) = = 3σ = (UPL x, or x LPL) 14 20 26 15 24
Going out of control When an observation is unusual, what can we conclude? The mean has changed X μ 1 μ 2
Going out of control When an observation is unusual, what can we conclude? σ 1 The standard deviation has changed σ 2 X
The SPC implementation process Identify what characteristics to be controlled Establish Control limits Find how to control the process Learn how to measure improvement of a process Learn how to detect shift and how to set alerts that take action. Learn about the two types of causes that affect your variation.
Setting up control charts: Calculating the limits 1. Sample n items (often 4 or 5) 2. Find the mean of the sample x-bar 3. Find the range of the sample R 4. Plot x bar on the x bar chart 5. Plot the R on an R chart 6. Repeat steps 1-5 thirty times 7. Average the x bars to create (x-bar-bar) 8. Average the R s to create (R-bar)
Setting up control charts: Calculating the limits 9. Find A 2 on table (A 2 times R estimates 3σ) 10. Use formula to find limits for x-bar chart: X A2 R 11. Use formulas to find limits for R chart: LCL D3R UCL D4R
Let s try a small problem smpl 1 smpl 2 smpl 3 smpl 4 smpl 5 smpl 6 observation 1 7 11 6 7 10 10 observation 2 7 8 10 8 5 5 observation 3 8 10 12 7 6 8 x-bar R X-bar chart R chart UCL Centerline LCL
Let s try a small problem smpl 1 smpl 2 smpl 3 smpl 4 smpl 5 smpl 6 Avg. observation 1 7 11 6 7 10 10 observation 2 7 8 10 8 5 5 observation 3 8 10 12 7 6 8 X-bar 7.3333 9.6667 9.3333 7.3333 7 7.6667 8.0556 R 1 3 6 1 5 5 3.5 X-bar chart R chart UCL 11.6361 9.0125 Centerline 8.0556 3.5 LCL 4.4751 0
R chart 10 9 8 7 6 5 4 3 2 1 0 9.0125 3.5 1 2 3 4 5 6 0
X-bar chart 11.6361 8.0556 4.4751
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Interpreting charts Observations outside control limits indicate the process is probably out-of-control Significant patterns in the observations indicate the process is probably out-of-control Random causes will on rare occasions indicate the process is probably out-of-control when it actually is not
Interpreting charts In the excel spreadsheet, look for these shifts: A B C D Show real time examples of charts here
Lots of other charts exist P chart C charts U charts Cusum & EWMA For yes-no questions like is it defective? (binomial data) For counting number defects where most items have 1 defects (eg. custom built houses) Average count per unit (similar to C chart) Advanced charts p 3 p(1 n p) c 3 c u 3 u n V shaped or Curved control limits (calculate them by hiring a statistician)
SPC Station
SPC as a triggering tool
Selecting rational samples Chosen so that variation within the sample is considered to be from common causes Special causes should only occur between samples Special causes to avoid in sampling passage of time workers shifts machines Locations
Chart advice Larger samples are more accurate Sample costs money, but so does being out-of-control Don t convert measurement data to yes/no binomial data (X s to P s) Not all out-of control points are bad Don t combine data (or mix product) Have out-of-control procedures (what do I do now?) Actual production volume matters (Average Run Length)
Statistical Process Control (S.P.C.) This is a control system which uses statistical techniques for knowing, all the time, changes in the process. It is an effective method in preventing defects and helps continuous quality improvement.
What does S.P.C. mean? Statistical: Statistics are tools used to make predictions on performance. There are a number of simple methods for analysing data and, if applied correctly, can lead to predictions with a high degree of accuracy.
What does S.P.C. mean? Process: The process involves people, machines, materials, methods, management and environment working together to produce an output, such as an end product.
What does S.P.C. mean? Control: Controlling a process is guiding it and comparing actual performance against a target. Then identifying when and what corrective action is necessary to achieve the target.
S.P.C. Statistics aid in making decisions about a process based on sample data and the results predict the process as a whole.
People Machines Material Output Management Methods Environment
The Aim of S.P.C. - Prevention Strategy Prevention Benefits: Improved design and process capability. Improved manufacturing quality. Improved organisation. Continuous Improvement.
S.P.C. as a Prevention Tool The S.P.C. has to be looked at as a stage towards completely preventing defects. With stable processes, the cost of inspection and defects are significantly reduced.
The Benefits of S.P.C. Assesses the design intent. Achieves a lower cost by providing an early warning system. Monitors performance, preventing defects. Provides a common language for discussing process performance.
Process Variations Process Element Variable Examples Machine.Speed, operating temperature, feed rate Tools..Shape, wear rate Fixtures..Dimensional accuracy Materials Composition, dimensions Operator Choice of set-up, fatigue Maintenance Lubrication, calibration Environment Humidity, temperature
Process Variations No industrial process or machine is able to produce consecutive items which are identical in appearance, length, weight, thickness etc. The differences may be large or very small, but they are always there. The differences are known as variation. This is the reason why tolerances are used.
Stability Common causes are the many sources of variation that are always present. A process operates within normal variation when each element varies in a random manner, within expected limits, such that the variation cannot be blamed on one element. When a process is operating with common causes of variation it is said to be stable.
Process Control The process can only be termed under control if it gives predictable results. Its variability is stable over a long period of time.
Process Control Charts Graphs and charts have to be chosen for their simplicity, usefulness and visibility. They are simple and effective tools based on process stability monitoring. They give evidence of whether a process is operating in a state of control and signal the presence of any variation.
Data Interpretation Consider these 50 measurements Bore Diameter 36.32 ±0.05mm (36.27-36.37mm) 1 36.36 11 36.37 21 36.34 31 36.35 41 36.36 2 36.34 12 36.35 22 36.37 32 36.35 42 36.37 3 36.34 13 36.32 23 36.34 33 36.36 43 36.37 4 36.33 14 36.35 24 36.35 34 36.37 44 36.35 5 36.35 15 36.34 25 36.34 35 36.34 45 36.37 6 36.33 16 36.34 26 36.35 36 36.36 46 36.36 7 36.33 17 36.35 27 36.36 37 36.38 47 36.35 8 36.34 18 36.33 28 36.33 38 36.34 48 36.34 9 36.35 19 36.32 29 36.36 39 36.35 49 36.35 10 36.35 20 36.35 30 36.38 40 36.35 50 36.34
Data Interpretation As a set of numbers it is difficult to see any pattern. Within the table, numbers 30 and 37 were outside the tolerance but were they easy to spot? A way of obtaining a pattern is to group the measurements according to size.
Data Interpretation Tally Chart 36.39 36.38 36.37 36.36 36.35 36.34 The tally chart groups the measurements together by size as shown. The two parts that were out of tolerance are now easier to detect (36.38mm). 36.33 36.32 36.31 36.30 36.29 36.28
Tally Chart - Frequency 36.39 36.38 36.37 36.36 36.35 36.34 36.33 36.32 36.31 36.30 2 6 7 16 12 5 2 The tally chart shows patterns and we can obtain the RANGE - 36.32mm to 36.38mm. The most FREQUENTLY OCCURRING size is 36.35mm. 36.29 36.28
Tally Chart - Information The tally chart gives us further information: The number of bores at each size; The number of bores at the most common size; The number of bores above and below the most common size (36.35mm) - number above 36.35mm is 7+6+2=15 number below 36.35mm is 12+5+2=19
Histogram We can redraw the frequency chart as a bar chart known as a histogram: 16 14 12 10 8 6 4 2 0 36.31 36.32 36.33 36.34 36.35 36.36 36.37 36.38 36.39