OpEx SPC Training Module

Operational Excellence – Statistical Process Control Presented by Frank Adler, Ph.D. www.Operational-Excellence-Consulting.com

Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

The History of Statistical and Process Thinking The quality control methods and techniques used today got their start in the American Civil War, when Eli Whitney tried in year 1789 to produce 10,000 rifles by copying one rifle, part by part. At that time most of the products were hand made by small owner-managed shops and product parts were thus not interchangeable. The result of Whitney’s mass production trail was that the rifles did not work as well as the handmade rifles. In addition, the copied parts did not fit as expected.

The History of Statistical and Process Thinking GO - Test NO-GO - Test The first time that one presented machine produced parts was 1851 at the industry exhibition in the Crystal Palace in London. An American gun smith took 10 working guns, took them apart, mixed all the parts in a box and re-assembled them again. This was found a quite surprising “experiment”.

The Traditional Production Concept The Detection Control Scheme Process Inspection Good Bad Repair Scrap + Monitor/Adjust

The Traditional Production Concept
The traditional production concept does not help us to produce only good products.
Every product has to be inspected.
Products have to be repaired or even scraped.
With respect to productivity and efficiency every activity after the actual production process is a non-value added activity.

An Advanced Production Concept Prevention Control Scheme Process Inspection Good Bad Repair Scrap + Monitor/Adjust Learn/Improve
Selective measurement
Product
Process

Statistical Thinking - A Definition All work is a series of interconnected processes All processes vary Understanding and reducing variation are keys to success ASQ

Customer Satisfaction Process/ System M aterial M achines M ethods M en E nvironment The Variation Management Approach

A defect is any variation of a required characteristic of the product or its part, which is far enough removed from its nominal value to prevent the product from fulfilling the physical and functional requirements of the customer.
Variation Management – Defect Definition

The A and O of process control and continuous process improvement is to understand the meaning and causes of variation in the outcome of the process. Variation Management – Continuous Improvement

Process Improvement vs. Process Development
Process Improvement
The continuous effort to learn about the cause system in a process and to use this knowledge to control and eventually change the process to reduce variation and so to improve product quality and customer satisfaction.
Process Development
The incorporation of improved technology is the end product - or, better yet, the next stage - of an ongoing process of learning and improvement.

Remarks or Questions ?!?

A histogram provides a first estimation about the location , spread and shape of the distribution of the process.
Collect at least 50 data points , but better 75 to 100 points. 0 10 20 30 40 50 The Histogram

Select the number of classes (bars) to be used on the histogram using the following guidelines:
Number of data points: Number of classes: < 50 50 - 100 100 - 250 over 250 5 - 7 (odd number) 5 - 11 (odd number) 7 - 15 11 - 19 The Histogram – Constructing a Histogram

1. The bell-shaped distribution :
Symmetrical shape with a peak in the middle of the range of the data.
While deviation from a bell shape should be investigated, such deviation is not necessarily bad.
The Histogram – Typical Patterns of Variation

2. The double-peaked distribution :
A distinct valley in the middle of the range of the data with peaks on either side.
This pattern is usually a combination of two bell-shaped distributions and suggests that two distinct processes are at work.

3. The plateau distribution :
A flat top with no distinct peak and slight tails on either sides.
This pattern is likely to be the result of many different bell-shaped distribution with centers spread evenly throughout the range of data.

4. The skewed distribution :
An asymmetrical shape in which the peak is off-center in the range of the data and the distribution tails off sharply on one side and gently on the other.
This pattern typically occurs when a practical limit, or a specification limit, exists on one side and is relatively close to the nominal value.

5. The truncated distribution :
An asymmetrical shape in which the peak is at or near the edge of the range of the data, and the distribution ends very abruptly on one side and tails off gently on the other.
This pattern often occurs if the process includes a screening, 100 % inspection, or a review process. Note that these truncation efforts are an added cost and are, therefore, good candidates for removal.

The Histogram – The Normal Distribution

The Histogram – Exercise 1 Distribution of Heights of U.S. Population: Use the plot area below to construct a histogram from the random sample of heights on the right:

Measure of Location – The Sample Average Example:
1 = 5
2 = 7
3 = 4
4 = 2
5 = 6
Definition:

Measure of Location – The Sample Median Example:
1 = 2
2 = 5
3 = 4
Construction : Order all observations from the smallest to largest. Then choose the middle observation if the number of observations is odd, or the mean value of the two middle observations if the number of observations is even. Example:
1 = 5
2 = 7
3 = 4
4 = 2
Example:
1 = 5
2 = 7
3 = 4
4 = 2
5 = 6
median = 4 median = 4.5 ?

Measure of Variability – The Sample Range Example:
1 = 5
2 = 7
3 = 4
4 = 2
5 = 6
Definition:

Measure of Variability – Sample Variance x 3 x 2 x 1 x 10 x average _

Measure of Variability – Sample Variance Example:
1 = 5
2 = 7
3 = 4
4 = 2
5 = 6
Definition:

Measure of Variability – Sample Standard Deviation Example:
1 = 5
2 = 7
3 = 4
4 = 2
5 = 6
Definition:

Measure of Variability – The Normal Distribution
Process capability is defined as the full range of normal process variation.
average average +1*s(igma) average -1*s(igma) average +2*s(igma) average -2*s(igma) average -3*s(igma) average +3*s(igma) 34.13 % 34.13 % 13.60 % 13.60 % 2.14 % 2.14 % 0.13 % 0.13 % Variability

Measure of Variability – The Principle of Subgrouping Time t Performance Characteristic Process not in control average Subgroup size n = 5 Number of subgroups N = 7

s ST , often notated as s or sigma, is another measure of dispersion or variability and stands for “short-term standard deviation”,
which measures the variability of a process or system using “rational” subgrouping.
Measure of Variability – Standard Deviation s ST Where is the range of subgroup j , N the number of subgroups, and d 2 depends on the size n of a subgroup (see handout).

Measure of Variability – Difference between s LT and s ST Long-term standard deviation : Short-term standard deviation : The difference between the standard deviations s LT and s ST gives an indication of how much better one can do when using appropriate production control, like Statistical Process Control (SPC).

Measure of Location and Variability – Exercise 2 Distribution of Heights of U.S. Population: Calculate the Mean Value or Average, Median, Range, and long-term Standard Deviation of the sample data. You may copy the data into MS Excel and simplify the calculations. Mean Value = Median = Range = Long-term Standard Deviation =

Process Control Charts – Types of Control Charts Count or classification (attribute data) Measurements (variable data) Count Classification (Yes/No) Incidences or nonconformities Defectives or nonconforming units Fixed oppor- tunity Variable oppor- tunity Fixed subgroup size Variable subgroup size Variable subgroup size Subgroup size of 1 Fixed subgroup size c - chart u - chart np - chart p - chart x chart x-bar R chart x-bar s chart Type of data

Process Control Charts – The x - Chart The x - chart is a method of looking at variation in a variable data or measurement. One source is the variation in the individual sample results. This represents “long term” variation in the process. The second source of variation is the variation in the range between successive samples. This represents “short term” variation. Individual or x - charts should be used when there is only one data point to represent a situation at a given time. To use the x - chart, the individual sample results should be sufficient normally distributed. If not, the x - chart will give more false signals.

Process Control Charts – x/mR Chart Example

Process Control Charts – The Central Limit Theorem Regardless of the shape of the distribution of a population, the distribution of average values, x-bar’s, of subgroups of size n drawn from that population will tend toward a normal distribution as the subgroup size n becomes large. Laplace and Gauss or The standard deviation s x of the distribution of the average values is related to the standard deviation s of the individual values by the following: _

Process Control Charts – The (x-bar/R) - Chart
The (x-bar / R) - chart is a method of looking at two different sources of variation. One source is the variation in subgroup averages. The other source is the variation within a subgroup.
The (x-bar / R) - chart should be used if
the individual measurements are not normally distributed,
one can rationally subgroup the data and is interested in detecting differences between the subgroups over time.
The x-bar - chart shows variation over time and the R - chart is a measure of the short-term variation in the process.

Process Control Charts – (x-bar/R) - Chart Example

Process Control Charts – The (x-bar/s) - Chart The (x-bar / s) - chart is a method of looking at sources of variation. One chart looks at variation in the subgroup averages x-bar. The other chart examines variation in the subgroups standard deviation s . The (x-bar / s) - chart can be used whenever one can use the (x-bar / R) - chart. The (x-bar / s) - chart should be used instead the (x-bar / R) - chart if the subgroup is larger than 10. In this case, the standard deviation is a better measurement than the range for the variation between individual measurements in a subgroup.

Process Control Charts – Exercise 3 Throw the Dice: Step 1: Throw the dice 30 times and record the results in the table on the right. Step 2: Draw a Histogram of the 30 data points in one of the spreadsheets below. Step 3: Calculate the average to 2 consecutive throws and draw the histogram of the resulting 15 data points. What do you see and why?

The number of defect phones produced per hour where
1. hour: 100 phones and 10 defect phones.
11. hour: 130 phones and _ defect phones ???
12. hour: 20 phones and 5 defect phones. Something wrong ???
Process Control Charts – The Binomial Distribution

What is the probability that in a subgroup of n = (20, 40) phones will be exactly
np = 0 defect phones ?
1 defect phone ?
2 defect phones ?
3 defect phones ?
4 defect phones ?
5 defect phones ?
6 defect phones ?
7 defect phones ?
8 defect phones ?
9 defect phones ?
10 defect phones ?
What is the standard deviation s of the distribution ?
Process Control Charts – Binomial Distribution Example where

Process Control Charts – The Binomial Distribution Number of defect items 1 0 2 3 4 5 6 7 8 9 Average

Process Control Charts – The p - Chart The p - chart is used to look at variation in the yes/no type. It can for example be used to determine the percentage p of defective items in a group of items. The number n of items in each group has not to be constant, but should not vary more than 25 %. Operational definitions must be used to determine what constitutes a defective item. The percentage of defect items is given by

Process Control Charts – The p – Chart Example

Process Control Charts – The np - Chart The np - chart, like the p - chart, is used to look at variation in yes/no type attributes data. np - charts are used to determine the number np of defective items in a group of items. The p - chart looked at the percentage of defective items in a group of items. Because the np - chart uses the number of defects, it is easier to use. However, the major difference between the np - chart and the p - chart is that the subgroup size has to be constant for the np - chart. This is not necessary for the p - chart.

The number of wrong assembled components in SMD made on 20 PCBs where
1 - 20: 10 wrong assembled components
160 - 180: _ wrong assembled components ???
180 - 200: 2 wrong assembled components. Something wrong ???
Process Control Charts – The Poisson Distribution

What is the probability that exactly
c = 0 components ?
1 components ?
2 components ?
3 components ?
4 components ?
5 components ?
6 components ?
7 components ?
8 components ?
9 components ?
10 components ?
are wrong assembled ?
What if the average number c-bar of wrong assembled components is 3 ?
What is the standard deviation s of the distribution ?
Process Control Charts – Poisson Distribution Example where and

Process Control Charts – The Poisson Distribution Number of defects 1 0 2 3 4 5 6 7 8 9 Average

Process Control Charts – The c - Chart The c - chart is used to look at variation in counting-type attributes data. It is used to determine the variation in the number of defects in a constant subgroup size. For example, a c - chart can be used to monitor the number on injuries in a plant. In this case, the plant is the subgroup. To use the c - chart, the opportunities for defects to occur in the subgroup must be very large, but the number that actually occur must be small.

Process Control Charts – The u - Chart A u - chart is used to examine the variation in counting-type attributes data. It is used to determine the variation in the number of defects per inspection unit (subgroup). The size of the subgroup does not have to be constant. The subgroup size, n , for a u - chart is expressed in terms of the number of inspection units. The u - chart is very similar to the c - chart. The only difference is that the subgroup size for the c - chart must be constant. This is not necessary for the subgroup size of a u - chart. To use the u - chart, the opportunities for defects to occur in the subgroup must be very large, but the number that actually occur must be small.

Process Control Charts – Charts for Attribute Data Defective Items Defects Number (constant subgroup size) Percentage (variable subgroup size) np - chart c - chart u - chart p - chart

Process Control Charts – Summary Statistics Mean Value Standard Deviation Normal Poisson Binomial Distribution x 1 , x 2 , ..., x N are the measurements and N is the number of measurements. (np) 1 , (np) 2 , ..., (np) N are the number of defects in the N subgroups and n, n 1 , n 2 , ...,n N are the number of items in each subgroup. (np) 1 , (np) 2 , ..., (np) N are the number of defects at each time and N is the number of measurements/subgroups.

Process Control Charts – Exercise 4 Black Beads: Step 1: Take 20 beads out of the bag and record the number of black beads in the sample. Step 2: Repeat Step 1 until you have 25 data points. Step 3: Draw the histogram of the 25 data points in the left spreadsheets below. Step 3: Select the correct process control chart and draw it in the right spreadsheet.

Process Control Limit – The Basic Idea
Process capability is defined as the full range of normal process variation.
Upper Control Limit Lower Control Limit average average +1*s(igma) average -1*s(igma) average +2*s(igma) average -2*s(igma) average -3*s(igma) average +3*s(igma) 34.13 % 34.13 % 13.60 % 13.60 % 2.14 % 2.14 % 0.13 % 0.13 % Variability

Process Control Limit – Upper & Lower Control Limit Upper Control Limit (UCL) = average + 3*sigma Lower Control Limit (LCL) = average - 3*sigma average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

Process Control Limit – Upper & Lower Control Limit Because the variation of a process is not known in before hand, one can not calculate or define the control limits in advance . Control limits are characteristics of a stable process . They bound the variation of the process that is due to common causes . The calculation of the control limits should be based on at least 20 to 25 data points from a process that was in statistical control (stable). The limits should not be recalculated and modified unless there is a reason to do so (e.g. a process change).

Process Control Limit – Two Types of Process Variability where the constant d 2 depends on the number of items in each subgroup used to calculate the range. The LT and ST subscripts represent long-term and short-term variability. The difference between s LT and s ST gives an indication of how much better one can do when using SPC.

Process Control Limit – The x - Chart Upper control limit = Lower control limit = Upper control limit = Lower control limit = The x- chart The R- chart , where x 1 , x 2 , ..., x N are the measurements, N the number of measurements, , and .

Process Control Limit – The x-bar/R - Chart Upper control limit = Lower control limit = The R- chart Upper control limit = Lower control limit = The x-bar - chart where x-bar 1 , x-bar 2 , ..., x-bar N are the averages of each subgroup, n the number of items in a subgroup, N the number of subgroups, . , and

Process Control Limit – Factors for x- and x-bar/R - Charts n 2 3 4 5 6 7 8 9 10 A 2 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 D 3 0 0 0 0 0 0.076 0.136 0.184 0.223 D 4 3.267 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.777 d 2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078

Process Control Limit – The x-bar/s - Chart Upper control limit = Lower control limit = Upper control limit = Lower control limit = The s- chart The x-bar - chart , and where x-bar 1 , x-bar 2 , ..., x-bar N are the averages of each subgroup, s 1 , s 2 , ..., s N are the standard deviations of each subgroup, n the number of items in a subgroup, N the number of subgroups, .

Process Control Limit – Factors for x-bar/s - Charts n 2 3 4 5 6 7 8 9 10 A 3 2.659 1.954 1.628 1.427 1.287 1.182 1.099 1.032 0.975 B 3 0 0 0 0 0.030 0.118 0.185 0.239 0.284 B 4 3.267 2.568 2.266 2.089 1.970 1.882 1.815 1.761 1.716 c 4 0.7979 0.8862 0.9213 0.9400 0.9515 0.9594 0.9650 0.9693 0.9727

Process Control Limit – The np - Chart Lower control limit = Upper control limit = with and where np 1 , np 2 , ..., np N are the number of defect items in each subgroup of constant size n, and N the number of subgroups.

Process Control Limit – The p - Chart Lower control limit = Upper control limit = for i = 1, 2, 3,..., N, where (np) 1 , (np) 2 , ..., (np) N are the number of defect items in the subgroups and n 1 , n 2 , ..., n N are the number of items in the N subgroups. Note : The sample sizes should not vary more than 25% around the average sample size when using control limits for the whole chart. with and or or Control limits for whole chart Control limits for each subgroup

Process Control Limit – The c - Chart Lower control limit = Upper control limit = with where c 1 , c 2 , ..., c N are the number of defects in each subgroup of constant size and N the number of subgroups.

Process Control Limit – The u - Chart Lower control limit = Upper control limit = with and where c 1 , c 2 , ..., c N are the number of defects in the subgroups and n 1 , n 2 , ..., n N are the number of items in each of the N subgroups. Note : The sample sizes should not vary more than 25% around the average sample size.

Process Control Charts – Exercise 5 Black Beads: Calculate the average and the upper and lower control limit for the “Bead” exercise.

USL LSL USL LSL large variation  problem exist  root cause analysis  process improvement trend  problem occurs  root cause analysis  corrective and/or preventive action Defect Defect nominal value nominal value Out-of-Control & Process Improvement

50 55 = USL LSL= 45 50 55 45 Sample Sample 50 55 45 50 55 45 Process Tempering & Overcontrol

50 55 45 LSL USL Process tampering may substantially increase the product variability since the process average is shifted each time an adjustment is made. Process Tempering & Overcontrol

Out-of-Control Criteria – Two Causes of Variation Common Causes : Causes that are implemented in the process due to the design of the process, and affect all outcomes of the process. Identifying these types of causes requires Design of Experiment (DOE) methods. Special Causes : Causes that are not present in the process all the time and do not affect all outcomes, but arise because of specific circumstances. Special causes can be identified using SPC. Shewhart (1931)

Out-of-Control Criteria – Two Types of Processes Unstable Process : A process in which variation is a result of both common and special causes . Stable Process : A process in which variation in outcomes arises only from common causes .

Time Target Target Target Target UCL LCL UCL LCL UCL LCL UCL LCL "In-Control" and "Out-of-Control" Processes

Target Time Target Target Target UCL LCL UCL LCL UCL LCL UCL LCL "In-Control" and "Out-of-Control" Processes

SPC Out-of-Control Criteria – The Types of Signals
A signal of a special causes of variation :
Is a systematic pattern of the characteristic charted.
Has a low probability of occurring when the process is in control.

P = 0.0013 (0.13 %) SPC Criteria – 1 Point above or below 3 Sigma Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

P = 0.001 (0.1 %) SPC Criteria – 2 of 3 Points above or below 2 Sigma Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

P = SPC Criteria – 4 of 5 Points above or below 1 Sigma Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

P = SPC Criteria – 8 Points on the same Side of the Average Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

SPC Criteria – Trend of 7 Points Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

P = SPC Criteria – 15 consecutive Points in the 1 Sigma Zone Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

*) The number of runs (crossing the average line) should be about one-half of the number of points on the control chart. SPC Criteria – Too few or too many Runs *) Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

P = SPC Criteria – 8 Consecutive Points with none in the 1 Sigma Zone Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

SPC Criteria – Seasonal Variation Patterns Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

SPC Out-of-Control Criteria – Summary x x / R x / s c u np p Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 Rule 6 Rule 7 Rule 8 Rule 9 Chart - -

SPC Out-of-Control Criteria – Exercise 6 Efficiency Out-of-Control Conditions: Determine why the process control chart below indicates that the efficiency of production line H300 is out-of-control. Notes:

1. Applying the Central Limit Theorem to make the average of the subgroups normally distributed.
2. Dividing the sources of variation in the process outcomes into two different subgroups (short-term and long-term variation).
3. Optimizing the probability of identifying a shift in the process average with the next observation.
Sample Size and Frequency – Rational Subgrouping

If a shift in the process average of “E” units will harm the customer or one of the next process stages, the necessary subgroup sample size (n) can be calculated as: where The next plotted point will with 90% confidence identify a process shift larger than “E” units, that means the next point will be above or below 3 sigma control limits. Sample Size and Frequency – Subgroup Size and Precision

avg avg + avg + E E Sample Size and Frequency – Subgroup Size and Sensitivity

The frequency of sampling of two consecutive subgroups can be determined by dividing the average time period between two out-of-control situations by at least 3 but not more than 6.
However, no general rule can be defined about which time interval works best. You have to start with a good guess and refine the time interval if necessary.
Sample Size and Frequency – Sample Frequency

Out-of-Control-Action-Plans (OCAP) Activators (out-of-control decision rules) Checkpoints (list of possible assignable causes) Terminators (corrective actions) An OCAP is a flowchart that guides the operator through a defined and repeatable response to “any” out-of-control situation .

Out-of-Control-Action-Plans (OCAP) Start Checkpoints Activators Corrective Actions No No No Yes Yes Yes Yes Yes Yes End No No

Out-of-Control-Action-Plans – Activators 1. One point outside the 3-sigma control limits. 2. A run of at least seven or eight consecutive points, where the type of run could be either a run up or down, a run above or below the centre line. 3. Two out of three consecutive points plot beyond from the 2-sigma warning level. 4. Four out of five consecutive points at a distance of 1-sigma or beyond. 5. One or more consecutive points near a 2-sigma warning or 3-sigma control level. etc.

Out-of-Control-Action-Plans – Checkpoints The checkpoints instruct the operator to investigate specific items as possible assignable causes for the out-of-control situation. Once a checkpoint has identified a probable assignable cause for the out-of-control situation, the OCAP will flow into a terminator or corrective action.

Out-of-Control-Action-Plans – Terminators The terminator contains a detailed description of the corrective action that the operator has to take to resolve the out-of-control situation.

An Analysis of Out-of-Control-Action-Plans ...
... typically generate one or more of the following actions:
Eliminate the most common assignable causes
Analyze the activators
Revise the order of the checkpoints and terminators
Train the operators to perform more of the corrective actions included into the OCAP to resolve out-of-control situations

Some Benefits of Out-of-Control-Action-Plans ...
The OCAP is a systematic and ideal problem-solving tool for process problems because it reacts to out-of-control situations in real time.
OCAPs standardize the best problem-solving approaches from the most skilled and successful problem solvers (experts/operators).
The OCAP also allows (and requires) off-line analysis of the terminators to continually improve OCAP efficiency.

When SPC fails, look in the mirror ...
People are trained without regard for the need to know or implementation timing.
Once the necessary charts are created, they are rarely reviewed.
Charts have characteristics or parameters that do not really represent the process.
Control limits are not reviewed or adjusted, or conversely, they are adjusted too often.
Someone other than the process operator maintains the chart. (This is not always bad, however)
The process is not capable or set up well off target.
Corrective actions and significant events are not recorded on the chart.

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