1. QUALITY IMPROVEMENT TOOLS
by Miles M. Hamby, PhD
Copyright©2014 Miles M. Hamby

2. QUALITY IMPROVEMENT TOOLS
1. TALLY SHEET
2. HISTOGRAM
3. PARETO DIAGRAM
4. CAUSE AND EFFECT DIAGRAM
5. SRATIFICATION
6. SCATTER DIAGRAM
7. CONTROL CHART

3. TALLY SHEET
Test data or defects filled in the related column in preprinted form immediately after the test.
Observed or measured value need not be written down but can be indicated by a stripe/line.

4. Frequency table Class limits number 3.30 3.275 - 3.325 1 3.35
mid-marks
Number
n = 100
Total 1 2 3 4 5 6 7 8 9
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70 32 38 10

5. Histogram
Frequency distribution with bars representing the frequency of occurrence of a specific category.
Raw data are grouped in value and frequency and plotted in graphical form.
Shape can show the nature of the distribution of the data, as well as central tendency and variability.
Specification limits can be displayed to depict process capability

6. HOW TO READ A HISTOGRAM Histogram with an isolated part.
Cause may be mixed products of different machines, different inspectors, test equipment.
Histogram with an interruption.
Possible errors made in measurement of the preparation of the histogram. Check measuring equipment, reading methods, change number of classes.

7. Histogram with two peaks.
Probably products from two manufacturing processes.
Study the subdivision of the groups and make a histogram per group.
Distribution cut off at the left.
Products have been selected before hand.

8. COMPARISON WITH TOLERANCE LIMITS
Range (R) of measured values exactly in the middle (normal distribution)
In this situation no risk of rejects, due to small variations in the process.
Although R is within the tolerance the mean of the process is too close to the lower limit. A minor change in the production process will result in increased rejects. R
Spec limits R
Spec limits

9. R and the tolerance are exactly the same.
This situation offers no room for a change in the process i.e. any change in the process leads to rejects.
The tolerance is wider than R.
It is possible to reduce the specified tolerance or the accuracy of the process. R
Spec limits
Spec limits/ R

10. Process mean is too far to the left
Must be shifted to the nominal value.
Distribution is too wide.
Change the process to limit distribution or extend tolerance. R
Spec limits R

11. The Pareto Diagram
Data arranged in hierarchical order to allow most significant problems to be corrected first.
Histogram of Contribution Categories (ie, causes of defects or errors) along the horizontal axis (X) and cumulative percentage or number along the vertical (Y) axis.
Cumulative contribution can be actual numbers or relative frequency (ie, percentage of the total for each contribution category.

12. The Pareto Principle
A small number of causes – the “vital few” is responsible for a large percentage of the effect – usually 20%/80% ratio.
Many applications
20% factors cause 80% of the defects
20% of workers do 80% of the work
20% of the individuals will cause 80% of your headaches
In US, 20% of Americans own 94% of wealth
20% of solutions likely to remain viable after adequate analysis
20% of the work % and the last 10%) consume 80% of the time and resources.

13. Constructing a Pareto Diagram
Identify the defect Contribution Category (eg, “Defect Type”
Rank order them largest to smallest
Calculate the cumulative defects (eg, “Cumulative Defects”) for the Contribution Categories
(In Excel) create a bar chart with cumulative data (“Cumulative Defects”) as Y-axis and cumulative Contribution Category (“Defect Type”) as X-axis and

14. Interpreting the Pareto
The same data converted to percentages reveals the same decreasing arc, but depicts the “80%” break point.
In this case, “Color Variation” and “Misregister” contribute about 85% of the defects.
Conclusion - the best return for your efforts and resources would be to correct those processes.

15. CAUSE AND EFFECT DIAGRAM
Depicts a relationship between the ‘effect’ (ie undesirable outcome of a process) and its causes. 
The undesirable outcome is shown as effect, & related causes are shown as leading to or potentially leading to said effect. 
This tool has one severe limitation, however, in that users can overlook important, complex interactions between causes. 

16. Cause and Effect Diagram (AKA Ishikawa or Fish Diagram)
Problems in the process are usually caused by a combination of factors.
Depicts relationship between the ‘effect’ (ie undesirable outcome of a process) and its causes.
Helps to identify where data should be collected.  
Limitation - user could overlook important, complex interactions between causes

17. Cause – Effect Diagram of Iron in the Product
Main contributors of “iron in product” are Materials, Measurement, Methods, Environment, Manpower, and Machines.
Factors in Materials include Raw Materials and Lab Solvents.
Factors in Raw Materials include H2O, DBT, and AKW-2.
Cause – Effect Diagram of Iron in the Product

18. Drawing a Fish Diagram
Define the characteristic of quality defect of the product
Write the quality characteristic in the “head” of the fish
Rib bones - Primary causes which directly affect the quality characteristic (connect to the spine) e.g., Materials, Methods, Men, Measurements, Machines.
Small bones – factors that influence the primary causes
Assign an importance to each factor and mark particularly important factors that seem to have a significant affect on the quality characteristic.
Evaluate each cause for the level of effect it has on the quality characteristics to determine the most probable root cause
Plan corrective action

19. Stratification
Organizing products into certain categories or ‘strata’ to compare product characteristics
Variations in the product characteristic produced by different strata indicates something may be wrong with one of the strata
Measure the product in each strata and determine – differences in product measurement may indicate a particular strata is the primary cause of the variation

20. Types of Strata
By supplier - variations in parts from different suppliers, brand, size of consignment, storage item and conditions.
By machine - variations in machine type, make, model, age position.
By operator – operator experience, age, training, gender.
By time - Are the data affected by time of day, season, position, in the operation lifecycle?
By environment - changes in humidity and temperature.
By material – different material makeup of product
Other strata – think of anything that could differentiate the product

21. Scatter Diagram (Scatterplot)
Depicts the relationship between two variables – X (horizontal) and Y (vertical)
Used to test for cause and effect relationships (but does not ‘prove’ one variable causes the change in the other)
Indicates strength of the relationship by ‘tightness’ of the scatter
X-axis values usually in order, eg, time, sample number
Y-axis values usually quantity, eg no. defects, dimensions

22. Example Scatterplot
Scatterplot of Defects in Pants
This example depicts the number of defects increased with each sample, ie, the process is producing more defects as time progresses.
Tightness of the scatter indicates strong correlation, ie, suggests causes of increase in defects is not random
Something is causing the process to produce more defects 2 3 4 5 6 7 1
Number of Defects 1 2 3 4 5 6
Sampling Sequence (3 samples, equal size, taken 6 in order)

23. Interpreting a ScatterplotY X Y X Y X
Y decreases as X increases -
tight data - strong negative correlation
Y increases as X increases –
loose data –
weak positive correlation
No apparent corresponding change in Y with change in X – loose data – no correlation

24. (proportion, dimension,
Control Chart
A scatterplot depiction of the measures of a product or process characteristic taken in sequence with the added plot of the desired allowable variation (control) limits.
Indicates a process may be going “Out of Statistical Process Control”, that is, the variation in product or process characteristics may be due to assignable causes (i.e., non-random).
Sample/lot No., Time, etc.
(proportion, dimension,
Statistic
count, etc)
Upper Control Limit (UCL)
Lower Control Limit (LCL)
Centerline
(mean, median, etc)
Upward trend and point exceeds UCL
Data points lying outside of specified limits (usually 3) indicate the process is not in “statistical process control”, ie the cause of the variation is not random.

25. Types of Control Charts
Variables Data
(measurement such as dimensions)
X-bar Chart (mean chart) ~ used for product with dimensions (normal distribution) – eg, diameters, throwing distance
R-Chart (range chart) ~ dispersion of data (normal distribution) – used same as X-bar
Attributes Data
(characteristics of the process, such as defects)
P-Chart ~ count-based (proportion defects in sample) – For binomial data, eg defective/not defective; used when ideal is 0% defects (Poisson distribution), eg typing errors, incorrect mailings

26. (Attributes Charts cont.)
C-Chart ~ count-based (no. of defects) – when samples have ≥1 defects (Poisson distribution) – eg, no. new infections per day in hospital; no. accidents per day
U-Chart ~ count-based - Average count per unit (Poisson distribution); eg, no. defects per lots of variable size
Other Charts Types
Cusum (Cumulative Sum) – sequential analysis technique used for monitoring change detection (normal distribution).
EWMA (Exponentially-Weighted Moving Average) – used to monitor either variables or attributes-type data using the entire history of output, ie, tracking all prior sample means (normal distribution).

27. X-bar Chart Example (cont.)
UCL = 5.08
LCL = 4.94
Sample number | 1 2 3 4 5 6 7 8 9 10
5.10 –
5.08 –
5.06 –
5.04 –
5.02 –
5.00 –
4.98 –
4.96 –
4.94 –
4.92 – =
x = 5.009
Rising trend of data indicate process is out of statistical control due to assignable causes
Diameter (CM)

28. Applications Summary Prioritizing cause analysis Pareto Diagram
Identifying effects & their root causes
Fish Diagram
Compiling data for analysis
Check sheets
Identifying patterns in a process
Histogram
Determining process consistency and capability
Control Charts
Testing hypothetical relationships between variables or characteristics
Scatter diagram
Identifying categories of causes of variation in product
Stratification

29. QUALITY IMPROVEMENT TOOLS
1. TALLY SHEET
2. HISTOGRAM
3. PARETO DIAGRAM
4. CAUSE AND EFFECT DIAGRAM
5. SRATIFICATION
6. SCATTER DIAGRAM
7. CONTROL CHART