Statistical Process control.

General Purpose. In all production processes, we need to

monitor the extent to which our products meet specifications.

In the most general terms, there are two "enemies" of product quality:

a. Deviations from target specifications, and

b. Excessive variability around target specifications.

Basic Techniques of Quality control.

Basic 7 Quality control techniques,X-bar and R charts.Gage R&R.Scatter plot.HistogramFlow chart.Cause and Effect Diagram.Pareto chart.

Gage R&R. Gage repeatability and reproducibility analysis addresses

the issue of precision of measurement. The purpose of repeatability and reproducibility

experiments is to determine the proportion of measurement variability that is due to

1) The items or parts being measured (part-to-part variation

2) The operator or appraiser of the gages (reproducibility), and

3) Errors in the measurements over several trials by the same operators of the same parts (repeatability).

In the ideal case, all variability in measurements will be due to the part-to-part variation, and only a negligible proportion of the variability will be due to operator reproducibility and trial-to-trial repeatability

Example. Overview. Suppose you are manufacturing small kilns that are used

for drying materials used in other manufacturing processes. Assume for this example that the temperature range at

which these kilns operate is usually between 90 and 110 degrees Celsius (°C).

Before performing a process capability analysis ,you want to be sure that the measurement system you are using is sufficiently precise to detect variability between kilns.

A repeatability and reproducibility (R & R) study will first be designed to assess the precision of the measurement system, and then the results of that experiment will be analyzed.

Component of Variance.

The last column of numbers reports the variability due to different sources relative to the total variability in the measurements:

Repeatability of measurements accounts for 6.5%, reproducibility across appraisers accounts for 8.1% of the total

variability, the part-to-part variation accounts for 85.4%, Using the common guidelines for evaluating the quality of the

measurement system (under 10% = OK, 10% to 30% = questionable, above 30% = needs improvement,You could now proceed to use this measurement system to put a quality control system.

Designing the R & R Experiments. Suppose you have five engineers who are routinely involved in the

production process. Those engineers will serve as your Operators of the gages; thus enter 5 in the Number of operators box. Also, assume that within the available time frame, you can manage to run a study where each engineer measures 8 kilns (Parts) three times (3 Trials). Therefore, enter 8 as the Number of parts and 3 as the Number of trials in the respective boxes.

Graphical presentation.

Identifying outliers: To identify outliers with regard to measurement precision, you want to chart the variability of measurements across trials. Two standard charts for controlling the variability of a process are the R chart of ranges and the S (sigma) charts of standard deviations both can be produced by operators or by parts(left side).

Box and whisker plot: For each operator, this plot summarizes the range of average measurements (averaged across trials) as well as the distribution of those average measurements. In this case, for each operator the median seems to fall in the upper part of each box.(right side).

X-bar and R chart.

X-bar chart. In this chart the sample means are plotted in order to control the mean value of a variable (e.g., diameter of piston rings, strength of materials, etc.).

R chart. In this chart, the sample ranges are plotted in order to control the variability of a variable.

X-bar and R chart.

Six graphs.

Run test.

Run test are designed to detect patterns measurement that may indicate that the process is out of control.

In quality control charting, when a sample point (e.g., a mean in an X-bar chart) falls outside the control lines, you have reason to believe that the process may no longer be in control.

In addition, you should look for systematic patterns of points (e.g., means) across samples, because such patterns may indicate that the process average has shifted. The Quality control module perform the standard set of tests for such patterns; these tests are also sometimes referred to as runs rules or tests for special causes

Descriptive statistics.

Process Capability Indices. Quality Control describes numerous methods for

monitoring the quality of a production process. However, once a process is under control the question

arises, "to what extent does the long-term performance of the process comply with engineering requirements or managerial goals?

A process Capability index is a numerical summary that compares the behavior of a product or process characteristics to engineering specifications.

A capability index relates the voice of the customer (specification limits) to the voice of process”.

A Capability index is convenient because it reduce the complex information about a process to a single number.

Example. Overview. This example is based on the Piston data .

suppose you are producing piston rings for a small automotive engine; the target diameter of the piston rings is “74 millimeter”.

Note that unless the production process is under control, performing these analyses is rather pointless; only when the process average and the process variability are stable can meaningful process capability indices be derived.

Assume for this example that the engineering specification limits for the process are ± .05 mm.

Piston rings with a diameter smaller than 74 - .05 = 73.95 or greater than 74 + .05 = 74.05 mm are considered scrap and can potentially cause significant quality problems later on if used in automotive engines.

The above spreadsheet showing the option of specification.

In the “Nominal” option we have to put our Target value, in this case it is “74mm”, and in Delta option we have to put tolerance value, in this case it is .05.

As expected, the Cp index (the ratio of the specification range over the process range) is greater than 1 (1.65), indicating a very capable process , also the k-value (non-centering correction) is close to zero indicating the process is centered around Target value.

From the above tables you can say with 95% confidence (Confidence Level) that 95% of the population (% of Population Included) fall within the limits denoted in the spreadsheet as the Lower and Upper Interval Limit.

Scatter plot. The scatter diagram graphs pairs of numerical data, with one

variable on each axis, to look for a relationship between them. If the variables are correlated, the points will fall along a line or

curve. The better the correlation, the tighter the points will hug the line.

When to Use a Scatter Diagram? When your dependent variable may have multiple values for each

value of your independent variable. When trying to determine whether the two variables are related

such as….a. When trying to identify potential root causes of problems.

b. After brainstorming causes and effects using a fishbone diagram, to determine objectively whether a particular cause and effect are related.

c. When determining whether two effects that appear to be related both occur with the same cause.

Example. A manufacturing team drew a scatter diagram to test whether product

purity and iron contamination were related, but the plot did not demonstrate a relationship.

Then a team member realized that the data came from three different reactors.

Now patterns can be seen. Even without doing any calculations, it is clear that for

reactors 2 and 3, purity decreases as iron increases. However, the data from reactor 1, the solid dots do not

show that relationship.

Cause and Effect Diagram. The cause-and-effect diagram provides an

efficient summary of factors that impact a process, and hence can be used as a map to guide the overall quality improvement efforts.

It is one of the important tools for the Define phase of Six Sigma quality control efforts.

The general idea of the chart is rather straightforward. Suppose you want to turn on a reading light in your house one evening, and it won't light up.

Now consider the various variables or characteristics that make up the process (cause the light to come on), and that should be considered in order to fix this quality problem.

The cause-and-effect diagram shown above spells out the various potential causes of the problem encountered.

Usually, the chart is constructed by identifying the major categories of causes that affect the process in this example

Power, Bulb, Plug/Cord, and Lamp. The individual factors or causes that can be classified into these

major categories like Power outage, No house current, etc.

Pareto Chart. The Pareto chart analysis is a simple but powerful way of

identifying the causes of quality problems or loss.

It amounts to constructing a histogram of the number of quality problems or loss by some meaningful units.

According to the so-called Pareto principle, “The majority of the quality loss is caused by a small

number of factors”. Put another way, in many cases, “20% of problems often cause 80% of quality loss”

Example.

The data contain information regarding the complains of customers on the following parts of computers.

Our objective is to find out which parts have given maximum problem to the customers.

From the above graph and spreadsheet we can conclude that Monitor, CPU and Harddisk are creating almost 78% of total problem.

Global Statutory and regulatory compliance.

It is specifically designed to ensure compliance with FDA 21 CFR Part 11 regulations, Sarbanes-Oxley legislation as well as ISO 9000, 9001, 14001 documentation requirements.

Thank You.

Krishnendu Kundu

(Statistician)

StatSoft India.

Email- kkundu@statsoftindia.com

Mobile - +919873119520