# process control charts

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Process Control Charts. VOCABULARY. IMPORTANT TERMS: Nominal: Data at expected value Discrete: Data with only a finite number of values Indiscrete: Data of Acceptable vs. Unacceptable Variable: Property being measured Under Control: Variables fall in a nominal range - PowerPoint PPT PresentationTRANSCRIPT

Process Control Charts

Process Control Charts

Process Control Charts

In a manufacturing assembly line, the quality control engineer needs to know and be able to prove that the manufacturing process is under control.

Many companies that buy parts from suppliers will not accept a delivery of parts unless the supplier running the manufacturing sub-component line can prove that they are producing quality products.

Statistical process control and process control charts are means by which the quality control engineer can determine if the line is working properly. Let us then examine process control charts. 1VOCABULARYIMPORTANT TERMS:Nominal: Data at expected value Discrete: Data with only a finite number of valuesIndiscrete: Data of Acceptable vs. Unacceptable Variable: Property being measuredUnder Control: Variables fall in a nominal rangeData Points: Measurements takenDatum: A fixed reference point for measurementsThis slide list a few important terms used in developing process control charts.

Normal Data is described as the data that is normally expected.A type of data is discrete if there are only a finite number of values possible.Indiscrete Data is data taken on the number of parts deemed to be defective vs. the number of parts which are acceptable.The variable being observed is the property of the part on the line which is measured. An example is the length or the diameter.A manufacturing line that is under control is one where all the measured variable fall within a prescribed normal range of measurements.A data point is simply the measurement made and plotted on the statistical process control chart.A datum is the fixed reference point for measured data.2Used to test if the process is in controlUsed to see if significant changes have occurred in the process over timeIndiscrete or Continuous Data Chart or X-R ChartMeasurement at time intervals Measurements compare the control over time

Example units of measurement to Use:Length (mm) Volume (cc)Weight (gm.) Power (kwh)Time (sec, min, hr.) Pressure (psi)Voltage (v)Discrete Data Charts or PN-P ChartsInspection on lot or batch of parts; Notation of the number of good and defective parts

Variable representation:The number of parts inspected in the lot = nFraction of defective in lot = pNumber of defectives = pn

Process Control Charts

Process control charts are used to test if the process is in control and to see if significant changes have occurred in the process over time. There are two type of process control charts: a.) Indiscreet or Continuous Data Chart sometimes called X-R Charts, andb.) Discrete Data Charts sometimes called pn-p charts

For the Indiscrete Chart, measurements of the product are taken over time. As an example, the diameter of a machined part might be taken every two hours as the assembly line is in operation.

For the Discrete Chart, an inspection is done on a batch of parts and the number of acceptable and the number of defective parts in that batch are noted.

3

In the manufacturing process, car engine valve stems are being machined with a nominal diameter of 13 mm. Samples are taken at the following times of day: 6:00, 10:00, 14:00, 18:00 and 22:00, for 25 consecutive days. The diameter measurements (data) from these samples are presented in the table on the next slide.Classroom Example - R CHART CONSTRUCTION

Indiscrete Chart

A classroom example of the construction of an Indiscrete Chart:

Engine valve stems are an integral part of an automotive engine. In the manufacturing process, valve stems are being machined with a nominal diameter of 13 mm.

Samples are taken at the following times of day: 6:00, 10:00, 14:00, 18:00 and 22:00, for 25 consecutive days.

The diameter measurements (data) from these samples are presented in the table on the next slide.

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Sample data obtained from the Classroom Example discussed on Slide 4.

Notice how the data is placed in a table format. The headings provide the times.

The use of the variable X is the mean of the five samples. The R, and (i.e., Summation Symbol), will be discussed as the table is explained.5

Steps to formulating the chart:

Step 1: Collect the data

Step 2: Sort the data into subgroups, such as lots, order number, or daysStep 3: Identify the values for the variables n and k, wheren = the size of the sub group (i.e., five times)k = the number of sub groups (i.e., 25 days)Steps to formulating the Indiscrete Chart:

The first step is to collect the data in the form required. Sometimes you will be told how the data should be collected, other times you will need to design the data table.

The second step is to sort the data into subgroups. In this case, there are five subgroups representing each of the five times per day that data was taken.

If you look at the data, you will notice that on day one, the diameter of the samples measured ranged from 12.1 mm to 14 mm in diameter. You will need to know this information when you determine the range for the data.

In step 3 the subgroup mean, that is the mean diameter of the samples read is calculated. This is repeated for all 25 subgroups in this example using the equation illustrated here.In step 4, the rage in subgroup data is determined using the largest diameter minus the smallest diameter measured in each subgroup.6

Steps to formulating the chart:

Step 4: Calculate the mean for each group that will be represented by

Steps to formulating the Indiscrete Chart continued:

Step 4: You will calculate the mean for each subgroup row of data collected.

The first subgroup, Subgroup #1: Has the following data:

14.012.613.213.112.1

The formula states that you add up the data for one subgroup, and divide it by the number (n) of entries. The result is 13.00, which is the mean of the five datum points.

You repeat this step for all 25 subgroup entries and place your result in the Mean Column for each respective entry.7

Steps to formulating the chart:

Step 5: Calculate the range for each subgroup represented by R Steps to formulating the Indiscrete Chart continued:

Step 5, the range in the subgroup data for Subgroup #1 has data that is from 12.1 mm to 14 mm in diameter. Using the largest diameter, subtract the smallest diameter. The resulting number is the range of the measured data for Subgroup #1.

8Upper & Lower Control Limits9

Learning how to plot two separate charts: X Control ChartR Control ChartThe Upper Control Limit and the Lower Control Limit set the tolerance level for the control of the manufacture of a product.Calculating the Upper Control Limit and the Lower Control Limit:

The Upper Control Limit and Lower Control Limit set the tolerance level for the control of the manufacture of a product.

When a product is above the upper control limit or below the lower control limit, the part is said to be scrap and this is factored into the statistical data as a loss in production. It is important to determine the upper and lower control limits in order to know if a production system is controlled (i.e. is stable, with variation only coming from sources common to the process) then no corrections or changes to the process control parameters are needed or desirable.

The next several slides will help you learn how to plot two separate charts: the X Control Chart and the R Control Chart. The upper and lower control limits will be plotted on these charts.

9Steps to Calculating the Upper & Lower Control Limits

Steps to Calculating the Upper Control Limit and the Lower Control Limit:

Step 6. The average mean, x double bar, is the sum of all the means calculated in Step 4 divided by the total number of subgroups (k).

NOTE: The mean for Sub Group #1 has been inserted into the Overall Mean formula as well as the value for k. You will need to finish the calculation to find the overall mean.10Continuation of Calculating theUpper & Lower Control Limits

Continuation of the Steps to Calculating the Upper Control Limit and the Lower Control Limit:

Step 7. The average value of the range (R bar) is the sum of all the ranges calculated in step 5 divided by the total number of subgroups (k).

NOTE: The finding of the average value of the range is left for you to calculate.11Manufacturing Statistics

A2 is from the table based on the size of the subgroup (i.e., Five reading times) D4 & D3 is from the table based on the size of the subgroup (i.e., Five reading times) Manufacturing Statistics:

Manufacturing statistics will now be used to finish the calculations. The table at the top of this slide provides the results of a rigorous statistical analysis of data. We do not need to go into the complexities of the statistical analysis at this time, but it is important for you to realize we are learning the early stages of manufacturing statistics.

For the X Control Chart, the central line is simply given by the overall mean calculated in Step 6. The Upper Control Limit is calculated as the overall mean plus the value for A2 from the table based on the size of the subgroup (in this case 5 reading times) times the average range value. The Lower Control Limit is the overall mean minus the statically calculated range.

For the R Control Chart, the central line is the average value of range, the upper control limit is the D4 value times the average value of range and the lower control limit is the D3 value times the average value of range.

With these calculations completed, you are now ready to plot the control charts.12

x bar RX double barR barCLxUCLxLCLxCLrUCLrLCLr = Using the previous slides to guide you, calculate the required values and complete the table.

NOTE: Your teacher may print this page out for you to use as your data collection table or you may be asked to create a similar table in an electronic program, such as Excel.

Be sure to keep the steps logged in your AMJT Notebook for future reference and to refer to during the remainder of the project. You will be asked to determine manufacturing statistical data for different projects throughout the remainder of the course.13Step 8:Plot Chart

Plot Chart

14

Chart Variations

Using Statistical Process Control Charts.

As an example, Distribution A is very similar to the process control chart we just developed and drew. This chart represents a process that is under control. The distribution of data in Distribution A is normal as illustrated by the data distribution curves immediately above the Distribution A region.

Notice how Distribution B data Range falls within the control limits and the data curves are normal, however, the Average Mean values fall on the high level, and in several cases are above the upper control limit. This means that the process is out of control by producing parts that are above the acceptable values of production.

Distribution C has Average Mean values falling for the most part within the control, except there is one point too large, but the Range is decidedly outside the acceptable control. This means that part sizes are falling all over the place and the process is out of control.

Based on what you have learned, what is your opinion about the three manufacturing processes depicted in the three charts at the bottom of the slide?15Future Prediction

Predicting the Future

The statistics from the control charts also helps manufacturers to predict the future.

In the top statistics chart, over time, everything seems to be running with stability. This allows the manufacturer to predict that unless something very unpredictable happens, the process will continue to run under control in the near future.

The lower series of samplings, however, show a large variation and unpredictability. This manufacturing process chart demonstrates that it may become very uncertain that the process will remain in control in the future.16An inspector of car wheel rims, working at the end of a manufacturing line, near the end of each shift must inspect the lot of wheel rims made during that shift.

On good days when the welder is running properly, over 400 wheel rims are made per batch. On poor days, as low as 50 to 60 wheel rims are made per batch. The inspector marks on the check sheet for each batch the total number of wheels inspected and the number of defects returned for rework for each lot. Classroom Example P-Control Chart Construction

P-Control Chart

The second type of control chart is the P Control Chart.

When generating this chart, inspections are performed on batches of product and the record of acceptable and defective parts observed during the inspection are noted.

Consider this classroom example:

An inspector of car wheel rims, working at the end of a manufacturing line, near the end of each shift must inspect the lot of wheel rims made during that shift.

On good days when the welder is running properly, over 400 wheel rims are made per batch.

On poor days, as low as 50 to 60 wheel rims are made per batch.

The inspector marks on the check sheet for each batch the total number of wheels inspected and the number of defects returned for rework for each lot.

1718

Data Collected of Wheel Rims Inspected:

This table depicts the results of the wheel rim inspections.

Some days as many as 440 wheel rims were produced and inspected (subgroup size n); on other days, as few as 65 wheel rims were made and inspected.

For each subgroup batch, the number of defective wheels are noted under the variable pn column.

Using this data, the percent of defectives and the upper and lower control limits may be calculated.18Steps to Calculating P-Control Chart

Step 1. Collect data

Step 2. Divide the data into sub groups (i.e., usually days or lot). Each sub group size should be larger than 50 units, wheren = the number in each subgrouppn = the number of defects in each sub groupSteps to Calculating P-Control Chart:

Step 1. Collect the data from the inspection of each batch.

Step 2. The number of items inspected in each subgroup (n) and the number of items determined as defective in each subgroup (pn) are noted. NOTE: In order to get acceptable data, subgroup sizes greater than 50 samples are usually required.

19Calculating Fraction of Defectives

Step 3. Calculate the fraction of defective parts using the following formula:Where p = fraction (decimal) of the number of defectivespn = number of defects in each subgroupn = number in each subgroupNOTE: To convert result to percentage(%), multiply the result by 100

Calculating the Fraction of Defectives:

Step 3. In this step, the fraction of defective parts for each subgroup are calculated. This fraction (p) is calculated using the equation p = pn divided by n, where p is the fraction or decimal result and is the fractional representation of the number defectives, pn is the number of defects in each subgroup, and n is the number of inspections in each subgroup.

20Calculating Average Fraction of Defectives

Step 4. Calculate the Average Fraction of Defectives using the following formula:Average Fraction of Defectives:

Step 4. The average fraction of defective is calculated by summing up the total number of defectives and dividing that total by the total number of samples tested.

The center line of the chart will be the average fraction of defective calculated. The Upper and Lower Control Limits for each subgroup is calculated using the equations giving in Step 5 presented on the next slide.21Calculating Control Limits

Step 5. Calculating the Control Limit for each Subgroup:Calculating Control Limits Upper and Lower for each Subgroup:

The Upper and Lower Control Limits for each subgroup is calculated using the equations provided.

The Central Line (CL) is equal to the average of the fraction of defectives found in Step 4.

The Upper Control Limit (UCL) is equal to the average of the fraction of defectives plus the value of three times the square root of the fraction resulting in the average of fraction of defectives times the result of one minus the average of fraction of defectives all divided by the number of inspections within a subgroup.

The Lower Control Limit (LCL) is equal to the average of the fraction of defectives minus the value of three times the square root of the fraction resulting in the average of fraction of defectives times the result of one minus the average of fraction of defectives all divided by the number of inspections within a subgroup.

NOTE: If students are weak in using the square root function, provide specific instruction on the mathematical order of operations and how the square root must be completed prior to continuing with the remaining operations in proper order.2223

For this wheel rims example, review the calculated data and confirm that you understand how each number is calculated.23Step 6:Draw P Control Chart

Plot Chart

Graphing the P-Control Chart:

Step 6. The plot the P-Control Chart, as seen in this slide, is completed as the prior plot charts. Refer to your notes to guide you and to verify you understand how this graphing is completed.

NOTE: The Center Line is constant throughout the subgroups, but the Upper And Lower Control Limits vary with each data sampling. The percent defective also changes with each data subgroup.

Based on how the data points fall within the UCL and LCL, it appears the process was under control for the entire duration of sampling.24Classroom Example On an assembly line of windshield wiper motors, the inspector selects randomly 100 motors per hour to examine.

The inspector notes on the check sheet the number of defective motors in each 100 selected.

The inspector samples 100 samples for a total of 30 sampling events.PN Control Chart

PN Control Chart

The PN Control Chart is used when the inspector who inspects each batch of samples elects to inspect some constant number of product sample per batch rather than inspecting all samples per batch. This is often useful when the total batch size is large and to inspect every sample would require an excessive amount of time.

Classroom Example:

On an assembly line of windshield wiper motors, the inspector selects randomly 100 motors per hour to examine. The inspector notes on the check sheet the number of defective motors in each 100 selected. The inspector samples 100 samples for a total of 30 sampling events.

25

PN Control Data Chart

PN Control Data Chart

Study the chart and see if you can determine, based on what you have learned what the variables may be and how you might determine the average pn, n, and the Upper and Lower Control Limits.

Recopy of the Classroom Example for reference:

On an assembly line of windshield wiper motors, the inspector selects randomly 100 motors per hour to examine. The inspector notes on the check sheet the number of defective motors in each 100 selected. The inspector samples 100 samples for a total of 30 sampling events.

26Calculating the PN Control Values27

27Plotting of PN Control Chart28

Plotting of PN Control Chart:

This example shows that the process was under control for most of the sampling time except for around the 20th and 21st sampling time.

Based on your experience to date, what do you suppose happened at these sample times?28Check For UnderstandingPlease Develop a Control Chart for This Valve Manufacturing line:

Your Company makes gate valves which you guarantee to flow water at 3 gallons per minute when fully open. Any restriction or misplaced gaskets in the opening will alter this flow rate. Your inspector at the end of the line tests one valve each hour by measuring the flow for one minute in sample valves. The flow rate is recorded for several days in the table in the next slide. Is this operation in control ?Your Company makes gate valves which you guarantee to flow water at 3 gallons per minute when fully open. Any restriction or misplaced gaskets in the opening will alter this flow rate. Your inspector at the end of the line tests one valve each hour by measuring the flow for one minute in sample valves. The flow rate is recorded for several days in the table in the next slide. Is this operation in control ?

29Check For UnderstandingFlow Rate in Gate Valve Inspection (gal/min)Day9 AM10 AM11 AMNoon1 PM2 PM3 PM13.113.202.992.853.003.082.9022.983.012.862.553.063.183.1132.862.993.013.103.032.993.1043.053.042.953.083.012.962.8952.583.253.163.083.012.992.9863.093.033.063.022.992.953.0173.123.042.652.993.303.032.9983.012.972.983.013.003.013.02Did you develop the statistical Process control chart? Was the process under control? Can you say anything about the data obtained and how the line is running?30Step 1:Collect Data

Step 2:Sort data into subgroups (i.e. lots, order #, days, etc.)

n = size of the subgroup {in this example 5 times per day)

k = number of subgroups {in this example 25 days}

Step 3:Find the mean for each subgroup (

)

=

Step 4:Find Range for each subgroup ( R )

R = X largest value - X smallest value_913787733.unknown

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Step 1:Collect Data

Step 2:Sort data into subgroups (i.e. lots, order #, days, etc.)

n = size of the subgroup {in this example 5 times per day)

k = number of subgroups {in this example 25 days}

Step 3:Find the mean for each subgroup (

)

=

Step 4:Find Range for each subgroup ( R )

R = X largest value - X smallest value_913787733.unknown

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Step 1:Collect Data (lot size set constant)

Step 2:Calculate Values

=

CL =

n

UCL =

n + 3

LCL =

n - 3

Step 3:Plot Chart

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