Six Sigma Test 11 (ASQ Handbook Part 4)

Types of Attribute Control Charts

Types of Attribute Control Charts P-charts i. Control charts dealing with the proportion or fraction of defective product within the group under review ii. Pieces either conform or are rejected-→ Rejected parts are expressed as a portion of the sample size. iii. Best used for binary data (each item is one of the 2 categories) iv. Also used for comparisons across conditions rather than over time. v. A p control chart is used to look at variation in yes/no type attributes data. There are only two possible outcomes: either the item is defective or it is not defective. The p control chart is used to determine if the fraction of defective items in a group of items is consistent over time.

Variables are selected based on these guidelines:

Variables are selected based on these guidelines: a. Key process inputs (KPIV), analyzed to determine the effect of a process. b. Key process output (KPOV) determine process capability and process monitoring using control charting c. DOE and ANOVA also used to find variables.

4 Types of Attribute Control Charts

4 Types of Attribute Control Charts: 1. P-chart 2. NP chart 3. C-chart 4. U-chart

Deciding between u-chart and p-chart

Deciding between u-chart and p-chart With Attribute data, decide on what type of distribution the data follows. Binomial data takes on two values, usually "good" or "bad". If the sample size is constant, use an np-chart. If the sample size changes, use a p-chart. Poisson data is a count of infrequent events, usually defects. If the sample size is constant, use a c-chart. If the sample size changes, use a u-chart

Variables that are critical for selection for control charts are based on:

Variables that are critical for selection for control charts are based on: a. Importance of customer perception b. Objectivity (counted or measured) c. Clear indicators to suggest whether quality achieved.

Run Charts--Control Charts for Variables

d. Run Charts-→ for single point data

Attributes Chart:

Attributes Chart: a. Larger subgroup sizes (50-200) required to get detectable process shifts. b. Subgroup sizes should not vary more than 20% c. Recalculate control limits if the sample size changes.

Control Chart's Role in Maintenance of Statistical Control:

Control Chart's Role in Maintenance of Statistical Control: i. Expected range of variation will be the established standard against which other samples are compared. ii. Provides traceable evidence in detection of process changes in 3 ways: 1. Collection -→ Run the process and collect the data for plotting on graph/chart. 2. Control-→ calculate control limits to support analysis and establish process variability 3. Capability-→ ability of the process to meet customer specifications

Control Charts for Variables: X-bar & R-charts

Control Charts for Variables: a. X-bar & R-charts-→ data is readily available b. In statistical quality control, the X-bar and R chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. c. The chart is advantageous in the following situations:[2] i. The sample size is relatively small (say, n ≤ 10—X bar and s charts are typically used for larger sample sizes) ii. The sample size is constant iii. Humans must perform the calculations for the chart

Use of Control Charts

Control Charts: a. Primary purpose is to detect the special cause i. Used to attain the state of statistical control, monitor a process, and determine process capability. ii. Can monitor process stability. iii. Other techniques are used to reduce variation after the control chart detects the variation. iv. Control limits can be estimated at +/- 3 standard deviations from the men

Deciding on the Type of Control Chart to use when working with variable data

Deciding on the Type of Control Chart to use when working with variable data First decide what type of data you're dealing with. Variable data takes on a measurable, numeric value. There are many possible values. Attribute data consists of categories. There are only a few (usually two) discrete values. With variable data, decide how large subgroups are. If the subgroup size is one, then use an Individual measurements chart, with or without a moving R chart. If the subgroup size is from two to ten (or possibly twelve), then use an X and R chart. If the subgroup size is over ten (or twelve), then use an X and S chart.

Examples of processes suitable for monitoring with a c-chart include:

Examples of processes suitable for monitoring with a c-chart include: Monitoring the number of voids per inspection unit in injection molding or casting processes Monitoring the number of discrete components that must be re-soldered per printed circuit board Monitoring the number of product returns per day

Examples of processes suitable for monitoring with a u-chart include:

Examples of processes suitable for monitoring with a u-chart include: Monitoring the number of nonconformities per lot of raw material received where the lot size varies Monitoring the number of new infections in a hospital per day Monitoring the number of accidents for delivery trucks per day

Guidelines for using Rational Subgrouping

Guidelines for using Rational Subgrouping 2. Processes must not be out of control to use control chart. 3. If processes are out of control, then use run chart. 4. Selection should result in groups that are homogenous. 5. First subgroup should reflect product all produced 6. Most uselful information comes from smaller groups (less than 25) 7. Attributes control charges are based on binomial distributions and require 50 or more samples within subgroups.

Types of Attribute Control Charts: U=chart

In statistical quality control, the u-chart is a type of control chart used to monitor "count"-type data where the sample size is greater than one, typically the average number of nonconformities per unit. The u-chart differs from the c-chart in that it accounts for the possibility that the number or size of inspection units for which nonconformities are to be counted may vary. Larger samples may be an economic necessity or may be necessary to increase the area of opportunity in order to track very low nonconformity levels.[1] As with the c-chart, the Poisson distribution is the basis for the chart and requires the same assumptions.

MX-MR charts

MX-MR charts i. An individuals and moving range (X-MR) chart is a pair of control charts for processes with a subgroup size of one. ii. Used to determine if a process is stable and predictable, iii. It creates a picture of how the system changes over time. iv. The individual (X) chart displays individual measurements. The moving range (MR) chart shows variability between one data point and the next. Individuals and moving range charts are also used to monitor the effects of process improvement theories

Median Control Charts:

Median Control Charts: i. Plots the median of the sample rather than the average. ii. Often used when outliers are expected. iii. All data points in the sample are plotted and user connects the middle point in successive samples. iv. Paper gage is used to detect ranges outside the control limits. v. If gauge cant cover all the points, then range exceeds the control limits.

NP Chart--Attribute Data Control Chart

NP Chart i. Control charts dealing with the number of rejected items expressed as an integer. 1. If sample size is constant and defectives are being used, then np can be used rather than p chart. ii. When each data point is based on the same sample size, a special version of the p chart can be used. The np chart follows the same principle as the p chart, but actually plots the number of instances in a category over time rather than the proportion in the category. iii. The np control chart is used to determine if the number of defective items in a group of items is consistent over time. The subgroup size (the number of item in the group) must be the same for each sample.

Operating Characteristic Curve

Operating Characteristic Curve a. Plot of the true value of a process parameter against the probability that a single sample will fall within the control limits b. Show the ability of the chart to detect process changes.

Difference in NP, P, C, & U control chart?

P-chart (fraction non-conforming) C-chart (number of defects) U-chart (non-conformities per unit) p charts For discrete attribute data, use the p chart. Recall that discrete attribute data results when you categorize or bucket each instance you are measuring. For example, you might track defective and non-defective components in a manufacturing process. This chart plots the proportion ("p") of the data falling into the relevant category over time. np charts When each data point is based on the same sample size, a special version of the p chart can be used. The np chart follows the same principle as the p chart, but actually plots the number of instances in a category over time rather than the proportion in the category. The name "np" derives from the convention of using "n" to refer to sample size. By multiplying sample size by proportion (n x p) you get the actual number in a category. c charts The c chart is similar to the np chart, in that it requires equal sample sizes for each data point. For example, in evaluating errors on loan applications, you would use this chart if you sampled the same number of applications each week. But instead of plotting the proportion of data in a certain category, as does the np chart, the c chart plots count data, such as number of errors. As with the other control charts, special cause tests check for outliers and process shifts. u charts The u chart is a more general version of the c chart for use when the data points do not come from equal-sized samples. For instance, if you review all loan applications each week, and the number submitted differs on a weekly basis, you could still count errors and plot the number of errors by week over time. Because of the difference in sample sizes, the control limits will not be constant for each data point. Thus while the same special cause tests apply as for other charts, the outlier test checks specifically for whether a given data point is outside its own control limits.

Process Behavior Charts:

Process Behavior Charts: a. Pictorial of process variation while the work is being done. b. Ensures that process is stable and continues to operate within the process boundaries established for that process. c. Variable data is continuous and comes from scales or measures d. Attribute data is discrete and comes from indicators. e. Ensures that the measurement from the process are recorded, calculated, and plotted correctly.

Rational Subgrouping Definition

Rational Subgrouping: 1. Definition: Method used to select samples for control chart. Rational Subgroup is a sample set that is sufficient to determine the common cause scenarios. It is applied to enhance the randomness and reduce " piece-to-piece" Variation.

Selection of Variable

Selection of Variable 1. May be the "leading indicator" of choice of special cause variation. 2. Contractual requirement specify the variable to be monitored. 3. If the root cause of the special variation is unknow, an input variable can be monitored. (best to pick the input variable that is most difficult to hold and has been identified by capability analysis) 4. Computerized control charts aid in the monitoring of multiple variables.

Setting up Control Charts:

Setting up Control Charts: i. Characteristic to be tested is based on what is defective or what can be controlled by worker ii. Attribute data (percent defective) and Variable Data (numerical measurements) are both selected to diagnose the cause) 1. Chart for attributes requires discrete measurements (pass/fail, counts)-→ data will usable only if the data has high defective rate and comes from a reasonable subgroup size. 2. Variable charts are on continuous scale (length, weight)

Should I use an S chart or an R chart?

Should I use an S chart or an R chart? Both S charts and R charts measure subgroup variability. The S chart uses the standard deviation to represent the spread in the data and the R chart uses the range. When to use the S chart Use the S chart when your subgroup sizes are 9 or greater. S charts use all the data to calculate the subgroup process standard deviations. You should consider using S charts for processes with a high rate of production or when data collection is quick and inexpensive. When to use the R chart Use the R chart when your subgroup sizes are 8 or less.

Statistical control

Statistical control-→ process that exists as having only common cause variation only after all the special cause variation is removed. It also means that the process is between the upper and lower control limits. i. Overadjustment-→ adjustment of a process in response to common cause variation leads to greater variation. ii. Underadjustment -→ Failure to respond to special cause variation results in addition process variation.

The X-bar & R-charts chart is advantageous in the following situations:[2]

The X-bar & R-charts chart is advantageous in the following situations: i. The sample size is relatively small (say, n ≤ 10—X bar and s charts are typically used for larger sample sizes) ii. The sample size is constant iii. Humans must perform the calculations for the chart

The X-charts & S-charts is advantageous in the following situations:

The X-charts & S-charts is advantageous in the following situations: 13. The sample size is relatively large (say, n > 10— and R charts are typically used for smaller sample sizes) 14. The sample size is variable 15. Computers can be used to ease the burden of calculation

Types of Attribute Control Charts: C-chart

Types of Attribute Control Charts: C chart In statistical quality control, the c-chart is a type of control chart used to monitor "count"-type data, typically total number of nonconformities per unit.[1] It is also occasionally used to monitor the total number of events occurring in a given unit of time. The c-chart differs from the p-chart in that it accounts for the possibility of more than one nonconformity per inspection unit, and that (unlike the p-chart and u-chart) it requires a fixed sample size. The p-chart models "pass"/"fail"-type inspection only, while the c-chart (and u-chart) give the ability to distinguish between (for example) 2 items which fail inspection because of one fault each and the same two items failing inspection with 5 faults each; in the former case, the p-chart will show two non-conformant items, while the c-chart will show 10 faults.

Variable Charts:

Variable Charts: a. Data is reported from a particular characteristic of the process output in small subgroups of 2-5 sequentially taken methodically. b. Data to be plotted results from measurement on a variable or continuous scale. c. Generally used when each pair of values have infinite number of possible values. d. Smaller subgroups can be used because data is always continuous and variable. (use 25 subgroups

What is an MR (moving range) chart?

What is an MR (moving range) chart? An MR chart plots the moving range over time to monitor process variation for individual observations. Use the MR chart to monitor process variation when it is difficult or impossible to group measurements into subgroups. This occurs when measurements are expensive, production volume is low, or products have a long cycle time. When data are collected as individual observations, you cannot calculate the standard deviation for each subgroup. The moving range is an alternative way to calculate process variation by computing the ranges of two or more consecutive observations.

What is an R chart?

What is an R chart? An R chart plots the process range over time for variables data in subgroups. This control chart is widely used to examine the stability of processes in many industries. For example, you can use R charts to examine process variation for subgroups of part lengths, call times, or hospital patients' blood pressure over time. Examine the process variation using an R chart before interpreting the process average with an Xbar chart. The process variation must be in control to correctly interpret the Xbar chart because the control limits of the Xbar chart are calculated considering both process spread and center. If the R chart is out of control, then the control limits on the Xbar chart may be inaccurate and may falsely indicate an out-of-control condition or fail to detect one. You can use the R chart when your subgroup size is 8 or less. Use the S chart when your subgroup size is 9 or more.

What is an Xbar-R chart?

What is an Xbar-R chart? An Xbar-R chart plots the process mean (Xbar chart) and process range (R chart) over time for variables data in subgroups. This combination control chart is widely used to examine the stability of processes in many industries. For example, you can use Xbar-R charts to monitor the process mean and variation for subgroups of part lengths, call times, or hospital patients' blood pressure over time. The Xbar chart and the R chart are displayed together because you should interpret both charts to determine whether your process is stable. Examine the R chart first because the process variation must be in control to correctly interpret the Xbar chart. The control limits of the Xbar chart are calculated considering both process spread and center. If the R chart is out of control, then the control limits on the Xbar chart may be inaccurate and may falsely indicate an out-of-control condition or fail to detect one. You can use the Xbar-R chart when your subgroup size is 8 or less. Use the Xbar-S chart when your subgroup size is 9 or more.

What is an Xbar-S chart?

What is an Xbar-S chart? An Xbar-S chart plots the process mean (Xbar chart) and process standard deviation (S chart) over time for variables data in subgroups. This combination control chart is widely used to examine the stability of processes in many industries. For example, you can use Xbar-S charts to examine the process mean and variation for subgroups of part lengths, call times, or hospital patients' blood pressure over time. The Xbar chart and the S chart are displayed together because you should interpret both charts to determine whether your process is stable. Examine the S chart first because the process variation must be in control to correctly interpret the Xbar chart. The control limits of the Xbar chart are calculated considering both process spread and center. If the S chart is out of control, then the control limits on the Xbar chart may be inaccurate and may falsely indicate an out-of-control condition or fail to detect one. Use the Xbar-S chart when your subgroup size is 9 or more. You can use the Xbar-R chart when your subgroup size is 8 or less.

What is the difference between types of attribute charts ? That is C- chart , P -Chart , Np-Chart and U-chart ?

What is the difference between types of attribute charts ? That is C- chart , and U-chart ? Attribute consists of two cause 1. Defect - No of defect in a given unit. (Units still can be used) 1. Defective - No of Units which are defective in a given bunch or bulk of unit. (Unit cannot be used as it is completely defective) Charts Chart for Defective are 1. P Chart - It calculate the proportion of defectives in each subgroup * Chart - It calcuate the number of defectives in each subgroup Chart for Defects are 1. C Chart - It calcuate charts the number of defects in each subgroup. Use C Chart when the subgroup size is constant. 2. U Chart - It calcuate charts the number of defects per unit sampled in each subgroup. Use U Chart when the subgroup size varies.

X-bar & R-charts:

X-bar & R-charts: a. X-chant detects any process shift b. R-chart only common cause variation. c. High probability of variation can occur between successive samples while the sample size is small-→ Best to use the same process to reduce "Within-in Sample" variation. d. Between- sample variation= process shifts.

X-charts & S-charts

e. X-charts & S-charts → Sigma available i. An Xbar-S chart plots the process mean (Xbar chart) and process standard deviation (S chart) over time for variables data in subgroups. This combination control chart is widely used to examine the stability of processes in many industries. ii. The Xbar chart and the S chart are displayed together because you should interpret both charts to determine whether your process is stable. Examine the S chart first because the process variation must be in control to correctly interpret the Xbar chart. The control limits of the Xbar chart are calculated considering both process spread and center. If the S chart is out of control, then the control limits on the Xbar chart may be inaccurate and may falsely indicate an out-of-control condition or fail to detect one. iii. Used to monitor variables data when samples are collected at regular intervals from a business or industrial process.