Advanced Control Charts for 6sigma

I & MR Chart (Within/Between)

*Not to be confused with I-MR Chart* This is an uncommon control chart. A three-way chart that indicates variation within a group and between groups. This chart is useful when the variation between batches is high compared to variation within batches or when variation is not randomly distributed.

When to use NP-Chart

- data is discrete - data is presented as a percent rather than a count - does require a constant sample size to be use; other than this you can use it for anything that you would use a p-chart for - plots the number of units that are nonconforming in each sample size

When to Use X-bar & S Chart

- data is variable (continuous) - data can be grouped into subgroups, letting you chart the mean of each group - data count in each subgroup is more than 8 - sigma can be easily calculated (otherwise, use x-bar & R) - x-bar control chart plots the mean in each subgroup - S chart plots the standard deviation

When to Use X-bar & R Chart

- data is variable (continuous) - data can be grouped into subgroups, letting you chart the mean of each group. Ex: in a call center data can be sub-grouped into production mean per hour, average answer speed of phones per hour, average number of customers each day, defects per hour. - data count in each subgroup is less than 8 (up to 100 in Minitab)

When to use I-MR Chart

- data is variable (continuous) - data cannot be easily grouped into reasonable subgroups, so you must track individual data points instead of subgroup means. Since data is very difficult or expensive to obtain, production is very slow, so waiting for enough data to create subgroups would take too much time and products have a low cycle time.

When to use C-Chart

- use when data is about the defects themselves, not the overall defective product - data is discrete - data is presented as a count (number of defects) - does require a constant sample/subgroup size - plots the number of defects per sample

When to use U-Chart

- used when data is about the defects themselves, not the overall defective product - data is discrete - data is presented as a count (number of defects) - doesn't require a constant sample/subgroup size - plots the number of defects per unit

X-bar & S Chart

- uses all the observations which makes it more sensitive than R chart that uses only two points, the largest point and smallest point - more precise dispersion

Common Control Chart Types

1. X-bar & R Chart 2. X-bar & S Chart 3. I-MR Chart (Individual and Moving Range) 4. P-Chart 5. NP-Chart 6. U-Chart 7. C-Chart

I-MR Chart (Individual and Moving Range)

A form of Time Series Plot that typically shown as two plots (one above, one below). Each includes a line for the average as well as the upper and lower control limits. Top chart shows actual values, and the bottom chart shows the difference between two values.

Control Chart

A graphic display of process data over time and against established control limits, which has a centerline that assists in detecting a trend of plotted values toward either control limit.

Moving Range

A moving range measures how variation changes over time when data are collected as individual measurements rather than in subgroups. A moving range is the distance or difference between consecutive points

Common Cause Variation

The normal variation within a process. The variation that is caused by the process itself. ex: phone operator occasional speaking or typing error while performing job duties

Special Cause Variation

Variation that which is caused by something outside of the normal expectations within a process. ex: phone operator errors due to inexperienced employee, bad headset or overworked employee.

Executive leadership often want to know audit results, first-run yields, scrap rates, or defect rates, all of which can be illustrated with ____________. (Fill in the blank from one of the following answers.)

a. NP-Chart b. C-Chart c. P-Chart d. Excel charts

When dealing with inconsistent subgroup sizes, the u-Chart is a good choice for analysis and it tracks ____________? (fill in the blank from the following answers.)

a. Number of defects per sample b. Number of errors per unit c. Number of defects per day d. Percent (percent defective)

Which of the following Is NOT a Minitab chart?

a. The I & MR Chart (Within/Between) b. Cumulative Sum c. Chart of accounts d. Exponentially Weighted Moving Average

NP-Chart

Control Charts designed for tracking the number of defective items for discrete data in consistently sized sub-groups. A classic example an nP Chart is to track the number of defective products per lot shipped where the lot size was constant.

U-Chart

Control Charts designed for tracking the number of defects per unit for discrete data. A classic example is to track the number of scratches on new smart phone cases at a manufacturing facility.

Cumulative Sum (CUSUM)

This is an uncommon control chart. This chart deals with the cumulative sums of the deviations of each sample as they relate to a target value. CUSUM is very adept at detecting a small shift from a target, particularly in a process that is in control.

EWMA = Exponentially Weighted Moving Average

This is an uncommon control chart. This chart delivers an individual and moving range graph. This graph is rarely used in common statistical analysis since it is difficult to work with. It is most often used when dealing with automatic data systems.

When to use P-Chart

Use when you aren't grouping data into subgroups, either because it is not feasible to gather enough data samples fro subgrouping or it is important for some reason to view the chart at the data-point level. - data is discrete - data is presented as a percent (percent defective) rather than a count - doesn't require a constant sample/subgroup size - plots the proportion of units that are nonconforming (are defective, don't meet specifications) - Use when: 1. it is impossible, very time-consuming, or not financially feasible to measure or analyze numerical measurements 2. sample or subgroups sizes are not equal, so percent of defect is more important than number of defects 3. data is rate-based because it comes from a binomial or attribute process. Ex: the measurement or process is pass/fail, yes/no, etc. You can't plot 1 and 0 on a control chart but you can plot the percent of 1 or 0 in each sample.

P-Chart

Used to track attribute, rate data, and is probably one of the most used attribute-based control charts because rates are often easier to work with than actual attribute data. You can also combine multiple types of defects in the same report because p-charts are typically concerned with whether the product, part, or test passed or failed, not with the specifics about the defects that caused the pass or fail. control chart for attributes, used to monitor the proportion of defective items in a process

In an NP chart, which of the following is not true?

a. Data is discrete b. Data is presented as a percent (percent defective) rather than a count c. Requires a constant sample size to be of use d. Plots the percent of units that are nonconforming in each sample size

X-Bar & R Chart

X-=bar plots the mean of each subgroup and R chart plots the range. Control Charts designed for tracking the average of sub-grouped continuous data. They consist of two separate charts; "X-Bar" stands for the "Average" Chart which tracks the mean of sub-groups of up to 6 data points and "R" stands for "Range" Chart which tracks the difference between the maximum and minimum values in the subgroup. These charts are not as sensitive to non-normal data as the I & MR Charts. A classic example is to track the average cycle time to deliver packages by sampling 5 packages per day.

On X-bar & R Chart generations, data is grouped in all EXCEPT which of the following?

a. Average number of customers each day b. Defects per day c. Production mean per hour d. Average answer speed of phones per hour

Which chart type lets you track the number of defects per sample?

a. C-Chart b. NP-Chart c. U-Chart d. P-Chart

In Minitab, which menu has all the control charts?

a. Calc b. Graph c. Stat d. Tools

Which of the following scenarios lends itself to using X-bar and R Chart control charts?

a. Data count in each subgroup is less than 8 b. Data is static c. Data cannot be grouped into subgroups, letting you chart the mean of each group d. Data count in each subgroup is more than 100

What is the name of the software that offers easy access to control charting?

a. Minitab b. Word c. Excel d. Microsoft project management

Are failed tests always indicative of process failures?

a. There's not enough information available to answer the question. b. Yes, failed tests always indicative of process failures. c. No, data above the control range tracked always represents more efficient processes and the range should then be increased. d. Not necessarily, sometimes the "failed" data represents efficiencies above or below the test parameters.

What chart should be used if all the sample sizes are the same and the team is concerned with the number of defects?

a. U-Chart b. C-Chart c. Stat d. NP-Chart

Select the control chart that allows you to evaluate data that cannot be easily grouped into reasonable subgroups and tracks individual data points.

a. X-bar & R Chart b. P-Chart c. I & MR Chart d. X-bar & S Chart

In which control chart type is data discrete rather than variable (continuous)?

a. X-bar & S Chart b. I & MR Chart c. P-Chart d. X-bar & R Chart

What control chart type presents data as a percent (percent defective) rather than a count?

a. X-bar & S Chart b. X-bar & R Chart c. P-Chart d. I & MR Chart

C-Chart

control chart for attributes, used to monitor the number of defects per unit