This widget is to be 5.50” in length, plus or minus .50”. This gives the total specification limit of 5.00” to 6.00”.

You have set up the production line to produce a test run of the widgets (Data Set 1). The sample size consists of a total of 20 samples per run, with a total of four (4) runs. A total of 80 samples will be used to determine if the process is capable of producing the widgets within the specification.

Due to the specifications of the customer, and the setup of the manufacturing processes, the systematic random sampling technique was used to ensure that samples from each run were collected at the same point in time on different days. This provides the basis for the X-bar chart to group the sample from each run into logical subgroups.

Perform the following for:

1. Data Set 1
2. Date Set 2

X-Bar Charts Requirements

1. Calculate the subgroup mean for each numbered sample
2. Calculate the grand mean and standard deviation of the subgroup samples
3. Calculate the UCL and LCL of the grouped samples
4. Create the X-bar chart
5. Provide detailed analysis of the X-bar chart

IM Chart Requirements

To ensure that the process in actually producing individual widgets within specification limits, you have decided to use an Individual Measurement chart that will plot each of the 80 samples against a calculated UCL and LCL, as well as plotting the data against the customer specification limits.

1. Stack the sample data (place the run data into a single column. Run 1 first, Run 2 second, etc)
2. Using the Data Analysis Toolpak, create the Descriptive Statistics for the stacked data
3. Using the Descriptive Statistics output, calculate the UCL and LCL
4. Create the IM chart using the calculated UCL and LCL
5. Recopy the stacked data, and enter the customer specification limits
6. Create the IM chart of the sample data against the customer specifications
7. Provide a detailed analysis of both IM charts