Question

Process Capability. R. Morris and E. Watson studied various aspects of process capability in the paper "Determining Process Capability in a Chemical Batch Process" (Quality Engineering, Vol. $10\left(2\right)$, pp. 389-396). In one part of the study, the researchers compared the variability in product of a particular piece of equipment to a known analytic capability to decide whether product consistency could be improved. The following data were obtained for 10 batches of product.

Construct a stem-and-leaf diagram for these data with

a. one line per stem.

b. two lines per stem.

c. Which stem-and-leaf diagram do you find more useful? Why?

Short answer

a). One line per stem

b). Two lines per stem:

c). The two lines per stem plot are more useful. c). The two lines per stem plot are more useful.

Step-by-step solution

Part (a) Step 1: Given Information

The data is given as,

Part (a) Step 2: Explanation

Concept:

Place the digits of the tens to the left of the vertical line in the stem-and-leaf diagram, and the digits of the ones to the right of the vertical line.

Calculation:

Create a vertical line to plot a stem-and-leaf diagram.

Place the tens digits to the left of the vertical line and the ones digits to the right of the vertical line for each data value.

Part (b) Step 1: Given Information

The data is given as,

Part (b) Step 2: Explanation

Concept:

Place the digits of the tens to the left of the vertical line in the stem-and-leaf diagram, and the digits of the ones to the right of the vertical line.

Calculation:

Create a vertical line to plot a stem-and-leaf diagram.

Place the tens digits to the left of the vertical line and the ones digits to the right of the vertical line for each data value.

Part (c) Step 1: Given Information

The data is given as,

Part (c) Step 2: Explanation

Concept:

Place the digits of the tens to the left of the vertical line in the stem-and-leaf diagram, and the digits of the ones to the right of the vertical line.

Calculation:

Because the distribution of values is more obvious on the two lines per stem plot, it is more useful.