Chapter 3, Problem 24P

A.

Summary Introduction

Interpretation:Process control needs to be analyzed using a X bar and R Chart created with the help of given data and process capability needs to be measured.

Concept Introduction:X bar and R chart helps in keeping check on mean and variability of any process.

B.

Summary Introduction

To determine the process capability, process capability index and process capability ratio needs to calculate:

  ${\text{C}}_{\text{pk}}\text{= Minimum of }\left[\frac{\text{<mover accent="true"><mover accent="true"><mo>x</mo><mo>¯</mo></mover><mo>¯</mo></mover><mo>- Lower Specification</mo>}}{3\sigma },\frac{\text{Upper Specification - <mover accent="true"><mover accent="true"><mo>x</mo><mo>¯</mo></mover><mo>¯</mo></mover>}}{3\sigma }\right]$

  ${\text{C}}_{\text{p}}=\frac{\text{Upper Specification - Lower Specification}}{6\sigma }$

  $\sigma =\frac{\overline{R}}{d_2}$