Exam 13: Methods for Quality Improvement: Statistical Process Control Available on CD

Control charts are useful for evaluating the past performance of a process, for monitoring its current performance, and for predicting future performance.

A process is considered capable if

(Situation D) A walk-in freezer thermostat at a restaurant is set at 5°F. Because of the perishability of the food in the freezer, the restaurant manager has decided to begin monitoring the temperature inside the freezer. The managers used a precision thermometer to take sample temperature readings at five randomly chosen times per day for 10 days. The data are presented below. $\text { Day }$ $\quad$ $\quad$ $\text { Temperature }\left(^{\circ}\right. \text { F) }$ 1 5.22 5.29 5.11 4.95 4.78 2 4.40 4.41 4.63 6.03 4.83 3 5.11 5.43 4.90 4.55 5.23 4 5.65 4.24 5.09 4.82 5.50 5 4.68 5.92 4.71 4.67 4.75 6 5.01 5.26 6.10 5.20 5.25 7 5.20 4.99 5.15 5.96 5.35 8 4.30 4.91 5.03 4.97 4.80 9 5.45 5.62 6.11 5.13 4.90 10 5.06 5.13 4.95 5.59 5.80 -Calculate the upper and lower control limits for the R-chart.

An in-control, centered process that follows a normal distribution has a $\mathrm { C } _ { \mathrm { p } } = 0.6667$ . How many standard deviations away from the process mean is the upper specification limit?

(Situation D) A walk-in freezer thermostat at a restaurant is set at 5°F. Because of the perishability of the food in the freezer, the restaurant manager has decided to begin monitoring the temperature inside the freezer. The managers used a precision thermometer to take sample temperature readings at five randomly chosen times per day for 10 days. The data are presented below. $\text { Day }$ $\quad$ $\quad$ $\text { Temperature }\left(^{\circ}\right. \text { F) }$ 1 5.22 5.29 5.11 4.95 4.78 2 4.40 4.41 4.63 6.03 4.83 3 5.11 5.43 4.90 4.55 5.23 4 5.65 4.24 5.09 4.82 5.50 5 4.68 5.92 4.71 4.67 4.75 6 5.01 5.26 6.10 5.20 5.25 7 5.20 4.99 5.15 5.96 5.35 8 4.30 4.91 5.03 4.97 4.80 9 5.45 5.62 6.11 5.13 4.90 10 5.06 5.13 4.95 5.59 5.80 -Calculate the centerline for constructing the $\bar { x }$ chart.

Conformance refers to the extent to which a good or service can be adapted for use in new situations.

(Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24 ounces. The company would like to use control charts to monitor the performance of the machine. The company decides to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty measurement times are selected and the following information is recorded. Time Mean (oz) Range (oz) Time Mean (oz) Range (oz) 1 23.8 1.05 11 24.5 1.21 2 24.5 0.85 12 24.7 0.65 3 23.9 1.12 13 24.0 0.55 4 24.2 0.95 14 25.5 3.21 5 23.7 1.22 15 24.2 1.25 6 23.5 1.42 16 24.4 1.35 7 24.2 1.02 17 24.5 0.98 8 24.4 1.10 18 25.0 1.30 9 24.1 0.75 19 24.1 0.88 10 24.2 0.60 20 24.2 1.01 -Find the upper and lower control limits for the R-chart.

Capability analysis is used to determine when process variation is unacceptably high.

Samples should be chosen in such a way that a change in the process mean occurs within a samplerather than between samples.