SCM $315$ Summary Assignment $2$ Statistical Process Control

Due $11$:$59$ pm on Saturday, March $23$

This assignment$$s objective is to summarize SPC steps, understand of kinds of variation, conclusions, and errors in conclusions in using statistical process control to check process control.

The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. To make sure that the process is in control, an inspector at the end of the filling line periodically selects a random box of $5$ packets and weighs each packet. Using $24$ such samples take, the overall mean of the filling line was $45$ grams, and the overall range was $6$ grams.

Step $1$: Estimating the distribution

$1.$ What is being measured to monitor the process? Is it an attribute measure? Or variable measure?

$2.$ What information provides information about the distribution of the process output from this step of the process? $($That is$,$ what are the distribution values?$)$

$3.$ What control chart$($s$)$ that should be used for these measures?

Step $2$: Designing the control charts

$4.$ For each of the charts you identified in #$3$ above, what are the values of the centerline, UCL and LCL$?$

Step $3$: Monitoring the process

Unit Weights Sample stats Hypothesis conclusions

Sample $12345$ X$-$bar R Decision about X$-$bar chart

$($in control or out of control$)$ Decision about R chart

$($in control or out of control$)$ Decision about the process

$($in control or out of control$)$

$14347454340$

$24750424445$

$34441465149$

$5.$ After setting the control limits $($see Q$4$ above$),$ the following three samples were collected today. The packets were measured, and the following results were obtained. Use the sample statistics from each of the samples in comparison to the control limits you designed in Q$4$ above to check for process control.

Is the process in control? Why? $($Fill the sample stats and use the control limits from Q$4$ to provide your conclusions.$)$

$$

Concepts:

$1.$ What is the possible error committed in conclusions you have drawn about the process based on each of the $3$ samples? $($This is about type $1$ and type $2$ errors in hypothesis testing.$)$

Sample $1$:

Sample $2$:

Sample $3$:

$2.$ What causes of variation $($common or assignable$)$ are present in the process now, after sample $3?($Based on your answer to #$5$ above.$).$ Consider what causes of variation are present when a process is in control and out of control.

$3.$ What should the manager$$s next step$($s$)$ be$?$