Question $2(40\%)$

Question $2$ fulfilled the Course Learning Outcome $3($CLO$3)$ of applying numeracy

skills in quality improvement and areas related to manufacturing activities $($C$3,$ PLO$6).$

A vendor has delivered aluminium rods to your company, as shown in Fig. Q$2.$ As a

Quality Engineer, you have planned to conduct various measurements to ensure the

delivered rods meet the quality requirements.

Fig. Q$2$: The steel plates with the specific dimensions

$($a$)$ The technical drawing specifies the diameter of the aluminum rod as $10\mathrm{.}1+-$

$0\mathrm{.}05$ mm $.$ A metric micrometer was used to measure the thickness, and the

measurement is shown in Figure Q$2$a$.$

Fig. Q$2$a: The Sleeve and Thimble scales of a Micrometer

$($i$)$ Show the smallest size that the Thimble scale can accurately read.

$(2$ Marks$)$

$($ii$)$ Compute the diameter of the aluminium rod from Fig. Q$2$a$.(3$ Marks$)$

$($ii$)$ If you measure the rod by using a steel ruler, show the most accurate

reading that can be obtained.

$($b$)$ The straightness or roundness of the aluminum rod are considered important

quality specifications. List THREE $(3)$ types of measuring instruments for

assessing these geometric features. Using diagrams, demonstrate in detail how

to perform the quality check with the three named measuring systems.

$(13$ Marks$)$

$($c$)$ Your factory ordered $500$ aluminium rods from your vendor, delivered in five

batches of $100$ rods each. A quality check was conducted on the diameter of

the rods, with a sample size of five rods per batch, to ensure compliance with

the specified diameter of $10\mathrm{.}1+-0\mathrm{.}05$mm$.$ The data collected are recorded in

Table $1.$

Table $1$: Steel plate thickness

Refer to the course material for the formulas for calculations.

$($i$)$ Compute bar$($delta$)$ and bar$($kappa$)$ values.

$($ii$)$ Produce the Z control chart.

$($iii$)$ Using the pi control chart, determine whether the products are

acceptable or should be rejected. Show reasons to support your decision.

pls help me solve this all question with provide calculation step by step