Problem $5(40$ pts$.)$

A particular product is delivered to a consumer in lots of $6,000$ units. The average percent defective is p $=1\%.$

a$)$ The sampling plan is as follows: $50$ units are drawn from the sample randomly. If $1$ or less defectives are found, the lot is accepted, otherwise it is rejected. Assuming N is infinite, construct a table as below and draw an OC curve $($p vs$.$ Pa$)$ for this sampling plan using a minimum of six points at: p$=0\mathrm{.}01,0\mathrm{.}02,0\mathrm{.}03,0\mathrm{.}04,0\mathrm{.}05,0\mathrm{.}06.$

P

Pa

AOQ

ATI

b$)$ What is the producer risk for this sampling plan?

c$)$ If a lot is received per day for $365$ days$/$year$,$ about how many lots will be rejected per year on the average?

d$)$ If the worst percent defective $[$Lot Tolerance Percent Defective $($LTPD$)]$ received at the by the consumer is $6\%,$ what is the corresponding probability of lot acceptance $($i$.$e$.,$ the consumer risk$)?$ Show it on the OC curve.

e$)$ How many bad lots of this quality $(6\%)$ are expected to be accepted per year?

f$)$ For the same question above, determine Average Outgoing Quality $($AOQ values$)$ for the same six p values $($p$=0\mathrm{.}01,0\mathrm{.}02,0\mathrm{.}03,0\mathrm{.}04,0\mathrm{.}05,0\mathrm{.}06)$ given above and plot the results. Explain its meaning with a sentence.

g$)$ Find Average Outgoing Quality Limit in this case. Explain what it means?

h$)$ Calculate the Average Total number Inspected $($ATI$)$ per lot for the same six p values and plot your result roughly $($p vs$.$ ATI$).$

i$)$ What would be the average cost of inspection per lot if the lots come with average quality $(1\%)$ and inspection cost is $0\mathrm{.}100$ KD$/$unit$?$