Homework $1$

An initial time study was done on a process with the following results $($in minutes$).$ Based on the data obtained so far, assuming an allowance of $20$ percent of the normal time, what do you estimated for the time per customer served, based on this preliminary sample?

$\backslash$table$[[$Element$,\backslash$table$[[$Performance$],[$Rating$]],$Obs $1,$Obs $2,$Obs $3,$Obs $4,$Obs $5],[$Element $1,70,4,3,5,4,3],[$Element $2,110,8,10,9,11,10],[$Element $3,90,6,8,7,7,6]]$

A contractor is preparing a bid to install swimming pools at a new housing addition. The estimated time to build the first pool is $35$ hours. The contractor estimates an $85$ percent learning rate. Without using the computer:

a$.$ How long do you estimate the time required to install the second pool?

b$.$ How long do you estimated the time required to install the fourth pool?

The manager of Perrotti's Pizza collects data concerning customer complaints about pizza delivery. Either the pizza arrives late, or the wrong pizza is delivered.

$\backslash$table$[[$Problem$,$Frequency$],[$Topping is stuck to box lid,$17],[$Pizza arrives late,$35],[$Wrong topping or combination,$9],[$Wrong style of crust,$6],[$Wrong size,$4],[$Pizza is partially eaten,$3],[$Pizza never arrives,$6]]$

Use a Pareto chart to identify the "vital few" delivery problems. Comment on potential root causes of these problems and identify any especially egregious quality failures.