Please answer these questions using the data presented! Thanks!

You are the quality engineer in a manufacturing company producing over 750,000 small spools per year. The spools are 1.5 inch in diameter and vary in length from 3 to 24 inches. Your company depends on one machine to make the spools. With the exception of maintenance activity, this machine runs 24 hours a day almost every day of the year. There are other operations such as inspection, cleaning and packing. but the beast is the heartbeat of the company. One of your jobs is to continually monitor the beast. Every day you select 31 spools and check to see if they pass or fail from the machine. Many adjustments have been made to this bottleneck operation to squeeze every spool possible from the machine. Your quality check monitors the machine. As stated, your quality program consists of pulling 31 spools per day and inspecting them as pass or no pass. You have gathered data for the last 27 days.

Here is the data:

The value column is the amount of failed spools in the sample of 31 for that day.

Using all of this data:

Questions:

1. What is the approximate population from which the 27-day sample was taken?

2. . Np = 2.48 / N(p-1) = 28.52 / Do the np and n(p-1) support assuming a normal model?

3. Upper limit of proportion failing = 0.0972 / Lower limit of proportion failing = 0.0628 / Do these limits seem to provide a suitable failure rate to ship to a customer?

4. Do you have a large enough population for this sample to be used and modeled with the normal? distribution? Show your calculations. In other words, just a yes or no will be insufficient.

Approximate Control Limits Using Average Sample Size Calculations LCLP 4. 8 9 4 5 Average (p-bar) 0.08004779 6 Avg. sample size 31 7 8 Sample Fraction Standard Sample 9 Day Value Size Nonconforming Deviation LCLP CL UCLP 10 1 3 31 0.0968 0.048739 0 0.080 0.2263 11 2 3 31 0.0968 0.048739 0 0.08 0.2263 12 3 2 31 0.0645 0.048739 0 0.08 0.2263 13 4 5 31 0.1613 0.048739 0 0.08 0.2263 14 5 3 31 0.0968 0.048739 0 0.08 0.2263 15 6 1 31 0.0323 0.048739 0 0.08 0.2263 16 7 3 31 0.0968 0.048739 0 0.08 0.2263 17 8 3 31 0.0968 0.048739 0 0.08 0.2263 18 9 3 31 0.0968 0.048739 0 0.08 0.2263 19 10 4 31 0.1290 0.048739 0 0.08 0.2263 20 11 2 31 0.0645 0.048739 0 0.08 0.2263 21 12 1 31 0.0323 0.048739 0 0.08 0.2263 22 13 0 31 0.0000 0.048739 0 0.08 0.2263 23 14 4 31 0.1290 0.048739 0 0.08 0.2263 24 15 5 31 0.1613 0.048739 0 0.08 0.2263 25 16 0 31 0.0000 0.048739 0 0.08 0.2263 26 17 5 31 0.1613 0.048739 0 0.08 0.2263 27 18 2 31 0.0645 0.048739 0 0.08 0.2263 28 19 1 31 0.0323 0.048739 0 0.08 0.2263 29 20 2 31 0.0645 0.048739 0 0.08 0.2263 30 21 2 31 0.0645 0.048739 0 0.08 0.2263 31 22 2 31 0.0645 0.048739 0 0.08 0.2263 23 1 31 0.0323 0.048739 0 0.08 0.2263 33 24 0 31 0.0000 0.048739 0 0.08 0.2263 34 25 2 31 0.0645 0.048739 0 0.08 0.2263 35 26 4 31 0.1290 0.048739 0 0.08 0.2263 36 27 4 31 0.1290 0.048739 0 0.08 0.2263 CL UCLP 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 0 0.080048 0.226265 32 4 27