# The control charts

Problem 1

A store has noticed that checking errors have been occurring. The question arose as to whether these errors are any different than has happened in the past. An employee suggested that control charts be used to monitor this process. Fortunately there were past records which shoed that the average number of errors were 4%. The plan is to use 3 std. dev. for the charts. A sample of 250 transactions were taken randomly over the next 10 days. The results of 10 samples with the following number of errors are 12, 11, 15, 12, 9, 14, 6, 13, 8, 12 The manager is convinced there is poor employee performance. What can you say about this process? Hint: construct control limits, and tell me how the samples plotted against these limits

Problem 2

A ND business is packaging sunflower seeds. From 10 samples of 30 units each taken 2 months ago, an average of the means was calculated to be 15.6 and an average of the ranges was 2.1. New samples(10 samples of 20 units each) were taken this week with the following results. x-bar= 15.5,15.7,15.4,14.9,15.5,15,15.5,15.6,15.5,15.6 r=2.2,1.8,1.7,2.0,1.5,3.0,2.2,2.0,1.5,1.6 What can you say about the process? Construct the control charts, provide me with the calculated control limits, tell me how the values plotted, and what you determined about the process ( is it in control/changing, etc.)

Problem 3

A professor keeps track of the grade point average of his students from semester to semester. Overall he has found that his students average 2.5 out of 4.0 with a std. dev. of .25 among all of his students. This semester , one of his classes with 65 students seems to be performing better on the standard exams. The class has a GPA of 2.63 and the professor wonders if this class might be academically better on standard exams.(from an acceptance standpoint would this class be accepted or rejected-treat as a lot). I want you to error on the side of rejecting a good lot, increasing producers risk. What would you tell the professor?(provide me with calculated acceptance limits--and your recommendations)

https://brainmass.com/statistics/normal-distribution/control-charts-checking-errors-218584

#### Solution Summary

Excel file contains the control charts and shows how the samples plotted against these limits.