# Case Study- Bayfield Mud Company

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Introduction

According to the case study of the bag weight problem, therefore the control department gathered the weight bag as a sample from three different shifts (morning, afternoon, night) every day. As per given report the six samples collected per shift, therefore the size of the sample is six. To analysis the report of three different shift, we will apply x-bar chart and range chart.

Moreover we will take mean value i.e is 50, explanation given below. In addition we will also calculate the range chart figure for every samples in different shifts, which will be find out by applying formula (Largest-Smallest).

Analysis

D3(Value taken from Sigma table)=0

D4 (Value taken from Sigma table)==2.004

N(Sample Size)=6

Standard Deviation=1.2

Desired Control Limit 3Sigma =99.73%

Formulation

For X Chart

UCL x (Upper Control Limit for x bar) = X-Dbl Bar+ZÃ¯â‚¬Â Ã¯ÂÂ³x

Lower Control Limit (Upper Control Limit = X-Dbl Bar-ZÃ¯â‚¬Â Ã¯ÂÂ³x

Ã¯ÂÂ³x= is calculated by Ã¯ÂÂ³/Sqrt(n)

For R Chart

UCLR (Upper Control Limit for the Range) = D4*RBar

LCLR(Lower Control Limit for the Range)= D3*Rbar

 Morning Shift For X Chart For R Chart Samples Time Shifts Average Smallest Largest Range X Bar (Averages) 49.80 R-Bar (CL) 3.45 1 6 Day 1 Morning 49.6 48.7 50.7 2.0 UCLx 51.27 LCL r 0.00 2 7 50.2 49.1 51.2 2.1 LCLx 48.33 UCL r 6.91 3 8 50.6 49.6 51.4 1.8 CL 50 4 9 50.8 50.2 51.8 1.6 5 10 49.9 49.2 52.3 3.1 6 11 50.3 48.6 51.7 3.1 7 12 48.6 46.2 50.4 4.2 8 1 49 46.4 50 3.6 9 6 Day 2 Morning 48.6 47.4 52 4.6 10 7 50 49.2 52.2 3.0 11 8 49.8 49 52.4 3.4 12 9 50.3 49.4 51.7 2.3 13 10 50.2 49.6 51.8 2.2 14 11 50 49 52.3 3.3 15 12 50 48.8 52.4 3.6 16 1 50.1 49.4 53.6 4.2 17 6 Day 3 Morning 48.4 45 49 4.0 18 7 48.8 44.8 49.7 4.9 19 8 49.6 48 51.8 3.8 20 9 50 48.1 52.7 4.6 21 10 51 48.1 55.2 7.1 22 11 50.4 49.5 54.1 4.6 23 12 50 48.7 50.9 2.2 24 1 48.9 47.6 51.2 3.6
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 Afternoon Shift For X Chart For R Chart Samples Time Shifts Average Smallest Largest Range X Bar (Averages) 48.93 R-Bar (CL) 4.38 1 2 Day 1 Afternoon 49 46 50.6 4.6 UCLx 50.40 LCL r 0.00 2 3 49.8 48.2 50.8 2.6 LCLx 47.46 UCL r 8.78 3 4 50.3 49.2 52.7 3.5 CL 50 4 5 51.4 50 55.3 5.3 5 6 51.6 49.2 54.7 5.5 6 7 51.8 50 55.6 5.6 7 8 51 48.6 53.2 4.6 8 9 50.5 49.4 52.4 3 9 2 Day 2 Afternoon 49.70 48.6 51 2.4 10 3 48.4 47.2 51.7 4.5 11 4 47.20 45.3 50.9 5.6 12 5 46.8 44.1 49 4.9 13 6 46.8 41 51.2 10.2 14 7 50 46.2 51.7 5.5 15 8 47.4 44 48.7 4.7 16 9 47 44.2 48.9 4.7 17 2 Day 3 Afternoon 49.8 48.4 51 2.6 18 3 49.8 48.8 50.8 2 19 4 50 49.1 50.6 1.5 20 5 47.8 45.2 51.2 6 21 6 46.4 44 49.7 5.7 22 7 46.4 44.4 50 5.6 23 8 47.2 46.6 48.9 2.3 24 9 48.4 47.2 49.5 2.3

 Night Shifts X Bar Chart R Chart Samples Time Shifts Average Smallest Largest R-Bar X Bar Average 48.65 R- Bar (CL) 3.36 1 10 Day1 Night 49.2 46.1 50.7 4.6 UCLx 51.50 UCLr 6.73 2 11 49 46.3 50.8 4.5 LCLx 45.80 LCLr 3 12 48.40 45.4 50.2 4.8 CL 50 4 1 47.6 44.3 49.7 5.4 5 2 47.4 44.1 49.6 5.5 6 3 48.20 45.2 49 3.8 7 4 48 45.5 49.1 3.6 8 5 48.40 47.1 49.6 2.5 9 10 Day 2 Night 47.2 46.6 50.2 3.6 10 11 48.6 47 50 3 11 12 49.8 48.2 50.4 2.2 12 1 49.6 48.4 51.7 3.3 13 2 50 49 52.2 3.2 14 3 50 49.2 50 0.8 15 4 47.2 46.3 50.5 4.2 16 5 47 44.1 49.7 5.6 17 10 Day 3 Night 49.2 48.1 50.7 2.6 18 11 48.40 47 50.8 3.8 19 12 47.2 46.4 49.2 2.8 20 1 47.4 46.8 49 2.2 21 2 48.8 47.2 51.4 4.2 22 3 49.6 49 50.6 1.6 23 4 51 50.5 51.5 1 24 5 50.5 50 51.9 1.9
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Analysis Report

Â Â  After calculating and analysing the three different shifts of three days. We can observe that second shift and third shift consistently out of control. Although, 21 Samples of range chart is only out of control which is 7.10 which is greater than UCLr which is 6.9. Despite, this is only shift which is in control.

Â  By observing the second shift it is clearly seen that x chart is out of control, whereasÂ  R chart of second shift is in control only 13 Samples is out of control which is 10.20 whereas UCLr is 8.7842

Â  Now, for third shift, the X bar Chart the process is consistently out of control whereas the R chart is perfectly in control.

Recommendation.

In order to control the system, Company should be done some changes, mention below

• In order to build up the productivity, training should be provide to the new employees especially in the night shift. Another solution company can shift experienced employee in night shift to maintain the balance.
• Bayfield Mud Company should examine their machinery on regular basis as prescribed by managers. As we know a small issued can convert into big hindrance at the time of execution.
• Company should hire some quality control specialist who can take proper responsibilities of audit and track every problems with all documents in efficient way.
• Bayfield Company should do automated testing device to observe the bag weights.

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