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LUT Engineering Science

BJ02A2020 Process Control

Prof. Satu-Pia Reinikainen

Task 2

Computation of Control Charts

(Fertilizer data Case 1)

Mohammadamin Esmaeili 0445024

Nnaemeka Ezeanowi 0445037

April 12, 2015

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Table of Contents

1. Introduction ......................................................................................................................................... 3

2. Aim ..................................................................................................................................................... 3

3. Computation Routine .......................................................................................................................... 3

4. Results ................................................................................................................................................. 6

4.1 Results for mass fraction of particles less than 0.03mm ............................................................... 6

4.1.1 Using X-bar and R control Chart ........................................................................................... 6

4.1.2 Using X-bar and S control Chart ............................................................................................ 8

4.1.3 Using the general model ........................................................................................................ 9

4.2 Results for mass fraction of particles less than 4.0mm ............................................................... 10

4.2.1 Using X-bar and R control Chart ......................................................................................... 10

4.2.2 Using X-bar and S control Chart .......................................................................................... 11

4.2.3 Using the general model ...................................................................................................... 12

5. Conclusion ........................................................................................................................................ 13

6. References ......................................................................................................................................... 13

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1. Introduction

Control charts are charts used in the study of process change with respect to time. There are

different charts available for various process control analysis and decisions as most charts dataset are plotted in time order. Here, we consider the case of granulation of fertilizer powders

into different sizes to reduce probable hazards within the manufacture of fertilizers thereby

improving the handling and monitoring of the amount of fine particles released. Twenty five

(25) batches were considered for calibration having five (5) sub samples each for the particle

diameters considered. The calibration samples were based on mass fractions of particles with

diameters less than 0.03mm and 4.0mm.

The control chart is adopted with the intention of accepting or rejecting data sets from an array

of batches which would fit for proper calibration. The Averages (X-bar) & Range (R) control

chart and Averages (X-bar) & Sigma (S) control chart are the variable control charts that have

been employed based on the data set properties. The control limits set in the control charts

would be used to determine the batches that would probably be rejected based on an identified

cause.

2. Aim

The aim of computing the control charts for the calibration test data sets for granulation of

fertilizer powders is to:

Determine if the test samples gotten at different batches are within the operating limits

highlighting if the batch is to be accepted or rejected.

Investigate the consistency pattern of the variables in the fertilizer granulation process

and reasons for causes that may be observed when some data points are found outside

the control limits.

Control the granulation process within the operating limits and rejecting batches which

are out of control.

Predict if the particle test data set from the calibration set is suitable.

3. Computation Routine

The two control charts to be computed are The Averages & Range (X-bar/R) control chart andAverages & Sigma (X-bar/S) control charts.

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Firstly, the mean (or average), range and standard deviation of the five sub samples were

calculated for each batch on a row which was done for mass fraction of particles with diameter

less than 0.03mm and 4.0mm. This was done using the following formulae;

, = ,

, ( )= 1

,

When these values have been determined then the average of the mean, range and standard

deviation of each batch would be calculated. At this point, the basic values necessary to create

plots have been calculated.

For the Averages & Range (X-bar/R) control chart plots, the upper control limits (UCL) and

lower control limits (LCL) for the X-bar chart and the R-chart can be calculated thus;

+

4 ,

& &

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The mean values of each batch, the average of the mean values, the upper and lower control

limits are plotted against the number of batches for d < 0.03mm and d < 4.0mm which produces

the X-bar chart while plots of the range of each batch, the average of the range, the upper and

lower control limits against the number of batches for d < 0.03mm and d < 4.0mm produces

the R-chart. The R-chart is analysed to locate any outlier or out of control point because the X-

bar chart is dependent on the average range. If outliers are observed, the batch can be rejected

and then values would be recomputed afresh to ensure there is no data set which is outside the

operating control limits.

For the Averages & Sigma (X-bar/S) control charts plots, the upper control limits (UCL) and

lower control limits (LCL) for the X-bar chart is derived from the average standard deviation; + 4 ,&

& Though this type of control chart is mainly used for subgroups greater than ten but this gives a

better estimate of the subgroup variation. The mean values of each batch, the average of the

mean values, the upper and lower control limits are plotted against the number of batches for

d < 0.03mm and d < 4.0mm which produces the X-bar chart which is dependent on the standard

deviation while plots of the standard deviation of each batch, the average of the standard

deviation, the upper and lower control limits against the number of batches for d < 0.03mm

and d < 4.0mm produces the s-chart. The s-chart is studied to locate any outlier or out of control

point because the X-bar chart is dependent on the value of the average of the standard deviation.

If outliers are observed, the batch can be rejected and then values can then be recomputed

afresh to ensure there is no data set which is outside the operating control limits.

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Furthermore, the general model of control charts which can be defined on the 3-sigma control

chart can also be used to ensure that accepted batches are within the warning and action limits

which are the normal operating conditions. The formula used are;

, 2

, 3The upper and lower warning limits (UWL & LWL) and the upper and lower action limits

(UAL & LAL) are set by the formulae above.

The values for the formula constants used in calculating control limits in the X-bar & R-chart

and the X-bar & S-chart are shown in Table 1 below and the values for five sub groups

highlighted

Table 1: Formula constants for control charts (Pqsystems.com, 2015)

4. Results

4.1 Results for mass fraction of particles less than 0.03mm

4.1.1 Using X-bar and R control Chart

Firstly, the data sets for the mass fraction of particles less than 0.03mm (d < 0.03) was analysed

for the 25 batches. The plot gotten is shown in Fig. 1

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Figure 1: X-bar and R control chart for d < 0.03mm

Looking at the range chart first, it is observed that the batch numbers 20, 21, 22 and 24 are out

of control which probably has been caused by high variations between the maximum and

minimum value of the subsamples thereby showing a higher range as compared to other

batches. Also, though computational observations, the batch 16, 18 and 25 have higher mass

fractions compared to most batches within the calibration set for particles less than 0.03mm.

These batches would be rejected from the calibration set and the average of the mean, the

average of the range, upper and lower control limits would be recomputed to put the process

within the operational control limits.

Figure 2: Recomputed X-bar and R control chart for accepted batches in the calibration set for d