University of Jordan

University of Jordan

Industrial engineering department

Statistical quality control project

Dr. Abbas Al-Refaie

Table Of Contents :

Introduction 4

Dimensions of Quality 5

Process Description 6

Quality Engineering Terminology 10

Statistical Method for Quality Control and improvement 10

Data Discussion 12

Describing Variation 14

Control chart 17

Extra Part 22

Our First Decision 29

Examples from statistical Quality control Book 30

Noman Al-Juneidi for Food Industries

Figure 1

Introduction
Noman Al-Juneidi for Food Industries - Jordan was established in 2008 as a pioneer in the field of dairy and food. It is one of the prominent leading companies operating in this field in Jordan.

At Al-Juneidi growth came as a direct result of the commitment to its objective to produce high quality products at reasonable prices that answer the different demands and tastes of the market.

Al-Juneidi factory produces many products as : yoghurt , cheese , shaninah , milk , and water .

In this project , the product which we choose is water .

Water manufactured as bottles and cups . There are many characteristics in water like total dissolved solids (TDS) , PH , ozone , color , and taste .

And we choose the TDS as a quality characteristics in water .

• Our product is Al-juneidi Viviane bottle of a pure distilled water which is one of the factory’s highest quality products.

Figure 2: Viviane Bottle

Dimensions of Quality

Performance :

One of the importance dimension of quality for our product is intended the main job and satisfy the customers demand such as it is easy to open.

Durability :

The durability of the water in the bottle lasts for one year.

Aesthetics :

The factory’s product produce in different shapes , colors and designs to satisfy all the customers with different ages.

Perceived quality :

In every store AL-Juneidi produce are always there , Because they satisfy the customer demand .

Conformance to standards :

The strategy for this factory aims to produce products that conform to universal standards and ISO standard.

Process Description

In our project we satisfy of studying the critical quality characteristics such as: PH , O3 and TDS. The Factory manufactured bottles and filtered water by this procedures :

Part A: Water desalination

1-  Pumping water from the well.

2-  Storage in the main reservoir.

3-  Filtering the water using a sand filter size 5 micron.(figure 3)

4-  Filtering the water using a carbon filter size 5 micron to get rid of some of the risks elements like chlorine.(figure 4)

Figure 3 : sand filter Figure 4 : carbon filter

5-  The water goes to a softener to mix the treated water with the well water.

6-  Processing by reverse osmosis.

7-  Water goes to an assembly tank and it will be filtered using a filter size 1 micron. (Figure 5 )

8-  Treating the water with (UV) and ozone.(Figure 6 )

9-  Fill the water in the bottles.

Figure 5 Figure 6: Ozone Treating

Part B : Manufacturing the bottles

1-  Entry of the raw material (preform) to the blowing machine.(Figure 7)

2-  The produced bottles move to an air conveyer then to a rinser to wash them. (Figure 8)

Figure 7 Figure 8

3- A filter fills the treated water in the washed bottles.(Figure 9)

4-The filled bottles move to a covering and labeling machine and then to a machine that print the date on the bottles.(Figure 10)

Figure 9 Figure 10

5- The last step is when the finished bottles move to a divider machine to divide every group of bottles together. (Figure 11and 12)

Figure 11 Figure 12

Quality Engineering Terminology

To Apply statistical quality control we study the most critical characteristic that factory interested in which is the Total Dissolved Solids (TDS) as example of physical characteristic , So we take samples every two hours to calibrate it by the TDS tester (Figure ) to decide wither the results is within Al-juniedi specifications limits (150 +-10 ) .

Statistical Method for Quality Control and improvement

·  Acceptance sampling

·  Statistical Process control

·  Design of experiment

A Design of experiment is the most effective method to reduce the variability , as well as the acceptance sampling is the least one.

Ø  Statistical process control : it has many application in improving the quality by detecting the nonconformities and preventing the poor quality .

A control charts is one of the primary technique of the statistical process control method ( SPC) .

This chart is very important chart to give the engineer the knowledge to recognize if the process is in statistical control or not.

The Control Chart are classified to variable and attribute control chart based on the type of quality characteristics wither continuous or discrete.

v  Variable control chart :

§  (X bar ,R chart)

§  (X bar , S chart)

§  ( Individual moving range)

v  Attribute control chart

§  (p chart )

§  (u chart)

§  ( c chart)

• Choosing the proper type of control chart

While studying the process we observed that all the water come from the same tank , so the sample have the same TDS value. As TDS is variable characteristic we choose the variable control chart and compare the three types to choose the suitable one based on the sample size so (X-bar , R chart ) ranges from 3-5 and (X-bar , S chart ) more than 10 or variable sample size , but individual moving range chart need just one sample size .

For our process the suitable chart is the I-MR chart .

Data Discussion

The Factory produce 7000 water bottles in one hour, and the quality department take six samples with one sample size on each day and fill the information on this Form :

Figure 13

So we take a 22 samples during 4 days respectively and arranged it on the following table :

Table 1

TDS measurement for water bottle

Sample
number / TDS
1 / 140
2 / 143
3 / 155
4 / 154
5 / 156
6 / 142
7 / 137
8 / 147
9 / 148
10 / 157
11 / 144
12 / 153
13 / 150
14 / 145
15 / 164
16 / 160
17 / 159
18 / 147
19 / 152
20 / 153
21 / 141
22 / 154

-Normal Probability Plot
After testing the data using the Normal probability plots it was Normal distribution with mean =150 and standard deviation = 7.194 as shown in Figure 14

Figure 14

Describing Variation

1-  Stem and leaf diagram

One of the graphical techniques to summarizing data and give visual impression of shape, spread or variability and the central tendency or middle of the data as shown :
Stem and Leaf Display : TDS
Stem-and-leaf of TDS N = 22

Leaf Unit = 1.0

1 13 7

6 14 01234

10 14 5778

(6) 15 023344

6 15 5679

2 16 04

Histogram
is a more compact summery of data than stem and leaf and it gives a visual impression of the shape of the distribution of the measurement.

Figure 15

2-  Boxplot

It's a graphical display that simultaneously displays several important features of the data such as location, central tendency, spread or variability as the below figure shows :

Figure 16

Control chart

After choosing the suitable control chart which is the individual Moving Range chart (I-MR) we arranged the data in table with sample size n =1 :
Table 2
TDS measure of water bottle

Sample
number / TDS / MR
1 / 140
2 / 143 / 3
3 / 155 / 12
4 / 154 / 1
5 / 156 / 2
6 / 142 / 14
7 / 137 / 5
8 / 147 / 10
9 / 148 / 1
10 / 157 / 9
11 / 144 / 13
12 / 153 / 9
13 / 150 / 3
14 / 145 / 5
15 / 164 / 19
16 / 160 / 4
17 / 159 / 1
18 / 147 / 12
19 / 152 / 5
20 / 153 / 1
21 / 141 / 12
22 / 154 / 13

-Individual and Moving Range chart For TDS readings(phase I)
For the control chart for the individual measurements, the parameters are : UCL = 169.55 , Cl= 150.05 , LCL= 130.54 .
if the moving range of n=2 observation is used, then d2= 1.128. For the Table 2 , we have UCL =23.96 , CL= 7.33 , LCL= 0

Figure 17

The control chart for individual TDS values is shown in Figure 17. There are no out-of-control observation on the moving range control chart. The interpretation of the individual control chart is that no indication that the process is out of control, so these limits could be adopted for phase II monitoring of the process.

• Calculations:

v Estimate the parameter the mean and standard deviation of the process :

ü  Mean (µ) = X-bar= 150.05

ü  ST.DEV = MR-bar /d2 =6.5

v Calculating the probability of type I error (α) :

α –Risk = 1-[ p(x<UCL) – p(x<LCL )] =

1-(p(z<(169.55-150.05)/6.5)-(p(z<(130.54-150.05)/6.5) =

1-(p(z<3)-(p(z<-3))=0.0027

v Calculating the fraction non-conforming to specifications if the USL =160 , LSL = 140

FNC= 1-[ P(x<USL) – p(x<LSL ) ]

1-(P(Z<1.53)-(P(Z< -1.55) = 1- (.93699-.06057)

= .12358 = 12.58%

Ø  WHICH IS LARGE FRACTION IT NEEDS IMPROVEMENT

v Calculating the process capability if it is Center process and the mean shifted about the target .

Target = (140+160)/2=150

Mean =150.05

To compute the process capability it must be in control and normally distributed and our example it is.

The process to be centered the value of the mean= (140+160)/2=150.

But the process mean =150.05

So the process is off centered and Cp can’t be used so we use CPk=min [ Cpu ,Cpl] Actual capability.

Cpu= ( USl -µ)/3*σ= (160-150.05)/3*6.5=.51

Cpl=( µ- LSl)/3* σ=(150.05-140)/3*6.5=.52

Cpk=0.51

Related to Table 8.3 page 365 and comparing our results with the minimum values in the table it seems the process capability is not good because 0.51 <1.33 .

Extra Part

To analysis more control charts we Change the data to get Out-of-control process by changing the fifth sample from 156 to 175 as shown in the following Table:

Table 3
TDS measurements after changing the data

Sample
number / TDS / MR
1 / 140
2 / 143 / 3
3 / 155 / 12
4 / 154 / 1
5 / 175 / 21
6 / 142 / 33
7 / 137 / 5
8 / 147 / 10
9 / 148 / 1
10 / 157 / 9
11 / 144 / 13
12 / 153 / 9
13 / 150 / 3
14 / 145 / 5
15 / 164 / 19
16 / 160 / 4
17 / 159 / 1
18 / 147 / 12
19 / 152 / 5
20 / 153 / 1
21 / 141 / 12
22 / 154 / 13

-Individual and Moving Range chart For TDS readings(phase For the control chart for the individual measurements, the parameters are : UCL = 175.23 , Cl= 150.91 , LCL= 126.59 .

if the moving range of n=2 observation is used, then d2= 1.128. For the Table 2 , we have UCL =29.87 , CL= 9.14 , LCL= 0

After setting up the I-MR chart , it is best to begin with the MR chart we indicate that there is a point beyond the UCL which is Sample number fife. Then we analyzed the data of the process to know wither the cause of this out point is assignable causes or chance causes, because if it is assignable causes the control chart is out-of-control , on the other hand if it is chance causes the control chart is in-statistical control.

We assume that the cause is assignable cause which was that the operator increased the opening well water pipe when it is mixing to the distilled water by the softener, which leading to increase the TDS reading . So now we can indicate that the Process is out-of-control .
but in the individual control chart no indication of an out-of-control condition is observed.

The Next step we recalculated the control limits for the I-MR chart by remove sample number fife from the calculations to have the following Table:

Sample
number / TDS / MR
1 / 140
2 / 143 / 3
3 / 155 / 12
4 / 154 / 1
5 / 142 / 12
6 / 137 / 5
7 / 147 / 10
8 / 148 / 1
9 / 157 / 9
10 / 144 / 13
11 / 153 / 9
12 / 150 / 3
13 / 145 / 5
14 / 164 / 19
15 / 160 / 4
16 / 159 / 1
17 / 147 / 12
18 / 152 / 5
19 / 153 / 1
20 / 141 / 12
21 / 154 / 13

-The New individual moving Range chart

Therefor the both individual and moving range charts exhibit control, we would conclude that the process is in statistical control at the stated levels and adopt the trial control limits for use in phase II , where monitoring of future production is of interest.

• Calculations :

v Estimate the parameter the mean and standard deviation of the process :

ü  Mean (µ) = X-bar= 149.76

ü  ST.DEV = MR-bar /d2 = 6.65

ü 

v Calculating the probability of type I error (α) :

α –Risk = 1-[ p(x<UCL) – p(x<LCL )] =1-(p(z<(169.71-149.76)/6.65)-(p(z<129.82-149.76)/6.65) =1-(p(z<3)-(p(z<-3)) = 0.0027

v Calculating the fraction non-conforming to specifications if the USL =160 , LSL = 140

Fr= 1-[ P(x<USL) – p(x<LSL ) ]

1-(P(Z<1.54)-(P(Z< -1.47) = 0.10271 = 10.271 %