INVESTAGATION OF THE PROCESS CAPABILITY OF WATER PUMP PLASTIC COVER MANUFACTURING

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 9, Issue 11, November 2018, pp. 349–359, Article ID: IJMET_09_11_035
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=11
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
INVESTAGATION OF THE PROCESS
CAPABILITY OF WATER PUMP PLASTIC
COVER MANUFACTURING
Sohaib Khlil
Middle Technical University, Iraq
Technical College-Baghdad, Department of Applied Mechanics
Huthaifa Alkhazraji
University of Technology, Iraq
Control and System Engineering Department
Zina Alabacy
University of Technology, Iraq
Control and System Engineering Department
ABSTRACT
In this study, a statistical analysis was conducted based on process capability indices
to investigate the ability of manufacturing process of a water pump plastic cover, which
is a product that is manufactured by the State Company for Electrical Industries in Iraq,
to meet the desired specifications. The control charts, normal probability plot and
histogram were constructed based on the data gathered from the production line. Matlab
software was used to perform the statistical calculations and plot the graphs. It was found
that the process capability during manufacture was inadequate and incapable of
achieving the specified requirements for a significant number of manufactured products.
Adjusting the process capability index by decreasing the process mean to the target value
and reducing the variations of the process to meet the allowable product tolerance are
two recommendations suggested for improving the quality level of the production.
Keywords: Quality Control, Process Capability Index, Control Charts, Water Pump
Plastic Cover
Cite this Article Sohaib Khlil, Huthaifa Alkhazraji and Zina Alabacy, Investagation of the
Process Capability of Water Pump Plastic Cover Manufacturing, International Journal of
Mechanical Engineering and Technology, 9(11), 2018, pp. 349–359.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=11

Sohaib Khlil, Huthaifa Alkhazraji and Zina Alabacy
1. INTRODUCTION
The challenge in today’s competitive markets is to produce products at high quality while keeping
the cost at a minimum (Motorcu and Güllü, 2006). A product is considered to be at a high-quality
level if it satisfies its specification or customer requirement (Judi et al., 2011). To achieve a high-
quality, various quality control techniques are implemented at every stage of the manufacturing
process (Kane, 1986). Among them, Process Capability Indices (PCIs) are common method that
utilises the concept of statistical process control to measure the ability of a process to manufacture
products that meet certain level of specifications (Yeh and Bhattcharya, 1998; Ebadi and
Shahriari, 2013). Over time, researchers shifted their focus from evaluating the capability of a
product to evaluating the capability of the overall production process (Deleryd, 1998). One of the
most common problems facing industry is the variability that exists in the production process
(Mohammadi et al., 2015). These variabilities can be categorised into two types: random and
assignable (Al-saady et al., 2012). Control charts, for example, are a well-known tool used to
recognise the causes of the assignable variability, whether it results from common causes or
special causes. However, control charts are not considered a suitable stand-alone tool to
determine if the customer's requirements are achieved. It is important to relate what the customer
expect (Voice of the Customer), which is determined by the specification limits, to what it known
about the production process (Voice of the Process), which is determined by the control limits.
Therefore, to ensure that product quality is continuously monitored and improved, the control
chart is recommended for use with PCIs (Adeoti and Olaomi, 2017).
Within the area of quality control, researchers have made many contributions evolving
process capability index. Juran (1974) presented the first process capability index as a ratio
between the desired specification limit and the actual process variation. The index has been
criticised of being unable to identify the scenario where the process is not centred in the middle
of the specifications limits (Chan et al., 1988). To overcome the drawback of the index , Kane
(1986) proposed the index by including the process mean. However, the two indices and
are calculated independently of the target value of the process. For this reason, an alternative
process capability index was developed by Chan et al. (1988) that take into account the
actual process variation with respect to the target value in the assessment of process performance.
By combining the indices and , Pearn et al. (1992) proposed a new index called .
Most PCIs consider the collected process data is normally distributed and if this is not the
case, then the use of these indices might be misleading (Kotz et al., 1993). Thereafter, it was
recognised that the properties of many processes do not satisfy this assumption (Johnson et al.,
1992). In addition, Munechika (1992) provided a number of machining process examples that
were generated with a non-normal distribution. Therefore, research attention was given to
alternative methods to compute PCIs under non-normal conditions (Borrini et al., 2010). For
example, Wright (1995) proposed a new index , which integrates a penalty for skewness. Pearn
and Kotz (1994) proposed a new generalisation of PCI, based on the assumption that population
has a Pearsonian distribution. Recently, Kovářík and Sarga (2014) reviewed the performance of
nine approaches that deal with non-normality. Further research on various methods to evaluate
the capability of non-normality processes have been proposed, including: Chen and Pearn (1997),
Tang and Than (1999), Deleryd (1999), Pal (2004), Abbasi and Niaki (2010) and Kovářík and
Sarga (2014).
Additionally, there is a large body of research on the applications of PCIs in various processes
of manufacturing products. For example, for the speaker driver (Chen and Pearn, 1997), Liquid
Crystal Display (LCD) (Pearn and Wu, 2005), spheroidal cast iron parts (Motorcu and Güllü,
2006), polyjet printing for plastic components (Singh, 2011), blow moulded for cleaning liquid
(Al-saady et al., 2012), connecting rod manufacturing process (Sharma and Rao, 2013),

Investagation of the Process Capability of Water Pump Plastic Cover Manufacturing
pharmaceutical production (Chowdhury, 2013), boring operation (Rajvanshi and Belokar, 2012),
crankshaft manufacturing (Sharma and Rao, 2014), carburettor manufacturing (Yadav et al.,
2018), aluminium alloy wheel machining (Sharma et al., 2018) and soft drinks processing unit
(Yogi, 2018).
The objective of this study is to assess of the quality control of a water pump plastic cover
based on PCIs. The State Company for Electrical Industries in Iraq manufactures this product.
For this purpose, the control charts, normal probability plot and histogram were
constructed based on the data gathered from the production line. Matlab software was used to
perform the statistical calculations and plot the graphs.
2. PROCESS CAPABILITY INDICES
Many quality control practitioners use PCIs as a tool to assess the performance of the
manufacturing process. These indices provide valuable information to evaluate the quality of the
production process (Genta and Galetto, 2018). The design of first-generation capability indices
was based on a classical philosophy of statistical process control. Based on that philosophy, all
measurement results within the determined tolerance interval are considered as good.
Measurements outside the tolerance interval are considered bad (Kureková, 2001). Among many
indices that are developed in literature, the most widely used is the capability index that was
introduced by Juran (1974) and is given by (Tsui, 1997):
= 1
where
The upper specification limit,
The lower specification limit,
The process standard deviation.
Potential Capability ( ) index is defined as the ratio of specification width to the process
spread; it indicates how the process conform to the specification limits (Kane, 1986). In general,
if the value of the potential process capability index is smaller than one ( < 1), this means that
the standard specified limit is less than the control limit (poor process). On the other hand, if the
value of the potential process capability index is greater than one ( > 1), this means that the
production might produces products that meet the customers’ requirements and the process is
potentially capable (Chowdhury, 2013). However, a > 1, does not imply that a manufacturing
process is not producing defect products. The value of control limits might be less than one for
the standard specified limits, but the process mean is not located in the centre of the specification
limit. For this reason, the process capability index as given in Eq. (2) was developed by Kane
(1986) in addition to the index as given in Eq. (3), are combined to determine the process
capability to achieve the customers’ requirements (Palmer and Tsui, 1999).
= min ( ", $) 2
" =
&
'
3
$ =
&
'
4
=
&
(
5
where
) The process mean.
* The midpoint of the specification interval, i.e. * = ( + )/2.

/ the half-length of the specification interval, , i.e. / = ( )/2.
The index indicates if there is any reduction in process capability resulting from a lack
of centring, whereas the index refers to the distance that the process lies off-centre (Palmer and
Tsui, 1999). Some authors added to the index an absolute value for the case where ≤ ) ≤
* (Kane, 1986). However, Palmer and Tsui (1999) believed that it is useful to keep the sign of
in order to know whether the process mean needed to decrease or increase to meet the process
target, which will be explained in Section 4. Both indices and are suitable for situations
where the reduction in the variability is the main contributor to improve the process capability
performance (Wu et al., 2009). Chan et al. (1988) developed the so-called Taguchi capability
index by including the process departure () − 1)
2
as given in Eq. (4) to reflect the degree of
process targeting.
=
3 45(& 6)4
6
where
1 The target of the product characteristic.
In calculating process capability indices, it is often assumed that the manufacturing process
is under statistical control and the collected process data is normally distributed (Pearn and Wu,
2005). This study adopted the following approach to conduct an analysis on the quality of a
process based on PCIs:
Step1. Select the critical component from the manufactured product (Deleryd, 1998;
Rajvanshi and Belokar, 2012).
Step2. Collect data from the manufacturing process regarding the selected component (Pearn
and Chen, 1999; Deleryd, 1998; Rajvanshi and Belokar, 2012).
Step3. Ensure the process data is collected as individual subgroup measurements at the time
sequence of the manufacturing process (Chan et al., 1988).
Step4. Estimate of the manufacturing process average ( 7), the range ( ) and standard
deviation (8) from the collected process data as given below (Kotz et al., 1993):
7 =
∑ :;
<
;=>
?
7
8 = @∑ A
(BC D̿)4
F G
HF
CIG 8
=
∑ J;
<
;=>
?
9
Step5. Construct , and 8 control charts to ensure that the manufacturing process data is
under statistical process control (Pearn and Wu, 2005).
Step6. Check the normality distribution of the collected process data (i.e. normal probability
plots, histograms and the Anderson-Darling test) (Chan et al., 1988; Deleryd, 1998; Rajvanshi
and Belokar, 2012).
Step7. Estimate the process capability indices from the estimated process average mean ( 7)
and standard deviation (8) as given by (Chan et al., 1988):
K =
L
10
K " =
:7
'L
11

K $ =
:7
'L
12
K = min( K ", K $) 13
M =
(:7 )
(
14
K =
@L45(:7 6)4
15
(a) (b)
Figure 1 a. Water pump plastic cover b. Distance between the two Screwed studs (Author)
3. CASE STUDY: WATER PUMP PLASTIC COVER
In this section, the approach of utilising PCIs to evaluate the quality of a manufacturing process
is provided through a practical application in an industrial case study. The State Company for
Electrical Industries (SCFEI) is an Iraqi manufacturing company that focuses on the development
and production of a variety of electrical appliances, including parts of water pumps. The water
pump plastic cover was selected for a case study in this research to analyse the capability of the
machining line to manufacture this type of product, as shown in Figure (1.a). The critical
character for this product is the distance between the two screwed studs on the plastic cover as
shown in Figure (1.b). For that particular model of the plastic cover of water pumps, the target
value for the distance between the two screwed studs is set to 66.0 mm with a tolerance of 0.4
mm. Given this, the lower and upper specification limits are LSL = 65.8 mm and USL= 66.2 mm.
Table (1) summaries the specification characteristic of the water pump plastic cover.
To assess the production process, (21) samples (P) were taken for seven weeks, three days
per week. Each sample consisted of four observations ( ). Samples were selected randomly
during the manufacturing process. The distance between the two screwed studs were measured
by using a micrometre with accuracy (0.001 mm) and scale range (0-150 mm). Table (2) presents
the collected process data. In addition, the last three columns of Table (2) summarises the
calculated sample mean ( ), the sample range ( ) and the sample standard deviation ( ) for the
samples. The software package MATLAB was used to check if the manufacturing process was
operates within statistical process control and the distribution is normal. Figure (2) plots , and
charts for the manufacturing process data. It can be seen from Figure (2) that no points are
outside of the control limits and all points are within the upper and lower control limits. As a

result, it can be claimed that the process of producing the water pump plastic cover is under
control and stable.
Table 1 The specification characteristic of the water pump plastic cover (Author)
Parameters Value
66.2
65.8
1 = * 66
Table 2 The 21 samples of 4 observations with calculated sample statistics (Author)
Samples
(F)
Observations (Q)
RS T U
RG RV RW RX
1 66.34 66.40 66.33 66.25 66.33 0.15 0.0616
2 66.32 66.77 65.57 65.94 66.15 1.20 0.5144
3 65.96 66.45 66.14 66.13 66.17 0.49 0.2041
4 65.89 65.89 66.13 66.55 66.12 0.66 0.3113
5 66.42 66.28 66.21 65.96 66.22 0.46 0.1926
6 66.19 66.61 65.95 66.03 66.20 0.66 0.2941
7 66.03 66.38 65.71 66.47 66.15 0.76 0.3480
8 66.32 66.65 66.66 66.15 66.45 0.51 0.2523
9 65.89 66.42 66.65 66.13 66.27 0.76 0.3321
10 66.61 66.21 65.86 66.32 66.25 0.75 0.3099
11 66.28 65.62 66.20 66.15 66.06 0.66 0.2998
12 66.15 65.89 66.42 65.96 66.11 0.53 0.2370
13 66.65 65.99 66.13 66.21 66.25 0.66 0.2849
14 66.51 65.76 65.89 65.92 66.02 0.75 0.3340
15 65.61 65.96 66.28 66.15 66.00 0.67 0.2913
16 66.15 66.02 66.51 65.81 66.12 0.70 0.2939
17 65.83 66.32 66.04 66.15 66.09 0.49 0.2053
18 66.51 65.89 66.56 66.12 66.27 0.67 0.3207
19 66.05 66.15 66.74 66.21 66.29 0.69 0.3088
20 66.13 66.61 65.88 65.89 66.13 0.73 0.3418
21 66.51 66.02 66.32 66.56 66.35 0.54 0.2446
Table 3 Summary of Results for Calculations 7, , 8 and Y − Z[]^ (Author)
Parameters Value
7 66.189
0.4450
8 0.0849
Y − Z[]^ 0.218

Figure 2 , and 8 charts (Author)
(a) (b)
Figure 3 a. Histogram b. Normal probability plot (Author)
Normal probability plots, histograms and the Anderson-Darling verified the normal
distribution. Figure (3) plots the normal probability and the histogram of the collected data. It can
be seen from Figure (3) that the sample data appears to be normal. Furthermore, Y − value that
is resulted from the Anderson-Darling test is 0.218 which is greater than the critical value (0.05).
Therefore, PCIs can be applied.
4. RESULTS ANALYSIS AND DISCUSSION
Based on the Eqs. (10, 11, 12, 13, 14 and 15), the indices , , ", $, and are
calculated as 0.785, 0.043, 1.527, 0.043, 0.954 and 0.322 respectively. Table (4) summarises the
calculation results for the indices , , ", $, and . Usually, the value of the indices

calculated from the sample data is used to make a conclusion on whether the given process meets
the specification requirement or not (Pearn and Chen, 1999).
Table 4 Summary of results for calculations , , and (Author)
Parameters Value
0.785
" 0.043
$ 1.527
0.043
0.945
0.322
Many researchers have made different explanations and interpretations of these indices (Tsui,
1997). Chao and Lin (2006) claimed that the interpretation of PCIs is still ambiguous. However,
in general two pieces of important information can be determined from PCI values: process mean
regarding the target value and the process variation regarding the specification limits (Wu et al.,
2009). In this paper, a similar procedure to the common understanding and interpretations from
Tsui (1997), Palmer and Tsui, 1999, Pearn and Chen (1999), Pearn and Wu (2005) are used to
determine whether a given process meets the capability requirement or not. Chen et al. (1988)
developed the index for those cases where the target (1) is not in the midpoint of the
specification limits (*). The index gives similar information as the when the target
value is the midpoint of the specification limits. In this particular case that is undertaken in this
study, the target (1) is in the midpoint of the specification limits (i.e. 1 = *). Therefore, the
analysis is based on the value of the , and indices.
Figure 5 Decision making for testing & (Author)

Figure 6 Decision making for testing d (Author)
By comparing Eq. (1) and Eq. (6), it can be notice that the only difference between the two
equations is the term () − 1)2
. This term becomes zero if the mean of the process () ) locates at
the targe value (1). As a result, if the mean of the process () ) locates at the targe value (1), the
indices , are equal ( = ). Based on that, Figure (5) shows how the decision is made
based on the value of & . If = and & ≥ 1 then the process is centred and
capable; If = and & < 1 then the process is centred but not capable; If ≠
and & ≥ 1 then the process is not centred but capable; If ≠ and & < 1
then the process is not centred and not capable; If ≠ and ≥ 1 and < 1 then the
process is not centred and not capable. As mention in Section2, the index is used to measure
the distance that the process lies off-centre. Figure (6) shows how the decision is made based on
the value of k. If > 0, then the process location needs to be adjusted by decreasing the process
mean until = . On another hand, if < 0, then the process location needs to be adjusted
by increasing the process mean until = . Therefore, from the value obtained
of , and from the collected data, it can be said that the process of producing the water
pump plastic cover is not centred and not capable. Further, minimizing process variation and
adjusting the process location by decreasing the process mean until = are two actions
need to be done in order to improve the process capability of the production process.
5. CONCLUSION
Process capability indices are a systematic approach based on statistical analysis have been
widely used in manufacturing industries to provide an indication of how a process has conformed
to its specifications. Process capability analysis has been proved over variety of industrial
application to be a very valuable engineering tool in make decision regarding quality control
problems.
In this paper, a process capability analysis was used to demonstrate the capability of a
machining line, of the State Company for Electrical Industries in Iraq, to meet the desired
specifications for a water pump plastic cover. The X-R control charts, normal probability plots
and histograms of the collected data were plotted and the process capability indices applied. The
results from the control charts clarified that the process of producing the water pump plastic cover
is under control and stable. However, it was revealed from the value of PCIs that the process
capability for the production process was inadequate and the process mean was not centred on
the target. Reducing the variations in the process and decreasing the process mean to the target
are two recommendations for improving the quality level of the production.

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