Department of Mathematics and

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Title: Comparison
of Robust Techniques in Process of Capability Index by                  Dealing Outlier

Name of the Student                  :       Muhammad Zeeshan Mustafa Shah

Registration Number                  :        2016-ag-1777



capability indices used to measure the variability and reduced the variability
of the data. One technique is that convert non normal data in to normal data by
using any transformation technique. Results of the process capability indices
compare with the Box-
Plot and Percentile methods. We will use the Burr Percentile method, weighted
variance method, distribution independent, tolerance independent interval,
probability graphs and root transformation technique. When the target value of
one product characteristic coincides with the mid-point of tolerance interval
the tolerance is called asymmetric. The case study results provide the insights
about the process in the term of process variation. The location of the mean in
the specification interval and fraction non confirming.











capability indices used for reduced and measures the variability. If outliers
are available then many indices will be unreliable. The outlier makes cause of
variability. Process capability indices have been discussed by many
researchers. Only two are the basis approaches estimating process capability
indices for non-normal process. First is to convert non-normal data into normal
data using any transformation technique. Used any conventional methods are easy
to deploy. Non-normal percentile may be another approach for transformation non
normal data to the  normal data. This
approach is not easy for converting non-normal data in to the normal data. Convert
non-normal into normal data by transformation technique called root transformation.
The effect of the technique by conducting simulation study using any
statistical distribution applies on the simulated data. Results compared with
process capability indices obtain using exact Box-plot and percentile methods.
The conventional methods give lead to erroneous interpretation of process
capability many methods may be proposed for computing process capability
indices under non normality. The improvement and quality improvement the
quality products control chart are consider compulsory tool. For control chart
used variables and attributes are unsatisfactory for process monitoring. For
this difficulty proposed monitoring scheme that is an improved technique based
on the joint matrices of the variables as well as attributes control chart.
Multivariate process capability indices are applied to the capability of the
process which quality of the product depends upon two or more related
characteristics. Process capability indices are widely used to the measure of
process potential and process performance. Used sample data to estimate process
capability indices means that any error in sampling consider uncertainty into
the assessment of process capability.

process capability indices or the process capability ratio measure how much
natural variation in the process. The process capability indices include upper
specification limits and lower specifications limits. The term T is the measure
of the trend process.

  Is the estimated mean and  is the estimated standard deviation.




This expression is for suitable if mean
may not be center between the specifications limits. The term specifications
are same as requirements.

The specification limits communicate to
the customer’s requirements desire and need for the process. The control limits
equal to prediction variation that the process will exhibit in the near future.
If the value of  are equal then means that producing product
meeting to the specifications.

The meaning of robust techniques as well
as to the resistance to errors in the results. Robust data make cause of the
bias. If the sample size tends to infinity then Bias will be equal to zero.


et al., (2017) urged that the compulsory
tool for monitoring were control charts. Through control chart quality improve
of any product. Variable control chart commonly used for overcome the
difficulty proposed monitoring scheme that the merits were improved the  techniques based on the merits of attributes
same to the control chart has been determined for out of control and in control
situations for specified average by using 
simulation. The efficiency of control chart was evaluated through
average. This technique practical example implementation on practical example
has been studied.

et al., (2017) urged that process
capability indices widely used as measure of process potential and process
performance. Use sample data to estimate process capability indices means any
error in sampling can introduce considerable uncertainty into the assessment of
process capability. Used of the lower confidence limit in estimation of minimum
process capability. The complexity of the sampling distribution of process
capability indices greatly hinder interval estimation only an approximation
only lower class limit can achieved. This paper purpose a novel approach to
deriving the 100( 1 – ? ) % lower class limit of indices,  and  by used Boole’s inequality and DE Morgan’s
Theorem. This technique is based on the sample data calculated from the stable
process. The quality for determine the process capability that  satisfied the customers requirements there
for this purpose used hypothesis testing.

and Sarga (2014) urged that the probability distribution of a process
characteristic was non-normal  and  indices estimated by using conventional
methods often lead to erroneous interpretation of process capability. Many
methods available have proposed for process capability indices of
non-normality. But for literature sources offer comprehensive evaluation and
comparison they were suitable process capability under severe departure form
normality. Overview nine methods to their preference when identified the
process capability indices non normality so carried out by the lognormal data
use box plots for results.

et al., (2010) urged that the concept
of process capability indices was given in early 1970 with the introduction of
“capability ratio” by Juan world known. He was quality expert. After the death
of Juan indices,  and  were developed. Many researchers concern about
the application of the diversified indices owing to the three reasons. First
was theoretical for practitioners. Second was mismatching with preference
values measure through many indices. Third was inadequacy to mimic the reality.
This study focused on the application of different indices developed. Results
obtained by comparing with percent conforming products as well as amongst the
indices themselves.

et al., (2009) is stated that non
normal process estimates the process capability indices has discussed by many
researchers. There were two approaches for process capability indices. First is
that transformation the non-normal data into normal data using any transformation
techniques and used any conventional method for calculating principal component
indices for transformation data. This approach was very simple to the second
method used non-normal percentiles to calculate the process capability
analysis. Second method was not easy to implement on the data for calculated
the principal component indices. In this paper used root transformation method
for calculating the process capability indices. The method transformation based
on simulation study on the gamma, weibull and beta distribution apply root
transformation on the simulation data.

(2008) urged that the four basis process capability indices have been made. The
relationship in these indices has been highlighted. The sample size has been
emphasized. Used non-normal distributions, skewed distributions and auto
correlated data were presented. Effects of measurement errors on process
capability indices have been dealt with in great detail.

(2006) urged that a procedure for determining the process capability indicates
was whole centers within a circular tolerance zone. In this procedure the  and  index practitioners can compare the two matrix.
Determine process capability is lacked due to the poor centering excessive

et al., (2006) studied that
analytical procedure validation means the evaluation of some performance
criteria as accuracy, linear range and capability detection. For checking there
procedures are robust or not we can applied many statistical techniques. If
outlier available then significant effect on the determination of sensitivity.

C (2004) urged that the short run facilities of production were become rapidly the
consumer requirements increased techniques of production improved. The product
was lie in the small lot. The researcher cannot collect sufficient samples for
determine the distribution of quality characteristics estimated process
parameters. The multiple quality characteristics must be simultaneously
evaluated for determine product quality. The complexity of the product design
on the high value. Conventional process capability indices as  and  not satisfy requirements. Multiple process
capability indices have been studied. This study focus on the characteristics
and mass production assumed that quality characteristic was normally
distributed in developed the multiple process capability indices. The multiple
process capability indices used the techniques of principal component analysis. 

et al., (2004) stated that the
deduction of outlier based on radical basis functions partial least squares
approach. Prescott test apply was used for detection of the outlier in complex
system. Weighted error back propagation algorithm proposed to keep the training
of multi-layer forward networks from the disturbance of outlier.

et al., (1999) urged that the
industrial statistics was generally familiar with the  and  process capability indices. Many additional
indices have been proposed and knowledge of there is less widespread. Regarding
the indices comparative behavior was lacking. In this study the behavior of
various indices under shifting process conditions. Both have been studied
useful and misleading characteristic of the indices are identified. Many
process capability indices have been reviewed. Application of capability
indices is also summarized. The indices are grouped according to the loss
functions which used in interpretation. Recommendations were made for selection
of indices at different levels of process performance.

(1998) studied that many organizations used process capability analysis was
estimated and measured the variability the used of indices as unreliable. The
integration of dependency structure and outliers may be caused of variations.
The monitoring was proposed that effectively classifies a first variability
into the component. There underlying correlation structure. Third unexplained
variance indices proposed to distinguish in these three components. The
approach helps to identify the appropriate corrective action to be taken to
reduced variability.

et al., (1996) stated that the
process capability index  was recently proposed to the measured the
degree of process capability of a system, . In this paper present
the estimators of  and derived its asymptotic distribution also
utilized the asymptotic variance of estimator of  to divide the two sided confidence interval
for  based on the percentile t bootstrap technique.
The new confidence intervals are shown to outperform the ones based on the
percentile and standard bootstrap on the basis of simulation.


process capability indices measure how much natural variation in the data. For
this purpose we will use different methods for checking variability and outlier
in the given data. The methods are given blew. The method
transformation based on simulation study on the gamma, weibull and beta
distribution (life time distributions) apply root transformation on the
simulation data.

1.      John

2.      Burr
Percentile method.

3.      Weighted
variance method.

4.      Distribution
independent Tolerance interval.

5.      Bool’s

6.       Use  and  conventiol methods.

7.      Probability

8.      Non
normal percentile.

9.      Root