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Course 1 Essay Example
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Statistical Process Control
Unit 036: Statistical Process Control

Two basic types of inspection used in sampling for process control
The two types of sampling used in inspection are:

Sampling inspection by attributes

Sampling inspection by variables

Sampling inspection by attributes
This is a method used to evaluate the quality or the characteristics of an item and classifying them as nonconforming or conforming depending on whether it is conforming to the standard specification. They can be characterized in terms of quantity or quality. The numbers of items which have nonconforming attributes are counted and if the number has not been exceeded, the lot is accepted. The advantage of this method is it simple to use and is more robust (Das, 2008).
b) Sampling inspection by variables
This method is used to evaluate the quality of items by measuring the value of the variable characterizing the inspected commodity. This method begins by selecting a number of items and measuring the characteristics or the dimensions so as to know if the characteristics of the sample are within the particular limits but not the actual value of the characteristics. The acceptance of a lot is based on the calculations of the variability or the average of the measurements in accordance with the set standards. This method requires smaller sample size compared to attribute method. It also provides more information about the effects of the process or mean on the quality (Das, 2008; Ravindran, 2008).

Significance of natural and assignable causes of variation
Causes of variation are important during a quality inspection of a product. Thus, an understanding variation is essential for the management and success of operation process. Variation can be classified as natural variation and assignable variation. Natural variation is common or chance causes of variability, which occurs and cannot be traced to a particular cause. It is created by number of influences of minor factors within a predictable range and little can be done other than revise the change the fundamental process. This variation is the sum of a number of effects of multifaceted interaction of random cause, which may be slight. A set of random or common causes that creates variation in the product quality may originate from the variation from the input to the process. An old machine, for example, has a higher degree of natural variability compared to a new machine. Sources of this variation include temperature changes, vibration of the equipment, changes in the emotion and physical conditions of the operator or electrical changes. The process is stable if the common variations are present (Harry, 2010; Ravindran, 2008).
Assignable variation represents large unsatisfactory interruptions to the normal performance process. They are those effects which can be detected and controlled. A process operating with the existence of assignable causes is said to be out of control. They may include defective raw materials, improperly adjusted machine or operator error. These effects can be traced in order to change the equipment, operation technique or the materials used. A control chart may be used for monitoring the process in order to detect the presence of assignable causes. Thus, if the plot point is outside the limits of the control charts, the assignable cause is likely to have occurred. The process of variability can be reduced by identifying these occurrences and working to remove the causes from their process (Harry, 2010).

Frequency distribution and mean, range and standard deviation
The table for Frequency distribution
Frequency 
(x_{mid} — x)^{2} 
(x_{mid} — x)^{2}f 

1667.089 

1037.849 

537.2642 

2745.193 

1171.057 
6520.833 
Mean is given by
= 840.61 ohms=
Sample standard deviation,
ohms=
The range is given by
861.9 — 826 = 35.9 ohms

Characteristics of the normal curve to the distribution of the means of small samples
Small samples in distribution graph shows normal distribution. For example, column 1, 2, and 3 are almost symmetrical about the central point. The same observation is shown in columns 2, 3 and 4. The last three columns are skewed. For normal the distribution, the median position coincides with the mean and the mode. The calculated mean value, which is 840.61 ohms, and the median, 844.5, does not coincide in the data set.

Appropriate control chart limits
The upper control limit = Average value + 3 x Standard deviation = 840.61 + (3×11.092) = 873.886 ohms
The lower control limit = Average value – 3 x Standard deviation = 840.61 — (3×11.092) = 807.334 ohms

Control charts for variables, rejects per unit and percentage defectives per batch

Control program for an application
Control Program Defective motors X = Subgroup Id (1 to 18) Numdef = Number of defective items in subgroup Size = Total number of items in subgroup Serial read numdef Serial read size Let x = Sequence 1 to 18 Lines solid solid dot dot Xlimits 0 18 Xtic offset 0 1 Ylimits 0 10 Ytic offset 18 P control chart numdef size x 

Ungrouped data (the mean, range and standard deviation)
Table showing the data set
Resistors (ohms) 

Sample number 

15126.87 
, where dStandard deviation, σ =_{n} =2.059 (Hartley’s constant) (Das, 2008).
Sample size, n = 3
Therefore, σ = 0.867/3 = 0.289 ohms
= 0.5 = 3 x 0.289/Standard errors =

Relationship between the normal curve and the mean values
The process mean is approximately at the median position, indicating that there generally normal distribution.

Select and group the data based on variable and attribute inspection methodology.
Based on variables aspects of the data, it is assumed that the quality of the characteristics of the data set follow normal distribution with the standard deviation σ and the mean, x.
The attributes aspects suppose that random samples of fixed value of the number size n taken from a group with a given number of defective products. Therefore, the number of defects follows binomial distribution.

Control charts, calculate the limits
0.5 ohms = 840.381Control limits =
Upper control limit = 840.881 ohms
Lower control limit = 839.881 ohms
Range chart
= 2.57 x 0.867 = 2.228 ohms Control line = 2.57

Control chart for variable inspection methodology, showing rejects per unit and percentage defects per batch
Control chart
References
Walker, H. F. (2012). The certified quality inspector handbook. Milwaukee, Wis: ASQ Quality Press.
Das, (2008). Statistical Methods (Combined), Tata McGrawHill Education
Harry, M. J. (2010). Practitioner’s guide for statistics and lean six sigma for process improvements. Hoboken, N.J: John Wiley & Sons.
Ravindran A. R,, (2008). Operations Research Applications, Operations Research Series
CRC Press