Statistical Quality Control

A Presentation BY-

Aman Wadhawan 89

Namish Mishra 86

Rahul Chowdhry 67

Mohit Singh 88

Akshay Karnatak 70

Meaning Of Statistical Quality Control

Statistical quality control can be simply defined as an economic & effective system of maintaining & improving the quality of outputs throughout the whole operating process of specification, production & inspection based on continuous testing with random samples

Categories Of SQC

Descriptive statistics

Statistical Process Control

Acceptance Sampling

Causes Of Variation In Quality

Common Causes Of Variation

Assignable Causes Of Variation

Method Of SQC

Process Control-

It extend the use of descriptive statistics to monitor the quality of the product and process

Under this the quality of the products is controlled while the products are in the process of production.

It is secured with the technique of control charts 

PURPOSE & USES OF CONTROL CHARTS

A control chart (also called process chart or quality control chart) is a graph that shows whether a sample of data falls within the common or normal range of variation.

Helps in determining the quality standard of the products.

Helps in detecting the chance & assignable variations in the quality standards by setting two control limits

Indicates whether the production process is in control or not.

Ensures less inspection cost & time in the process control.

Types Of Control Charts

Control Chart For Variables X-Chart R-Chart

Control Chart For Attributes P-Chart NP-Chart C-Chart

X-Chart

A mean control chart is often referred to as an x-bar chart. It is used to monitor changes in the mean of a process.

To construct a mean chart we first need to construct the center line of the chart.

To construct the upper and lower control limits of the chart, we use the following formulas.

Upper control limit(UCL) =

Lower control limit (LCL) =

Where,

= the average sample means

Z = standard normal variable (2 for 95.44% confidence, 3 for 99.74% confidence)

= standard deviation of the distributed sample means, computed as

= population (process) standard deviation

N = sample size

Question

A quality control inspector at the Cocoa Fizz soft drink company has taken 5 samples with four observations each of the volume of bottles filled. The data and the computed means are shown in the table. If the standard deviation of the bottling operation is 0.14 ounces, use this information to develop control limits of three standard deviations for the bottling operation.

Solution

= 15.95

The control limits are

UCL =

LCL =

RANGE - CHART

Range (R) charts are another type of control chart for variables.

Whereas x-bar charts measure shift in the central tendency of the process, range charts monitor the dispersion or variability of the process.

The method for developing and using R-charts is the same as that for x-bar charts. The center line of the control chart is the average range, and the upper and lower control limits are computed as follows.

CL = R

UCL = D4. R

LCL = D3. R

Where as , CL =central line

UCL = upper control limit

LCL = lower control limit

D3 and D4 are factors of r chart

Using Mean and Range Charts Together

You can see that mean and range charts are used to monitor different variables. The mean or x-bar chart measures the central tendency of the process, whereas the range chart measures the dispersion or variance of the process. Since both variables are important, it makes sense to monitor a process using both mean.

C-CHART

A control chart used to monitor the number of defects per unit.

Examples are the number of returned meals in a restaurant, the number of trucks that exceed their weight limit in a month, and the number of bacteria in a milliliter of water.

WHEN TO USE C-CHART?

Use C-Charts for discrete defects when there can be more than one defect per unitNumber of flaws or stains in a carpet sample cut from a production run

Number of complaints per customer at a hotel

Note that the types of units of measurement we are considering are a period of time, a surface area, or a volume of liquid.

The average number of defects, is the center line of the control chart. The upper and lower control limits are computed as follows:

ccLCL

ccUCL

c

c

z

z

C-CHART EXAMPLE

EXAMPLE USING SPREADSHEET

NP Chart

• Sometimes it is necessary (or convenient) to look at the number of defective items rather than the proportion of defective items.

• we use np - charts instead of p – charts

• Difference between p - charts and np - charts is that in the later case y-axis represents the number of defective items in a subgroup

Example

Serial No. Sample Size No Of Defective Pens

1 100 2

2 121 2

3 81 0

4 100 1

5 121 2

Total 523 7

Solution

CL= np- bar Np-bar= total no of defects/

total no inspected samples Np-bar= 7/5= 1.4

LCL = np − 3√np(1 − p), 1.4- 3√1.4(1-0.0133)=-2.13 UCL= np+3√np(1-p) UCL= 4.93 P= proportion of defect/total

units

SQC in Services

Service Organizations have lagged behind manufacturers in the use of statistical quality control

Statistical measurements are required and it is more difficult to measure the quality of a service Services produce more intangible products

Perceptions of quality are highly subjective

A way to deal with service quality is to devise quantifiable measurements of the service element Check-in time at a hotel

Number of complaints received per month at a restaurant

Number of telephone rings before a call is answered

Acceptable control limits can be developed and charted

© Wiley 2007

SQC Across the Organization

SQC requires input from other organizational functions, influences their success, and are actually used in designing and evaluating their tasks Marketing – provides information on current and

future quality standards Finance – responsible for placing financial

values on SQC efforts Human resources – the role of workers change

with SQC implementation. Requires workers with right skills

Information systems – makes SQC information accessible for all.

© Wiley 2007