Statistical Quality Control Presented by :- Amit kumar Verma PGDM(2011-2013) Batch -A

Statistical Quality Control (SCQ):

Statistical Quality Control (SCQ) Process:- Any activity or set of activities that takes inputs and create a product. The process for an industrial plant takes raw materials and creates a finished product is an example. Statistical Quality Control (SQC) or statistical process control (SPC) The analysis of processes for improving quality.

Origins:

Origins 1924 – Sir Walter A. Shewhart Sir W. Edwards Deming,

Kind of Variation :

Kind of Variation Controlled is native to the process, resulting from normal factors called "common causes“ Uncontrolled is the result of "special causes" and need not be inherent in the process

Controlled Variation:

Controlled Variation There is Variation that you can never eliminate it totally. There are bound to be many small, unobservable, chance effects that influence the outcome. this kind of variation is said to be "in control ," not because the process operator is able to control the factors absolutely, but rather because the variation is the result of normal disturbances, called common causes, within the process. This type of variation can be predicted. In other words, given the limitations of the process, each of these common causes is controlled to the greatest extent possible.

Uncontrolled Variation:

Uncontrolled Variation Variation that arise sporadically and for reasons outside the normally functioning process, induced by a special cause. Special causes include differences between machines, different skill or concentration levels of workers, changes in atmospheric conditions, and variation in the quality of inputs. Unlike controlled variation, uncontrolled variation can be reduced by eliminating its special cause.

Control Charts:

Control Charts As long as the points remain between the lower and upper control limits, we assume that the observed variation is controlled variation and that the process is in control

Control Chart:

Control Chart The process is out of control. Both the fourth and the twelfth observations lie outside of the control limits, leading us to believe that their values are the result of uncontrolled variation.

Control Chart:

Control Chart Even control charts in which all points lie between the control limits might suggest that a process is out of control. In particular, the existence of a pattern in eight or more consecutive points indicates a process out of control, because an obvious pattern violates the assumption of random variability.

Control Chart:

Control Chart The first eight observations are below the center line, whereas the second seven observations all lie above the center line. Because of prolonged periods where values are either small or large, this process is out of control.

Categories of control charts:

Categories of control charts those that monitor variables and those that monitor attributes. Variable charts display continuous measures, such as weight, diameter, thickness, purity, and temperature. Its statistical analysis focuses on the mean values of such measures. Attribute charts differ from variable charts in that they describe a feature of the process rather than a continuous variable such as a weight or volume. Attributes can be either discrete quantities, such as the number of defects in a sample, or proportions, such as the percentage of defects per lot.

PowerPoint Presentation:

Each point in the x-chart displays the subgroup average against the subgroup number: subgroup 2 occurring after subgroup 1 and before subgroup 3. As an example, consider a clothing store in which the owner monitors the length of time customers wait to be served. He decides to calculate the average wait-time in half-hour increments. The first half-hour (for instance, customers who were served between 9 a.m. and 9:30 a.m.) forms the first subgroup, and the owner records the average wait-time during this interval. The second subgroup covers the time from 9:30 a.m. to 10:00 a.m., and so forth.

PowerPoint Presentation:

It is based on the standard normal distribution. The standard normal distribution underlies the mean chart, because the Central Limit Theorem states that the subgroup averages approximately follow the normal distribution even when the underlying observations are not normally distributed.

Control Limits when s is known:

Control Limits when s is known Standard deviation No of observation in the subgroup Mean

Calculating Control Limits:

Calculating Control Limits Standard deviation NO of observation in the subgroup Mean of all of the subgroup average

Control Limits when s is unknown:

Control Limits when s is unknown In many instances, the value of s is not known. The normal distribution does not strictly apply for analysis when s is unknown. In this case we will use t-distribution instead standard normal distribution. Because SQC is often implemented on the shop floor by workers who have had little or no formal statistical training (and might not have ready access to Excel), the method for estimating a is simplified and the normal approximation is used to construct the control chart. The difference is that when a is unknown, the control limits are estimated using the average range of observations within a subgroup as the measure of the variability of the process.

Control Limits when s is unknown:

Control Limits when s is unknown The control limits are R represents the average of the subgroup ranges, and X is the average of the subgroup averages. A i is a correction factor that is used in quality-control charts. There are many correction factors for different types of control charts. Average Range

The r-Chart:

The r -Chart The range chart or the R-chart is constructed for controlling the variation in the dispersion or variability of the product. This type of analysis gives a better idea about whether the process is in control or is out of control. The UCL and LCL are:- 1

The p-Chart:

The p -Chart If the sample size is uniform the number of defective or d in in a sample would be P where n is the sample size and p the fraction defective. Thus the estimated control limits are given by

Reference:-:

Reference:- Fundamental of statistics By D. N. Elhance Business statistics By S. P. Gupta & M. P. Gupta, Internet

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