Production Management

State and Techniques of Statistical Control

State of Statistical Control: When the variability in a manufacturing process is confined to chance variations, the process is said to be in a state of control. In such a situation the measurements result in a normal curve or a normal distribution.

Assignable or external variations are not inherent in the production process. Rather they arise due to human failure, e.g., poorly trained operators, defective raw materials, faulty machine settings, worn-out or broken Parts, etc. In the long run, no production process is completely free from these problems. Therefore, a systematic method is required for detecting and correcting these deviations from a state of control before they occur. SQC is a technique of finding and eliminating assignable variations.

Thus the state of statistical control may be defined as

When assignable causes have been eliminated from the production process so that practically all observations lie within control limits, the process is said to be in a state of statistical control.

In this state the process is influenced only by chance (random) causes.

Techniques of Statistical Quality Control (SQC):

The statistical techniques used in SQC can be divided into two broad categories

1. Control charts

2. Acceptance sampling.

1. Control Charts: Control charts are used to control quality of products and parts during the course of their actual manufacture. A control chart may be defined as

a graph with lines which indicate the tolerances, i.e., limits within which variations from the average quality are to be permitted.

It consists of three horizontal lines

(a) Control line indicating the desired (standard) level of quality

(b) an upper line indicates the upper quality level (UQL) while,

(c) the lower line shows the lower quality level (LQL).

The middle line represents the standard quality. A random sample of output is taken periodically at frequent intervals (each hour, half day or day) and the results are plotted on the control chart. A graphical comparison of measurements with acceptable limits will show the rapacity of the production process to produce desired quality level. Any deviation from the limits will mean that the process is influenced by external causes. The upper and lower control limits serve as the decision criteria. When a sample point falls beyond these limits, steps are taken to locate and eliminate the sources of assignable variation, otherwise the process is left free.

Thus, a control chart helps to separate out chance variation from assignable variation. It detects ‘out of control’ situation and gives warning of impending trouble. As a running record of quality, a control chart provides continuous monitoring of the production process. Control charts can be used for other purposes also. Such charts can indicate the average level at which a process under control is capable of operating and the magnitude of chance variation inherent therein.

Some suppliers send control charts with each shipment so that the buyer himself can judge the quality level supplied.

Types of Control Charts

There are two main types of control charts

1. Control charts for variables

2. Control charts for attributes.

1. Control charts for variables (measurable characteristics) are designed for the following objectives :

(i) to analyze the production process with a view to establish or change specifications, production procedures and inspection procedure.

(ii) provide a basis for decision as to when to leave the production process alone and when to look for assignable causes.

(iii) to provide a basis for decisions on acceptance or rejection of a manufactured or purchased product.

Control charts for variables are of two types

(a) Mean and range (X, R) charts

(b) Mean and standard deviation (X, σ) charts.

2. Control charts for attributes (non-measurable characteristics) can also be of two kinds :

(a) Control charts for proportion of defectives (ρ-chart)

(b) Control chart for number of defects (ō-chart).

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