Muhammad Aslam - Introduction to Statistical Process Control

Quality Assurance Cost: The establishment of a system for the overall management of the product or service to ensure whether the desired quality is maintained.

Cost on Inspection Equipment: The equipment used for the inspection of the design and corresponding specifications, the incoming material, etc.

Training Cost: The training of the supervisors, operators, managers, workers, etc. for the production of set quality and maintaining it for the future production.

Miscellaneous Cost: It includes the cost of general office management for the said quality, i.e. travel, communication, shipping, and clerical.

b) Appraisal Cost

These are the costs associated with checking whether the products are going to be produced according to the specifications. Normally, these costs are associated with the evaluation of goods and services administered by the producers or the purchasers as testing of raw materials, in‐between process checking, etc. These costs include the following (Garvin, 1987):

Verification Costs: The cost associated with the verification of raw materials, verification of process settings, and final product verification.

Quality Audit Costs: The cost associated with checking of the management for its satisfactory working.

Inspection Kit Costs: The cost on the tools used for the inspection of the whole production process associated with the quality.

Vendor Scoring Cost: Different suppliers are associated with the production process. The cost incurring on the rating of these suppliers is included in the vendor scoring costs.

c) Internal and External Failure Cost

These are the costs associated with the products during its manufacturing that do not meet the designed standards; these failures are detected before transforming/delivering the products to the consumers. The failures/defective items till these are delivered to the consumers are known as the internal failures, while the after‐sale failures/defective items are known as external failures (Oakland, 2008):

i) Internal Failure CostsScrape Cost: It is cost of items which do not meet to the specifications of quality. These items are declared as scrape when these are unable to rework as well as unable to use.Reinspection Cost: When the items are reinspected after setting of all standards.Rework Cost: The cost on the minor defects, which can be addressed only some small activity.

ii) External Failure CostsWarranty Claims: The cost associated with the claims of defective items if these are delivered to the consumers.Complaints: The cost associated with the complaints of the consumers when the products are not working properly.Loss of Repute and Liability: Due to the sale of defective items to the consumers, the administration and firm have to face the loss of repute and its whole liability, which brings huge financial burden for the firm.Return of Products: Most of the times the customers are so fed up with the articles that they do not want to use it anymore and prefer to return.

Statistics is the science used for the collection, presentation, analysis, and the interpretation of data. Descriptive statistics aims to describe various aspects of the data obtained in any data collection activity. The descriptive statistics consists of the listing, summary statistics, and the graphing of the collected data. The important measures of descriptive statistics are the mean, the median, the mode, the geometric mean, the harmonic mean, range, quartile deviation, mean deviation, variance, and standard deviation.

i) The Mean

The mean is defined as the average of the data set. It can be defined as the value obtained by dividing the sum of the values by their numbers. It is denoted by . The formula for the calculation of the mean is

The weights of 10 items selected from the assembly line are given as

24.3, 24.9, 23.6, 25.1, 26.7, 22.0, 21.8, 23.4, 24.1, and 20.8. Calculate mean of the weights:

The mean for the group data can be calculated as

ii) The Median

The median is defined as the value that divides the data into two equal parts. It is denoted by . The median calculation for the ungrouped data can be made as

The weights of nine items selected from the assembly line are given as

24.3, 24.9, 23.6, 25.1, 26.7, 22.0, 21.8, 23.4, and 20.8. Calculate median of the weights.

Arranging the values in ascending order

20.8, 21.8, 22.0, 23.4, 23.6, 24.3, 24.9, 25.1, and 26.7.

In case of even number of observations, the median is defined as the mean of the two most middle values.

The weights of 10 items selected from the assembly line are given as

24.3, 24.9, 23.6, 25.1, 26.7, 22.0, 21.8, 23.4, 24.1, and 20.8. Calculate median of the weights.

Arranging the values in ascending order

20.8, 21.8, 22.0, 23.4, 23.6, 24.1, 24.3, 24.9, 25.1, and 26.7.

The median for grouped may be defined as