Application of Sampling and Sampling Distribution at Quickfire

Application of Sampling and Sampling Distribution at Quickfire

Quickfire, a well-established manufacturer of safety matches in South India since 1990, supplied cardboard and wax matchsticks. The company used automatic machines, skilled and semi-skilled employees for the entire process including packaging. Once the matchsticks were ready, they were stored in cardboard boxes. Each box had 70/80/100 matchsticks. These boxes were packed in a corrugated cardboard carton. Each carton would have the counting of 1,000 match boxes.

With its reliable quality at affordable prices, the company witnessed a steady growth and soon occupied a remarkable position in the domestic and international markets. The Founding Director found to his dismay that past success is not getting converted into substantial sales. So, the company announced few special offers like increased margin for distributors, incentive schemes, etc., to attract new customers...........

1. What will be the probability that the batch will be acceptable to the customer? Will the probability be high enough to possess an acceptable level of performance?

2. To increase the probability of acceptance, if the supervisor plans to adjust the population mean and standard deviation of the number of match boxes in a carton. ............

Application of Sampling and Sampling Distribution at Quickfire

Prerequisite Conceptual Understanding

Prerequisite Conceptual Understanding (PCU) material is the background material that would aid immensely in mapping the decision areas of this caselet and bring a synthesis amongst the relevant concepts. The participants/students should be encouraged to read this material to benefit from the broader perspectives outlined in the caselet.

• • Richard I. Levin and David S. Rubin, “Chapter 6: Sampling and Sampling Distributions”, Statistics for Management, 7^th Edition, Pearson Education, 2008

Synopsis

This caselet facilitates an understanding of the application of sampling and sampling distribution. Quickfire, a well-established safety matches manufacturing company in South India, used automatic machines and semi-skilled employees for the entire manufacturing process including packaging. A potential customer while discussing about the packing, had doubts about the number of boxes in a carton pack. Based on the past experience, the supervisor informed that the boxes are normally distributed with a mean of 1,008 with a standard deviation of 45. It was dicided that the potential customer will reject the order, if in the first lot, the sample mean is not within the sample acceptable limit. This caselet attempts to discuss how the sampling distribution can be adjusted to improve the quality or characteristics of a population.

Pedagogical Objectives

• • To understand the basics of sampling
• • To discuss the details of sampling distribution
• • To discuss and analyze how the sampling distribution can be adjusted to improve the quality or characteristics of a population

Assignment Questions

I. What is the probability that the batch will be acceptable to the customer? Is the probability high enough to possess an acceptable level of performance?
II. To increase the probability of acceptance, the supervisor plans to adjust the population mean and standard deviation of the number of match boxes in a carton.

• a. To adjust the mean of the number of match boxes at any desired value, what should it be adjusted to? Why?
• b. Suppose, the mean cannot be adjusted, but the standard deviation can be adjusted. What maximum value of the standard deviation would make 90% of the parts acceptable to the consumer? (Assume the mean to be 1008). Repeat with 95% and 99% of the parts acceptable.
• c. In practice, which one do you think is easier to adjust, the mean or the standard deviation? Why?

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Exhibits

Exhibit (TN)-I: Sampling Methods with Examples